The study modeled a closed ammonia OTEC cycle whose evaporator received heat from a PVT field through an intermediate heat exchanger. The PVT coolant simultaneously cooled the photovoltaic cells and delivered recovered heat to the OTEC cycle. The analysis compared this hybrid with Case A, an uncooled photovoltaic array beside a standalone OTEC plant, and Case B, an actively cooled array that rejected its recovered heat to ambient.

Researchers optimized collector aperture area, specific heat-transfer-fluid flow, evaporator conductance and one of five commercial photovoltaic technologies. NSGA-III simultaneously optimized net plant power, system exergy efficiency and the crossover price, defined as the break-even electricity price for the incremental hybrid investment. Annual energy was calculated from long-term monthly solar climatology, with no thermal storage credited at night.

Machine-learning surrogates replaced repeated high-fidelity calculations during the search. Gaussian-process models were selected for the physical regression targets, while gradient-boosted trees classified whether a cycle solution existed. The annual hybrid energy increment relative to the uncooled reference had a cross-validated R² of 0.9980 and mean absolute error of 0.19 kWh per square metre per year.

Among 26 front designs re-evaluated with the full model, 25 were feasible. The surrogate overestimated the crossover price relative to the uncooled reference by a mean $0.002 per kilowatt-hour, and its Spearman rank correlation with verified values was 0.9985. Verification also identified one design that violated the evaporator approach limit by 0.012 K, which was removed from the reported results.

The verified Pareto front covered net hybrid outputs of 39–588 kW and exergy efficiencies of 11.6–21.7%. A selected knee design used 2,411 m² of collectors with TOPCon cells and delivered 459 kW at 19.7% exergy efficiency, but had a verified crossover price of $2.53 per kilowatt-hour. Multicrystalline silicon produced the lowest crossover price because its larger temperature coefficient produced a greater benefit from cooling; efficiency alone did not determine the ranking.

Relative to the actively cooled array, routing recovered heat to the OTEC evaporator had a coupling crossover price of $0.12–$0.13 per kilowatt-hour along the design-site front, below the reported diesel-cost range. This comparison excluded the cost of obtaining the cooled PVT field because that hardware was common to both configurations. The result supports using recovered heat once a PVT field has been justified for other reasons, rather than using OTEC coupling alone to justify the field.

At an electricity price of $0.40 per kilowatt-hour, the break-even PVT-specific cost was $43–$82 per square metre, compared with a documented range of about $200–$550 per square metre. A 20,000-draw Monte Carlo analysis produced a 5th–95th percentile crossover-price range of $1.76–$3.74 per kilowatt-hour, and every draw exceeded $0.80 per kilowatt-hour.

The analysis was limited to a steady-state model, one ammonia-based plant scale, no thermal storage and uncertain utility-scale PVT procurement costs. Collector areas above 2,000 m² and conditions outside the design-site climatology were extrapolations, and the diesel range was regional rather than a site-specific avoided-cost estimate.

Subject of Research: Techno-economic optimization of a hybrid photovoltaic-thermal and ocean thermal energy conversion plant

Article Title: Locating the economic threshold of a hybrid PVT/OTEC plant: a surrogate-assisted multi-objective optimization with high-fidelity verification

Article References: Ahmadi, M., Aghanajafi, C., & Vojdani, M. M. (2026). Locating the economic threshold of a hybrid PVT/OTEC plant: a surrogate-assisted multi-objective optimization with high-fidelity verification. Results in Engineering, 32, Article 113607. https://doi.org/10.1016/j.rineng.2026.113607

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113607

Keywords: PVT/OTEC hybrid, photovoltaic-thermal, ocean thermal energy, techno-economic optimization, crossover price, surrogate modeling, NSGA-III, high-fidelity verification, Locating, economic, threshold, hybrid

The proposed pipeline targets two coupled controls in a battery thermal management system: coolant flow rate and coolant inlet temperature. Higher flow generally improves heat removal, while a colder inlet creates a larger temperature difference between the coolant and cells. The neural network predicts peak battery temperature, temperature non-uniformity and a dimensionless thermal-runaway risk index in a single forward pass. Differential Evolution then searches for coolant settings that balance peak temperature against spatial uniformity, which matters because hot cells in a module can age faster than cooler cells even when the absolute temperature remains within a broader acceptable range.

To build the training data, the researchers used a reduced heat-generation formulation inspired by the Bernardi model and a calibrated cooling-conductance expression based on the Dittus–Boelter correlation. They generated 3,000 samples for each of two cell formats, Tesla 21,700 and Tesla 4680, for a total of 6,000 synthetic cases. Each case varied charge or discharge rate from 0.5C to 5C, coolant flow from 0.01 to 0.15 litres per minute and inlet temperature from 20 to 35 degrees Celsius. Gaussian noise was added to emulate measurement or discretization uncertainty, and a fixed random seed was used for reproducibility.

The thermal-runaway risk measure is not a probability of a battery fire. It is a relative screening index that becomes positive only when both peak temperature exceeds 45 degrees Celsius and temperature non-uniformity exceeds 3 degrees Celsius. The index then grows with both exceedances. Its double-threshold construction reflects the model’s assumption that a high absolute temperature combined with localized thermal gradients is more concerning than either condition alone. However, the index has not been calibrated against observed thermal-runaway events, and a percentage reduction describes the model-predicted joint threshold exceedance rather than a measured reduction in real-world failure probability.

The neural network used three inputs, three outputs and hidden layers containing 128, 64 and 32 neurons, with hyperbolic-tangent activations, L2 regularization and early stopping. On a held-out set of 1,200 samples, it achieved an R-squared value of 0.9068 for peak temperature, with a root-mean-square error of 3.87 degrees Celsius, and 0.9972 for temperature non-uniformity, with an error of 0.0966 degrees Celsius. Its risk-index R-squared was 0.8854. A five-fold cross-validation of peak-temperature prediction produced an R-squared of 0.9014 plus or minus 0.0029, broadly consistent with the single test result. The model also substantially outperformed a linear-regression baseline for the risk index, whose R-squared was 0.4128.

Those accuracy figures describe how closely the network reproduces the equations that generated its training data. They do not establish how accurately those equations represent real batteries. The temperature calculation is a calibrated, lumped mapping whose numerical coefficients combine several physical effects without strict dimensional consistency, while the cooling relation uses an effective square-root dependence on flow in a regime where fully turbulent Dittus–Boelter scaling may not strictly apply. The dataset was neither produced by computational fluid dynamics nor measured experimentally. Consequently, systematic errors in the underlying reduced-order model would be inherited by the surrogate and its optimization results.

Across 20 charging conditions, the uncontrolled baseline used constant flow of 0.05 litres per minute and a 30-degree inlet temperature. It produced an average peak temperature of 45.23 degrees Celsius, average non-uniformity of 3.35 degrees Celsius and an average screening index of 0.1690. A threshold controller switched to 0.10 litres per minute and a 20-degree inlet when temperature exceeded a preset limit, improving the three averages to 30.61 degrees Celsius, 2.33 degrees Celsius and 0.0227. The optimized strategy, based on a weighted objective assigning 0.6 to peak temperature and 0.4 to non-uniformity, achieved averages of 28.46 degrees Celsius, 1.89 degrees Celsius and 0.0087. These are model-based controller comparisons, and the benchmark did not account for all practical costs of varying coolant settings.

A weight sweep at a charging rate of 3C revealed that the competing thermal objectives were only weakly conflicting within the assumed hardware limits. Across nine weight combinations, predicted peak temperatures ranged from 25.21 to 25.54 degrees Celsius, while non-uniformity ranged from 1.24 to 1.68 degrees Celsius. Extreme weighting of temperature uniformity selected maximum flow and the minimum inlet temperature, whereas strong weighting of peak temperature chose about 0.115 litres per minute at the minimum inlet because additional flow produced little further reduction. Retraining five networks with different initialization seeds produced optimized flow rates between 0.137 and 0.150 litres per minute, indicating that the flat temperature response leaves the precise flow optimum weakly determined.

The clearest hardware limitation appeared during extreme charging. At 1C to 3C, optimized peak temperatures remained near 25 degrees Celsius and the screening index was close to zero. At 4C, the optimizer reached the assumed limits of 0.15 litres per minute and a 20-degree inlet while keeping peak temperature below the critical threshold. At 5C, however, predicted peak temperature rose to 46.45 degrees Celsius and non-uniformity to 4.49 degrees Celsius, with a screening index of 0.085. In the calibrated model, the 5C heat-generation term exceeded the maximum available cooling term for both cell formats. The authors therefore conclude that safe 5C operation would require more pump capacity, colder coolant or another cooling-system upgrade rather than better set-point tuning alone.

Several safety and deployment qualifications remain. In the safety-relevant 40-to-45-degree band, the network’s local root-mean-square error was about 4.89 degrees Celsius and it showed a 0.72-degree tendency to underpredict temperature. The reported 0.125-millisecond inference time covers only the neural-network forward pass on a general-purpose processor, excluding sensing, communications and actuator response. Before safety-critical use, the authors propose conservative margins, an independent hardware over-temperature cutoff, validation against representative computational fluid-dynamics cases and hardware-in-the-loop testing with an instrumented battery module. The study therefore offers a promising computationally efficient control strategy and a clear 5C hardware benchmark, but its quantitative safety implications remain model-based until those validation steps are completed.

Subject of Research: Neural-network surrogate modeling and evolutionary optimization for multi-objective electric-vehicle battery thermal management

Article Title: Artificial neural network surrogate modeling and evolutionary optimization for multi-objective control of electric vehicle battery Thermal Management Systems

Article References: Tabeshmoghaddam, M., Zadehbagheri, M., Nejatian, S., & Kiani, M. J. (2026). Artificial neural network surrogate modeling and evolutionary optimization for multi-objective control of electric vehicle battery Thermal Management Systems. Results in Engineering, 32, Article 113618. https://doi.org/10.1016/j.rineng.2026.113618

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113618

Keywords: electric vehicles, lithium-ion batteries, battery thermal management, artificial neural networks, surrogate modeling, differential evolution, fast charging, thermal runaway, multi-objective optimization, model validation, Artificial, neural

The work targets a computationally demanding part of cerebrovascular analysis. Patient-specific computational fluid dynamics can estimate three-dimensional velocity, pressure and wall-shear-stress fields from medical images, but each analysis requires segmentation, geometry repair, mesh generation and an iterative numerical solution. Repeating that process across many aneurysm shapes or inlet-flow conditions can become prohibitively expensive. A reusable surrogate could accelerate parametric studies and potentially provide rapid hemodynamic estimates during vascular interventions, although the study did not test clinical use or robot navigation. Its results concern steady, incompressible Newtonian flow in idealized vessel models derived from a computational dataset.

PIReN represents a flow field as the sum of a learnable baseline and a residual correction. Its inputs are a point’s three-dimensional coordinates, the local equivalent vessel diameter and the inlet mass flow rate; its outputs are three velocity components and pressure. A compact baseline branch with two fully connected hidden layers supplies the overall flow pattern. A dual-branch decoder then adds localized corrections. One branch processes the baseline together with the input variables, while a second, “prior-aware” branch extracts flow-conditioning features independently of the baseline. Both use residual multilayer perceptron blocks with 128 features in the default configuration, and a channel-wise gate adaptively combines their outputs.

Training combined a supervised mean-squared-error loss with dimensionless residuals from mass continuity and the steady Navier–Stokes momentum equation. The continuity term penalizes violations of incompressibility, while the momentum term measures the consistency of velocity gradients and pressure gradients with fluid motion. Automatic differentiation calculated the required spatial derivatives in physical units, and characteristic scales estimated from the training subset made the two residual terms numerically comparable. Their weights rose gradually: continuity was inactive for the first 15 epochs and reached its final value after epoch 40, while momentum began at epoch 40 and reached its final value after epoch 90. This staged activation was intended to prevent the physics terms from overwhelming data fitting early in optimization.

The dataset was assembled from the open Aneumo intracranial-aneurysm computational fluid dynamics collection. Seven deformable models derived from one patient anatomy formed geometry set A, while 16 models from a second anatomy formed set B. Each model was evaluated at five inlet mass flow rates from 0.0025 to 0.0040 kilograms per second, corresponding to Reynolds numbers of approximately 250 to 720. Points where all velocity components vanished were removed as no-slip wall locations, and 20,000 interior points were sampled from each file. The researchers used a blood density of 1,060 kilograms per cubic meter and dynamic viscosity of 3.45 × 10−3 pascal-seconds, matching the original simulations.

The main in-domain experiment was an optimistic interpolation test rather than a test of extrapolation. Geometry set A was divided into training, validation and test subsets at an 8:1:1 ratio, allowing a held-out point to have nearby training neighbors. Under that protocol, PIReN used 186,472 trainable parameters, compared with 199,940 for the standard physics-informed network and 173,956 for the supervised model. Its mean normalized absolute error was 1.11%, versus 1.61% for the standard network and 1.84% for the supervised model. Its continuity residual, DIV, was 0.0113, compared with 0.0858 and 4.7996, respectively, while its momentum residual, MOM, was also lower. On representative sections, 72.1% of PIReN test points met the predefined continuity criterion |DIV| < 0.01, against 28.3% for the standard network and 4.8% for the supervised model.

Ablation experiments separated the effects of architecture from those of the physics losses. Removing the residual decoder was the most damaging architectural change: aggregate relative error rose from 11.34% to 30.89%, and DIV increased to 1.2314. Removing the baseline field produced a smaller accuracy penalty, with error reaching 12.16%, but DIV rose to 0.0442. Replacing channel-wise gating with simple concatenation and linear projection yielded 12.69% error and a DIV of 0.0514. The physics constraints produced a different trade-off. Removing both governing-equation losses actually lowered in-domain pointwise error to 9.64%, but DIV surged to 3.0351, about 269 times the full model’s value, and MOM increased to 26.4607. Their principal role was therefore to suppress physically inconsistent solutions rather than minimize interpolation error in this setup.

In a zero-shot test, a model trained only on geometry set A was evaluated without adaptation on all 16 models in set B. PIReN’s aggregate error increased from 11.34% on set A to 42.71% on set B, whereas the standard physics-informed network rose from 16.57% to 121.92%. On the unseen geometry, PIReN reduced error by 65.0% relative to the standard network; it also produced 82.1% lower mean normalized absolute error, 93.1% lower DIV and 82.2% lower MOM. This was nevertheless a compound distribution shift: the two sets came from different anatomies, had different morphologies and occupied nonoverlapping coordinate frames about 29.7 millimeters apart. Their characteristic physical diameters differed by only 1.2%, so the result cannot isolate generalization to morphology alone.

Five-fold leave-one-flow-rate-out testing produced a similar pattern. In each fold, one of the five flow rates was entirely withheld while the model was trained on the other four. Across the folds, PIReN’s average aggregate error on the held-out conditions was 36.83%, compared with 106.11% for the standard physics-informed network, a 65.3% relative reduction. PIReN also had lower mean normalized absolute error, DIV and MOM in all five held-out conditions. A stricter spatial-block test then removed neighboring-point leakage by holding out one of five contiguous regions along the vessel axis. Averaged over the five flow conditions, PIReN achieved an aggregate relative L2 error of 0.3035 ± 0.0255 under this protocol, versus 0.3927 ± 0.0285 for the standard network. PIReN performed better in all 40 combinations of four metrics, two partition schemes and five flow configurations, and its absolute error margin widened when the test became spatially stricter.

Several limitations define what the experiments do—and do not—establish. The models assumed steady flow, rigid walls, incompressible Newtonian fluid and no explicit boundary penalties; physics losses were evaluated only at sampled interior points. The continuity formulation also omitted an additional geometric contribution where local diameter changes rapidly, particularly near bifurcations and aneurysm necks, so reported DIV values may underestimate local mass-conservation errors there. The study used synthetic CFD reference data, rigid-wall models and two related anatomy groups rather than independent patient cohorts. It did not evaluate pulsatile flow, compliant vessels, fluid–structure interaction or clinical decision-making. The researchers also note that simply enlarging either model did not guarantee better performance: both architectures worsened at their largest tested sizes, underscoring that the favorable result came from a specific combination of architecture, data protocol and physics-based regularization rather than from raw model capacity alone.

Subject of Research: Physics-informed neural-network reconstruction of cerebrovascular flow fields in intracranial aneurysm models

Article Title: Cerebrovascular flow field reconstruction method based on residual network of physical information

Article References: Teng, Z., Hou, Y., Liu, J., & Wang, Q. (2026). Cerebrovascular flow field reconstruction method based on residual network of physical information. Frontiers in Bioengineering and Biotechnology, 14, Article 1970931. https://doi.org/10.3389/fbioe.2026.1970931

Image Credits: AI Generated

DOI: 10.3389/fbioe.2026.1970931

Keywords: physics-informed neural networks, intracranial aneurysms, cerebrovascular flow, surrogate modeling, Navier–Stokes equations, computational fluid dynamics, out-of-distribution generalization, hemodynamics, Cerebrovascular, flow, field, reconstruction

The new model, called HG-KAN, short for heterogeneous graph Kolmogorov-Arnold network, was developed by Faming Gong, Junjie Xu, Yanpu Zhao, Xiaofeng Ji, and Chengze Du. Their goal was not to replace reservoir simulators entirely but to build a fast, reliable proxy that engineers could run over thousands of candidate injection strategies during operational screening, the stage at which the fate of a waterflood plan is often decided. The work was partially supported by the Natural Science Foundation of Shandong Province and the Qingdao Natural Science Foundation, and it reflects a growing trend in petroleum engineering: treating the subsurface as a network rather than a grid.

That network view is the first key ingredient. In HG-KAN, wells and geological layers are represented as different types of nodes in a heterogeneous graph, and the connections between them are not arbitrary. Instead, the graph construction is guided by physics, specifically by layer-wise transmissibility relations, which quantify how easily fluid can flow from one part of the reservoir to another through each geological layer. This matters because two injection wells sitting side by side on a map may be practically strangers in the subsurface if a fault or a low-permeability barrier separates them, while wells kilometers apart can be intimately connected through a highly transmissive sand layer. By encoding these layer-specific connectivity relationships directly into the graph structure, the model gives the neural network a head start: it does not have to rediscover the reservoir’s plumbing from production data alone.

The second key ingredient is the Kolmogorov-Arnold network, or KAN, an architecture that has generated considerable excitement since its introduction. Where conventional multi-layer perceptrons, the standard workhorse of deep learning, place fixed activation functions on nodes and learn weights on edges, KANs invert that arrangement: they place learnable, flexible activation functions on the edges themselves. This design, rooted in the Kolmogorov-Arnold representation theorem from mathematics, allows KANs to approximate complicated multivariate functions with potentially fewer parameters and, crucially for this application, with greater interpretability, because each learned edge function can be inspected and visualized. The authors argue that fixed nonlinear blocks like those in MLPs can reduce robustness and interpretability in strongly heterogeneous settings, precisely the conditions found in layered fault-block reservoirs where the relationship between injection rates and production responses shifts dramatically from one layer to the next.

HG-KAN combines these ideas in a dual-stream framework for injection-rate allocation. One stream processes the physics-guided heterogeneous graph, propagating information between wells and layers along transmissibility-weighted connections, while the architecture as a whole is designed to capture how fluid injected at one well propagates through specific layers and influences production at distant wells. The authors are careful to note an important nuance: while the graph construction is physics-guided, the current training objective does not explicitly include partial differential equation residual constraints of the kind found in fully physics-informed neural networks. In other words, the physics enters through the structure of the model rather than through the loss function, a design choice that keeps training simpler while still respecting the geology that governs subsurface flow.

The team evaluated the model on two proprietary field datasets drawn from a fault-block reservoir, a setting notorious for its geological complexity. The first was a 20-well pilot block, a smaller testbed where the model achieved a root mean square error of 37.31 cubic meters per day in predicting injection-production behavior. The second, more demanding dataset covered a 67-well management area, a scale at which inter-well interactions multiply combinatorially, and there HG-KAN reached an RMSE of 33.72 cubic meters per day. In both cases the model consistently outperformed strong heterogeneous graph baselines in the authors’ experiments, suggesting that the KAN-based nonlinear blocks, rather than the graph structure alone, contribute meaningfully to the accuracy gains.

Speed is where the results become genuinely striking for field operations. HG-KAN delivered inference times of 340 milliseconds per 100 samples on the pilot block and 884 milliseconds per 100 samples on the management area. Those figures translate into a practical capability that numerical simulation cannot match at screening scale: an engineer could evaluate thousands of injection-rate allocation scenarios in the time it takes a simulator to grind through a handful. In digital oilfield workflows, where operators increasingly rely on continuous data streams from smart wells to adjust waterflood strategies in near real time, that kind of throughput is not a luxury. It is the difference between reacting to reservoir behavior weeks after it happens and anticipating it.

The implications extend beyond one reservoir or one company. Waterflooding accounts for a substantial share of global oil production, and as fields mature, the fraction of water produced alongside oil tends to climb, driving up energy costs and environmental burdens. Studies of heterogeneous carbonate reservoirs have shown how uneven water injection can leave large volumes of oil unswept while water cycles uselessly through high-permeability channels. A surrogate model that respects layer-wise connectivity could help operators steer injected water into the layers that need it, improving sweep efficiency and reducing wasted injection. The same graph-based reasoning, moreover, echoes developments elsewhere in the geosciences, from graph neural networks for groundwater contaminant tracking to transformer models for production forecasting in unconventional reservoirs, indicating a broader convergence on relational, physics-aware machine learning for subsurface problems.

The authors are candid about the framework’s boundaries. The training data are proprietary and confidential field data that cannot be publicly shared, which means independent verification will depend on other operators testing the approach on their own assets. The absence of explicit PDE-residual constraints in the training objective leaves open the possibility that future versions could incorporate those residuals, potentially improving generalization in scenarios far from the training distribution. And like all data-driven surrogates, HG-KAN is only as trustworthy as the historical injection and production records it learns from, which in mature fields can be noisy, incomplete, and shaped by decades of changing operational practices.

Still, the study marks a notable step in a fast-moving field. Kolmogorov-Arnold networks have already been adapted for time series forecasting, anomaly detection, molecular property prediction, and physics-informed solutions of partial differential equations, and their marriage with heterogeneous graph structures for reservoir engineering appears here as one of the more consequential applications to date. If the accuracy and speed reported on these two fault-block datasets hold up across other geological settings, the humble decision of how much water to inject into which well, long a matter of simulation campaigns and engineering intuition, could become a task performed in milliseconds on a graph that knows the reservoir’s hidden architecture. For an industry under pressure to extract more with less, that is a compelling proposition, and it signals that the next generation of oilfield optimization may be written not in finite-difference solvers but in learnable functions along the edges of a graph.

Subject of Research: A physics-guided heterogeneous graph Kolmogorov-Arnold network for optimizing water injection rates in multi-layer oil reservoirs

Article Title: HG-KAN: heterogeneous graph kolmogorov-arnold network for multi-layer reservoir injection optimization

Article References: Gong, F., Xu, J., Zhao, Y., Ji, X., & Du, C. (2026). HG-KAN: heterogeneous graph kolmogorov-arnold network for multi-layer reservoir injection optimization. Cluster Computing, 29(15), Article 840. https://doi.org/10.1007/s10586-026-06623-7

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06623-7

Keywords: HG-KAN, Kolmogorov-Arnold networks, heterogeneous graph neural networks, reservoir optimization, waterflooding, injection-rate allocation, physics-guided machine learning, surrogate modeling, digital oilfield, fault-block reservoir, multi-layer reservoir, machine learning

The work, carried out by David Jin Tao Leong and Doreen Ying Ying Sim of the University of Nottingham Malaysia, tackles a stubborn weakness in the growing field of simulation-driven antenna optimization. Physics-aware active learning, in which analytical antenna knowledge guides a surrogate-assisted search, has already proven it can cut the cost of full-wave electromagnetic analysis. But the sampling rules and probe locations in such systems are usually tuned to one specific design case. Constants that work beautifully for an FR4 patch at 2.4 gigahertz may fail completely on a low-loss Rogers laminate at 5.8 gigahertz, quietly reintroducing the manual tuning the optimizer was supposed to eliminate.

The researchers’ answer is an integrated workflow that combines four ideas: online calibration, matching-first recovery, physics-informed probes, and a lightweight surrogate model. Instead of prescribing where the optimizer should look for a matched design, the workflow estimates sampling bands from its own observations after every batch of simulations. When too few designs achieve a good impedance match, the system switches into a recovery mode that focuses the search on the best near-miss geometry until matches appear. A radial-basis-function surrogate, seeded with closed-form patch equations and deterministic physical transforms such as effective permittivity and electrical length, then ranks candidate designs so that each expensive simulation is spent where it is most informative.

The headline experiment was deliberately austere. Four optimizers, the integrated workflow, random search, a budget-limited genetic algorithm, and an unstructured surrogate search, were each given exactly 37 attempted simulations per run using the open-source openEMS solver. They competed on four substrate and frequency cases, spanning FR4 and Rogers laminates at 2.4 and 5.8 gigahertz, with ten replicate random seeds per case. The integrated workflow won decisively: it produced the lowest mean and median final objective in every single case and returned a properly matched design in all forty runs. The baselines, while competitive on individual seeds, showed far heavier upper tails and between one and eight unmatched endpoints depending on the case and method.

The statistical treatment was unusually careful for an engineering study. Using exact Mann-Whitney rank tests with Holm adjustment within each case, the integrated workflow was significantly lower than the three baselines in nine of twelve directional comparisons. Six contrasts remained significant in a stricter two-sided unpaired analysis, and seven in a paired-by-seed sensitivity analysis. The authors are candid about the limits: comparisons on the easier fourth case against the genetic and unstructured surrogate baselines were not statistically resolved, suggesting the method shines brightest when an unfamiliar substrate or band makes impedance matching genuinely hard.

The second major contribution is a multi-fidelity screening protocol that exploits the huge cost gap between coarse and fine simulation meshes. The workflow runs its entire 37-call search on a coarse mesh, then promotes the twelve best candidates to full resolution for confirmation. Measured in equivalent high-fidelity simulations, this cut the mean cost by 19 to 46 percent across cases, an overall reduction of 36.9 percent, while still returning a matched full-resolution design in 39 of 40 runs. The researchers are equally clear about the trade-off: endpoint objective quality was not uniformly preserved, with one case showing a modestly worse average result than a full-resolution search. Cost savings and final quality, they show, must be reported together rather than cherry-picked.

To check that the optimized designs were not artifacts of one particular numerical setup, the team subjected the four selected finalists to twelve stability checks involving a finer mesh, a 50 percent larger air domain, and perfectly matched layer boundaries. All twelve checks preserved the impedance match, with maximum changes of just 0.180 decibels in broadside directivity and 0.121 decibels in realized gain. Nominal far-field calculations gave directivities of 6.51 to 7.00 dBi and realized gains of 3.59 to 5.77 dBi. Notch depth and threshold-defined bandwidth proved more sensitive, varying by up to 3.7 decibels and 27.8 percent respectively, a useful reminder that some antenna metrics are inherently fragile under small numerical perturbations.

Two exploratory extensions probe how far the approach can stretch. A ten-variable E-shaped patch case, adding slot geometry and two-dimensional probe placement to the search, matched all ten integrated-workflow runs and beat random search with statistical robustness, though comparisons with the adaptive baselines were inconclusive. A five-seed pilot that folded realized gain into the acquisition loop alongside impedance produced a directionally favorable but non-significant hypervolume trend, establishing feasibility rather than a demonstrated multi-objective win. The authors frame both studies as bounded extensibility tests, not claims of high-dimensional or multi-objective superiority.

What makes the study notable is its intellectual honesty. The authors state explicitly that all evidence is numerical and openEMS-based, that no commercial-solver replication, fabricated prototype, or anechoic-chamber measurement is claimed, and that the advantage belongs to the integrated workflow as a whole rather than to any single component. They also disclose that one legacy implementation detail involving solver-inert feature columns was corrected before the primary comparisons, and that the second through fourth cases should be read as cross-case transfer evaluations rather than a formal held-out validation set.

The implications reach beyond patch antennas. As wireless systems multiply across the Internet of Things, 5G and 6G bands, and satellite constellations, the demand for rapidly optimized radiators on wildly different substrates keeps growing. A workflow that transfers across materials and frequencies without case-specific retuning, and that documents its own statistical evidence with per-seed tables and exact rank tests, offers a template for how simulation-hungry engineering design might adopt machine learning responsibly. The authors point toward tolerance and yield studies, richer multi-objective acquisition, and tests on arrays and multilayer structures as the next frontier. For now, the message is clear: with the right physics in the loop, even 37 simulations can be enough to tame an antenna.

Subject of Research: Self-calibrating multi-fidelity active learning for low-budget full-wave optimization of microstrip patch antennas across substrates and frequency bands

Article Title: Self-calibrating multi-fidelity active learning for microstrip patch optimization across substrates and bands

Article References: Leong, D. J. T., & Sim, D. Y. Y. (2026). Self-calibrating multi-fidelity active learning for microstrip patch optimization across substrates and bands. Frontiers in Antennas and Propagation, 4, Article 1935948. https://doi.org/10.3389/fanpr.2026.1935948

Image Credits: AI Generated

DOI: 10.3389/fanpr.2026.1935948

Keywords: active learning, antenna design optimization, microstrip patch antenna, full-wave electromagnetic simulation, multi-fidelity simulation, surrogate modeling, openEMS, impedance matching, Bayesian-inspired optimization, radial basis function, computational electromagnetics, self-calibrating priors

The research team, led by Kuineng Chen of the Hunan Engineering Research Center of Special Robot Control Technology and Equipment in Complex Environment, together with Huan Liu of State Grid Changle Power Supply Company and Fenglu Li of State Grid Shouguang Power Supply Company, tackled a problem that has frustrated condition-monitoring engineers for years. Infrared thermography is widely used to inspect electrical equipment without contact, but a measured surface temperature is not determined by contact degradation alone. Load current, ambient temperature, enclosure airflow, conductor geometry, and heat-transfer conditions all jointly shape the observed thermal field. A sound joint under a heavy load may look hotter than a severely degraded joint under a light load, which limits the usefulness of any single temperature reading as a fault indicator.

To disentangle these coupled influences, the researchers first constructed a three-dimensional electro-thermal finite-element model of a real bolted busbar joint: two overlapping copper bars, each 300 millimeters long, 50 millimeters wide, and 8 millimeters thick, connected over an 80-millimeter lap joint by two steel bolts spaced 40 millimeters apart. Rather than representing the degraded interface as a uniformly high-resistance block, the model divided the 0.5-millimeter contact layer between the bars into an effective conducting region and a degraded near-insulating region. This representation reproduces the physical mechanism by which deterioration contracts the conducting area and intensifies current constriction, forcing current through annular conducting patches centered on the bolt axes. As the effective contact ratio decreases, the conducting annuli shrink and localized Joule heating concentrates accordingly.

A crucial methodological decision was to assign distinct physical roles to the two contact parameters. The prescribed joint contact resistance specifies the target lumped resistance of the effective current path, while the effective contact ratio determines the spatial extent of that path and hence the degree of current constriction. When the contact ratio changes, the equivalent resistivity of the contact layer is recalculated so that the prescribed lumped resistance is retained, avoiding the double counting of conducting-area reduction through both geometry and resistance. The degraded region was assigned a resistivity contrast of one thousand relative to the effective region, which a parallel-path analysis showed limits bypass current to approximately 0.023 percent of the total, below the baseline power-consistency deviation of 0.056 percent.

Before any machine learning began, the team verified the numerical integrity of the simulation itself. Four mesh refinement levels were evaluated, from 21,958 to 368,625 tetrahedral elements, and a locally refined production mesh of 190,271 degrees of freedom was retained because it resolved the steep current-density and temperature gradients around the contact regions, bolt holes, and washers. More strikingly, the integrated Joule-heating power generated within the effective contact region was checked against the theoretical lumped relation P = I²Rc across all 400 parametric simulations. The maximum relative deviation was just 0.173 percent, with a mean of 0.059 percent, confirming that the distributed contact-heating implementation remained internally consistent throughout the entire dataset. Such explicit consistency checks between simulated contact heating and the theoretical relation are rarely reported in existing electro-thermal studies.

The parametric dataset was generated using Latin hypercube sampling across five physically defined inputs: load current from 400 to 1,200 amperes, contact resistance from 50 to 300 microohms, effective contact ratio from 0.10 to 0.50, ambient temperature from 293.15 to 313.15 kelvin, and convective heat-transfer coefficient from 5 to 20 watts per square meter per kelvin. Eighteen cases with effective-contact temperature rises exceeding 106.9 kelvin were excluded as high-temperature boundary-risk cases outside the intended applicability domain of the constant-property, sequentially coupled model, leaving 382 retained cases with temperature rises up to 106.9 kelvin. The team also introduced load-normalized thermal descriptors, dividing temperature responses by the squared load current, which reduced the direct correlation with current and provided a more comparable basis for evaluating contact-related thermal effects under different operating levels.

Four candidate model families were then compared for two complementary learning tasks: continuous prediction of the effective-contact temperature rise and four-class simulation-oriented thermal-risk classification using thresholds of 5, 15, and 30 kelvin. Evaluation used repeated five-fold cross-validation with 10 repeats, giving 50 train-validation iterations, with strict target-leakage controls ensuring that only the five original physical inputs served as predictors. The XGBoost regressor achieved a coefficient of determination of 0.990 ± 0.005, a root-mean-square error of 1.877 ± 0.542 kelvin, and a mean absolute error of 1.042 ± 0.198 kelvin, with performance comparable to random forest. For classification, XGBoost reached an accuracy of 0.938 ± 0.026 and a macro F1-score of 0.941 ± 0.033, with a more balanced macro recall than random forest. Across three threshold schemes, all out-of-fold classification errors occurred between adjacent classes, meaning the classifier never confused a Normal case with a Critical one.

Interpretability came through SHapley Additive exPlanations analysis, which decomposed each prediction into additive feature contributions. The results identified load current and prescribed contact resistance as the dominant contributors, with mean absolute SHAP values of 8.899 kelvin and 5.558 kelvin respectively for regression, while convection, ambient temperature, and effective contact ratio produced smaller, condition-dependent effects. The comparatively low global importance of the effective contact ratio reflects the area-averaged nature of the temperature-rise target rather than any claim that current constriction is physically unimportant. Once current and resistance establish the overall electrical power scale, variation in the contact ratio primarily redistributes current transfer within the contact region and produces a smaller average contribution to the area-averaged response. The non-monotonic dependence of the contact ratio further demonstrated that its contribution varies with the accompanying operating and contact conditions.

The authors are explicit about what the framework is and is not. Physics enters through finite-element generation of the training data, physically defined input variables, and post hoc consistency checks, rather than through constraints embedded in the learning algorithm, distinguishing the approach from physics-informed neural networks. The model is a forward surrogate that predicts internal effective-contact temperature rise from prescribed inputs; it does not inversely estimate contact degradation from infrared images, and relating the predicted internal quantity to surface measurements requires further validation. The framework is geometry-specific, built on one busbar configuration, and has not been experimentally validated, so its reported performance quantifies reproduction of finite-element outputs within the simulated design space rather than agreement with operating switchgear.

Future validation should proceed in controlled stages, the authors suggest: laboratory bolted-joint specimens with documented geometry and independently measured contact resistance, tested over multiple current levels and cooling conditions, followed by repeated heating cycles, bolt relaxation, and controlled surface degradation to determine whether prescribed contact scenarios adequately represent evolving joints. Until such work is completed, the framework stands as an interpretable tool for simulation-based scenario assessment and sensitivity analysis, capable of evaluating dense combinations of load, contact state, and thermal boundary conditions essentially instantaneously instead of the roughly 8.4 seconds of solver time each finite-element case requires. For an industry where a single overlooked hotspot can cascade into insulation failure and equipment outage, an explainable model that shows exactly how loading and contact condition jointly shape thermal risk represents a meaningful step toward smarter, load-aware inspection of the joints that hold the power grid together.

Subject of Research: Interpretable surrogate modeling for load-aware thermal risk assessment of bolted switchgear busbar joints using electro-thermal finite-element simulation and XGBoost with SHAP analysis

Article Title: Interpretable surrogate modeling for load-aware thermal risk assessment of bolted switchgear busbar joints using electro-thermal simulation

Article References: Chen, K., Liu, H., & Li, F. (2026). Interpretable surrogate modeling for load-aware thermal risk assessment of bolted switchgear busbar joints using electro-thermal simulation. Frontiers in Mechanical Engineering, 12, Article 1904437. https://doi.org/10.3389/fmech.2026.1904437

Image Credits: AI Generated

DOI: 10.3389/fmech.2026.1904437

Keywords: surrogate modeling, electro-thermal simulation, busbar joints, XGBoost, SHAP, thermal risk, switchgear, finite element analysis, Interpretable, surrogate, modeling, load-aware

The research team, led by Ala Ameryan, Mansour Ghalehnovi and Mohsen Rashki, tackled a problem that has haunted reliability engineers for decades: the sheer computational expense of evaluating a performance function. In realistic engineering settings, each evaluation may require running a full finite element model of a structure, a calculation that can take minutes or hours on high-performance computers. The gold standard, Monte Carlo Simulation, demands millions of such evaluations to reliably estimate a small failure probability, making it utterly impractical for real-world design work. Alternative approaches such as the First Order Reliability Method, known as FORM, are cheap but stumble badly when the boundary between safety and failure is strongly curved or irregular, sometimes failing outright to locate the critical design point.

The new method builds on two earlier lines of research. The first is the Kriging surrogate model, a statistical technique borrowed from geostatistics that constructs a probabilistic approximation of an expensive function. Kriging has a remarkable property: it not only predicts the value of the function at any point but also quantifies its own uncertainty, reporting a variance that signals how much it trusts each prediction. The second ingredient is active learning, embodied in the well-known AK-MCS method. Instead of blindly sampling the expensive function everywhere, AK-MCS uses a so-called U-learning function to hunt for the sample points where the surrogate is most uncertain about whether the structure is safe or failed. Each such point is evaluated with the true model and added to the training set, so the surrogate grows smarter precisely where it matters most: along the limit state surface that separates survival from collapse.

AK-MCS alone, however, struggles with rare events. When the failure probability is extremely small, the Monte Carlo candidate pool must be enormous, and the surrogate must classify millions of points. The authors’ solution was to fuse this active learning machinery with the First Order Control Variates Method, or FOCM, a technique they had previously developed for high-dimensional, highly nonlinear problems. FOCM works by locating the most probable failure point, linearizing the performance function around it, and then using the control variates principle to correct the bias introduced by that linearization. The correction factor, denoted lambda, is estimated by a modest simulation and multiplies the first-order failure probability to recover the true value. Crucially, FOCM is largely insensitive to the dimensionality of the problem, a property that most surrogate methods lack.

The mathematical elegance of AK-FOCM lies in how the two components divide the labor. The active learning Kriging model concentrates computational effort on the narrow, critical band around the limit state surface, aggressively filtering out the vast safe and failed regions where classification is trivial. Once the surrogate has converged, FOCM takes over: the design point is refined, the performance function is linearized without ever computing explicit partial derivatives, and a correction factor absorbs the truncation error. The authors justify a key simplification, the decoupling of a statistical weighting term from the failure indicators, using the concentration of measure phenomenon in high-dimensional spaces, which guarantees that the residual error shrinks as the number of random variables grows. For rare events, an n-sigma scaling trick artificially inflates the failure probability to a measurable level and then maps it back analytically, sidestepping the statistical wall that defeats ordinary Monte Carlo.

The validation campaign was extensive, spanning twenty mathematical and engineering benchmark problems. In the first test, a two-dimensional exponential function so nonlinear that both FORM and AK-MCS failed completely, AK-FOCM delivered a reliability index of 3.99 against the Monte Carlo reference of 4.01, an error of just half a percent, using only 89 function evaluations. The original FOCM needed 1,818 evaluations for comparable accuracy, meaning the new integration cut the computational cost by 95.1 percent. In a second, severely nonlinear example with exponentially distributed variables, AK-FOCM reached the correct answer with 63 evaluations, roughly 22 percent of what FOCM required, while AK-MCS produced an error three times larger.

The method then faced genuine engineering challenges. A conical shell structure loaded by compression and bending, whose dominant failure mode is buckling, was analyzed with six random variables following lognormal, normal and Gumbel distributions. Monte Carlo demanded one hundred million samples; AK-FOCM matched the reference reliability index of 4.79 with only 115 function calls, whereas AK-MCS failed to converge even with twenty times more initial samples. A fourth case study examined the static strength of an automobile front axle beam, an I-section component carrying the entire weight of the vehicle’s front end. Here AK-FOCM again reproduced the Monte Carlo reliability index of 2.06 with 92 evaluations, outperforming FOCM’s 123 calls while matching its accuracy.

Because surrogate methods involve random initial sampling, the team also ran a rigorous statistical robustness analysis. Thirty independent runs of the hardest nonlinear example produced a mean reliability index of 2.514 with a coefficient of variation below one percent, demonstrating that the method is remarkably insensitive to the luck of the initial sample draw. Sensitivity tests showed that varying the initial training set size from 10 to 30 points changed the final answer by less than half a percent, and enlarging the Monte Carlo candidate pool beyond a critical threshold drove the variance of the estimate essentially to zero. Boxplots of the required function calls across repeated runs showed not only a lower median cost for AK-FOCM but also tighter variability, indicating predictable, stable performance rather than occasional lucky runs.

The authors are candid about the boundaries of their framework. If the initial design of experiments completely misses a small, isolated failure region, the active learning loop could converge prematurely and underestimate risk. Severely discontinuous or highly oscillatory performance functions may violate the assumption that the linearization error can be fully compensated by the correction factor. And although FOCM itself tolerates high dimensions, the Kriging surrogate remains vulnerable to the curse of dimensionality, so problems with thousands of random variables would still degrade its fidelity and inflate its overhead. The method has so far been tested on static structural problems, and the authors call for future comparisons against emerging deep learning-based reliability frameworks and validation on full-scale, time-variant dynamic finite element models.

Even with those caveats, the implications for engineering practice are substantial. Reliability analysis has long been trapped in a trade-off between methods that are accurate but unaffordable and methods that are affordable but fragile. By coupling a self-aware surrogate that learns where to look with a dimensionally robust variance-reduction core, AK-FOCM offers a way to estimate the probability of catastrophic rare events at a fraction of the traditional cost. For designers of critical infrastructure, vehicles and aerospace structures, that could mean running reliability checks routinely during design rather than as a final, expensive afterthought, ultimately translating abstract probability mathematics into safer buildings, safer cars and safer machines in the physical world.

Subject of Research: A hybrid active learning Kriging and first order control variates method for efficient structural reliability analysis of rare failure events

Article Title: AK-FOCM: Integration of active learning Kriging with first order control variates reliability method

Article References: Ameryan, A., Ghalehnovi, M., & Rashki, M. (2026). AK-FOCM: Integration of active learning Kriging with first order control variates reliability method. Results in Engineering, 32, Article 113197. https://doi.org/10.1016/j.rineng.2026.113197

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113197

Keywords: structural reliability, AK-FOCM, active learning, Kriging, Monte Carlo simulation, control variates, failure probability, surrogate modeling, finite element analysis, FORM, rare events, computational efficiency

The research team built their antenna system step by step, starting from a single radiating element and progressively extending it to two ports, then four, and finally a full eight-port MIMO configuration. The single-element antenna measures just 0.4 by 0.4 millimeters and is built on a polyimide substrate with a dielectric constant of 4.3 and a loss tangent of 0.004, chosen for its balance between compactness and acceptable dielectric loss at terahertz frequencies. Copper is used for both the radiating patch and the ground plane because of its excellent conductivity and compatibility with standard fabrication processes.

The design evolved through four successive iterations. The team began with a conventional rectangular microstrip patch, then added two crossed rectangular extensions that lengthened the effective current path and improved impedance matching. A circular metallic element was incorporated along the lower edge of the patch in the third iteration, redistributing current flow and exciting additional resonant modes. Finally, a large circular slot was etched into the ground plane, creating a defected ground structure that suppresses surface-wave transmission and widens the operational bandwidth. The finished single-port antenna resonates at 0.418, 0.555, and 0.718 terahertz, with reflection coefficients of −28, −37.47, and −31.58 decibels respectively.

Parametric studies revealed how sensitive terahertz antenna performance is to small geometric changes. Varying the microstrip feed width from 0.035 to 0.050 millimeters showed that the narrowest feedline produced the best impedance matching across all three bands, while wider feeds degraded the return loss significantly. Substrate thickness was similarly critical, with an optimal range between 0.035 and 0.040 millimeters balancing bandwidth against matching quality. The team also compared polyimide against gallium arsenide and silicon substrates, finding that polyimide delivered wider bandwidths and superior impedance matching across all three resonant frequencies.

Once the single element was optimized, the researchers arranged multiple copies into MIMO configurations. A two-port version was tested in both parallel and orthogonal arrangements, with the parallel layout achieving isolation as deep as −31.5 decibels between ports. The four-port design, occupying a 0.8 by 0.8 millimeter substrate, maintained reflection coefficients between −25.40 and −37.9 decibels across its three bands, with isolation reaching −48.93 decibels in the third band. Each step preserved the multiband character of the original element while adding channel capacity.

The final eight-port antenna sits on a compact 1.6 by 0.8 millimeter substrate and resonates at 0.400, 0.555, and 0.718 terahertz. Reflection coefficients across the eight ports range from −22.5 to −42.13 decibels depending on the band, confirming strong impedance matching at every port. Inter-port isolation varies from −18 to −70 decibels, with the worst-case coupling still deep enough to ensure independent operation of each element. The antenna achieves a maximum gain of 10.04 decibels at 0.555 terahertz and maintains radiation efficiency above 95 percent across the operating range.

Diversity metrics are equally impressive. The envelope correlation coefficient, which measures how independently the antenna elements radiate, remains below 0.0017 across the operating band, far under the typical acceptance threshold. This translates to a diversity gain of essentially 10 decibels, the theoretical maximum, indicating near-perfect spatial diversity. The mean effective gain ratios between ports approach 0 decibels, confirming balanced power reception, and the total active reflection coefficient stays low under simultaneous multiport excitation, validating the design under realistic operating conditions.

The deep-learning component of the study is where the work makes its most distinctive contribution. The researchers generated 130,000 training samples from full-wave HFSS simulations, with 32,500 samples for each of the four antenna configurations. Each sample paired geometric parameters and operating frequency with the real and imaginary components of the reflection coefficient. The dataset was partitioned by complete antenna geometries rather than individual frequency points, ensuring that 65 unseen geometries per configuration were held out entirely from training to prevent data leakage. A deep feed-forward neural network then learned the nonlinear mapping from design space to the complex-valued scattering parameter.

The team compared three optimizers during training: stochastic gradient descent, RMSProp, and Adam. Adam delivered the best performance for the two-port and eight-port models, achieving a coefficient of determination of 0.983296 for the two-port case. For the single-port configuration, RMSProp reached an R-squared of 0.963030. Prediction accuracy declined for the four- and eight-port models, with R-squared values around 0.46 to 0.47, reflecting the increased complexity of modeling more ports. Against conventional regression baselines including random forest, gradient boosting, and support vector regression, the neural network proved competitive, though ensemble methods occasionally edged it out on individual configurations.

The computational savings are dramatic. Generating the full HFSS dataset required approximately 405 hours of simulation time, but once trained, the neural network produces a prediction in 0.051 to 0.106 milliseconds, a speed advantage of roughly 424,000 to 874,000 times over individual full-wave evaluations. A break-even analysis showed that after the initial dataset is generated, the surrogate model pays for its training cost after only 16 to 26 repeated evaluations. The researchers note that the present study is based entirely on numerical simulations, and experimental fabrication and on-wafer measurement remain the immediate next steps. They also caution that the framework has been demonstrated only for this specific antenna topology in the 0.3 to 0.8 terahertz range, and extending it to other geometries, reconfigurable designs using graphene, and full multi-port scattering matrix prediction constitutes future work. Still, the approach offers a practical path toward taming the design complexity of the dense antenna arrays that 6G and next-generation Internet of Things applications will demand.

Subject of Research: Deep learning prediction of S-parameters for a progressively extended eight-port terahertz MIMO antenna designed for 6G and IoT applications

Article Title: Deep learning–based S-parameter prediction of a progressively extended eight-port terahertz MIMO antenna for 6G and next-generation IoT

Article References: Azzouz, A., Alqurashi, A., Zafar, E. Y., Zakaria, Z., & Al-Gburi, A. (2026). Deep learning–based S-parameter prediction of a progressively extended eight-port terahertz MIMO antenna for 6G and next-generation IoT. Results in Optics, Article 101171. https://doi.org/10.1016/j.rio.2026.101171

Image Credits: AI Generated

DOI: 10.1016/j.rio.2026.101171

Keywords: terahertz, MIMO antenna, deep learning, 6G, S-parameters, neural network, polyimide substrate, envelope correlation coefficient, diversity gain, IoT, HFSS simulation, surrogate modeling

The device at the heart of the study is a deterministic lateral displacement, or DLD, microfluidic chip, a technology first demonstrated in the early 2000s. A DLD device is essentially a dense forest of tiny pillars arranged in tilted rows. As blood flows through the array, particles smaller than a critical size follow the fluid streamlines and pass straight through, while particles larger than that threshold are nudged sideways each time they collide with a pillar. Because the displacement is deterministic rather than diffusive, the device can continuously sort cells by size without any chemical labels, antibodies, or centrifugation. That makes DLD attractive for liquid biopsies, where the goal is to pluck tumor cells from a blood sample while leaving red blood cells and white blood cells behind.

The catch is that DLD performance depends on a tangle of coupled variables. The gap between pillars, the tilt angle of the post array, and the flow rate of the sample all interact in nonlinear ways to determine how far a target cell is displaced laterally. A small change in one parameter can shift the effective critical diameter that separates tumor cells from blood cells, and a change in another can amplify or suppress that effect. Traditionally, engineers have navigated this design space by trial and error, running simulation after simulation or fabricating chip after chip. Each evaluation is computationally expensive, and brute-force parametric sweeps offer little insight into how the parameters actually interact with one another.

The research team, led by Sadia Anjum Mim and corresponding author Xiaolin Chen, with Mohammed Raihan Uddin as a co-author, replaced that brute-force search with Bayesian optimization. The approach treats each simulation of the DLD device as an expensive black-box function whose output is the lateral displacement of the target particle. Instead of blindly sampling the design space, Bayesian optimization builds a Gaussian process surrogate model, a probabilistic statistical model that learns the relationship between the design variables and the displacement response. The Gaussian process not only predicts the displacement for any candidate design but also quantifies how uncertain that prediction is. An acquisition function then uses both the prediction and the uncertainty to decide where to sample next, balancing exploration of poorly understood regions against exploitation of promising ones.

The team used three design variables in the optimization: the pillar gap size, the tilt parameter of the post array, and the flow rate. Each candidate design was evaluated with detailed numerical simulations of the fluid and particle dynamics, and the results fed back into the surrogate model, which grew more accurate with every iteration. The final Gaussian process model achieved a coefficient of determination, R-squared, of 0.9873 on an independent validation dataset, with a mean absolute error of just 1.24 micrometers. In practical terms, the surrogate could predict how far a target cell would be pushed sideways by a given chip design with remarkable fidelity, without needing to run the full simulation every time.

The efficiency gains were striking. When the researchers compared Bayesian optimization against an Evolution Strategy benchmark, the Bayesian approach needed 67.2 percent fewer evaluations to identify the best-performing design within the prescribed design space and cut the time to solution by 80.0 percent. It also outperformed Genetic Algorithms, Differential Evolution, Particle Swarm Optimization, and conventional parametric sweeps. Because each evaluation of the underlying simulation is costly, reducing the number of required evaluations translates directly into days or weeks of saved computation, and it opens the door to exploring design spaces that would be intractable with exhaustive methods.

The winning design identified by the optimizer produced a target-particle lateral displacement of 75.51 micrometers. Follow-up analyses of particle size and outlet regions revealed an effective critical diameter of approximately 11.4 micrometers, a threshold that cleanly separates the investigated non-small-cell lung cancer CTC surrogate from smaller blood-cell-relevant background particles. The team demonstrated distinct collection of the target and background particles across three different release positions, meaning the separation remained robust regardless of where cells entered the device. That kind of positional robustness matters in a real clinical sample, where cells arrive at the chip inlet distributed across the full width of the channel rather than in a tidy single stream.

Beyond finding a single optimal design, the Gaussian process surrogate turned out to be a rich analytical tool in its own right. Because the model covers the entire design space, it enables response-surface mapping, which visualizes how displacement varies across combinations of parameters. It also supports global sensitivity analysis, which quantifies how much each design variable contributes to the output. The analysis identified the post-array tilt parameter as the dominant factor governing target-particle lateral displacement, while the flow rate was found to interact strongly with the geometric variables. That interaction is precisely the kind of insight that trial-and-error approaches miss, and it gives device designers a physical intuition about which knobs matter most and how they couple.

The framework also incorporates uncertainty quantification, a feature that distinguishes it from many purely data-driven design pipelines. Uncertainty analysis confirmed that the optimized device maintains stable performance under perturbations, meaning that small manufacturing imperfections or operating fluctuations are unlikely to destroy the separation quality. For microfluidic devices that must eventually be fabricated at scale and operated outside pristine laboratory conditions, this reliability-aware perspective is essential. A design that performs brilliantly only at one exact point in parameter space is of limited clinical value; one that tolerates realistic variation is far more likely to survive the journey from simulation to bedside.

The broader implications extend past cancer diagnostics. DLD devices have been used to separate parasites from blood, fractionate blood components, and sort particles across a wide range of sizes, and the optimization framework described here is general enough to be applied to any of these applications. By making the design process faster, more interpretable, and more reliable, Bayesian optimization could accelerate the development of an entire family of label-free cell-sorting chips. For liquid biopsy, in particular, the prospect of a cheap, antibody-free, continuously operating chip that reliably isolates circulating tumor cells is compelling, and this study demonstrates that intelligent algorithmic design, rather than exhaustive manual tuning, may be the fastest route to getting there. The work was supported in part by the National Science Foundation under Grant No. 2243980.

Subject of Research: Machine learning-driven optimization of microfluidic deterministic lateral displacement devices for label-free circulating tumor cell separation

Article Title: Bayesian optimization of deterministic lateral displacement devices for circulating tumor cell separation

Article References: Mim, S. A., Uddin, M. R., & Chen, X. (2026). Bayesian optimization of deterministic lateral displacement devices for circulating tumor cell separation. Biomedical Microdevices, 28(4), Article 72. https://doi.org/10.1007/s10544-026-00856-4

Image Credits: AI Generated

DOI: 10.1007/s10544-026-00856-4

Keywords: Bayesian optimization, Gaussian process, deterministic lateral displacement, circulating tumor cells, microfluidics, liquid biopsy, surrogate modeling, cell separation, uncertainty quantification, sensitivity analysis, biomedical microdevices, machine learning

The technique, called a graph-guided data-driven evolutionary algorithm with multi-feature weight-fused modeling, or GGDDEA-MFWM, was developed by Ruxin Zhao, Jiajie Kang and colleagues at Yangzhou University, along with Chang Liu of Yangzhou Polytechnic Institute. Their target is a notoriously difficult optimization problem known as distribution network reconfiguration. In principle, the idea is simple: distribution networks contain normally open switches and normally closed switches, and by changing which lines are active, operators can reroute power flows to reduce losses, relieve overloaded equipment and stabilize voltages. In practice, the number of possible switch combinations explodes combinatorially with network size, and every candidate configuration must satisfy strict engineering constraints, including that the network remain connected and radial, meaning power flows along tree-like structures without loops, and that voltages and currents stay within safe limits.

Compounding the difficulty is the rise of renewable energy. Solar panels and wind turbines inject power at scattered points across the network, and their output fluctuates with weather and time of day. That variability means a switch configuration that minimizes losses at noon may perform poorly at dusk, and the physics of power flow shifts continuously as injections change. Traditional approaches either evaluate every candidate configuration with full power-flow simulations, which is computationally expensive, or rely on heuristic rules that can miss the best solutions. The Yangzhou team took a third path: use machine learning to build fast surrogate models that approximate the expensive physics, then let an evolutionary algorithm search the vast space of configurations guided by those models.

The heart of the method is its multi-feature weight-fused modeling. Rather than training a single predictor of power loss, the researchers trained three separate radial basis function models, each capturing the relationship between power loss and a different family of physical features: voltage characteristics, current characteristics and network topology. Radial basis function networks are a class of machine learning models that interpolate from known data points, making them well suited to approximating smooth physical relationships. Because each model captures a different aspect of how the grid behaves, fusing their predictions can yield more accurate estimates than any single model alone. But how much should each model be trusted? The answer changes with the amount of empirical data available, the scale of the network and the density of feature distributions in the data.

To handle that variability, the team dynamically tuned each model’s k value, a parameter controlling how many neighboring data points influence the model’s prediction, balancing prediction accuracy against computational efficiency under changing conditions. Then, to resolve the uncertainty in how much each feature model should contribute to the final prediction, they turned to an optimization technique called sequential least squares programming, or SLSQP. This method assigns optimal weights to the three models according to their prediction errors, so a model that is performing well on the current network state earns more influence, while a poorly performing one is downweighted. The result is a surrogate ensemble that adapts itself to the problem at hand rather than relying on fixed assumptions about which features matter most.

The second major innovation addresses a bottleneck specific to network reconfiguration: generating feasible topologies. In a generic evolutionary algorithm, candidate solutions are created by randomly modifying branches, opening some switches and closing others. But most random modifications produce invalid networks, ones with loops that violate radiality or disconnected islands that leave customers without power. Filtering out these invalid candidates wastes enormous computational effort. The researchers’ graph-guided adaptive recombination strategy instead starts from minimum spanning trees, the tree-like subnetworks that connect all nodes with the fewest possible active branches, and iteratively generates new feasible topologies from there. By performing comparative analysis on candidate structures, the strategy also retains configurations with structural advantages, so useful wiring patterns survive across generations rather than being discarded by blind random mutation.

To test their approach, the researchers ran comparative experiments on three standard benchmark systems from the Institute of Electrical and Electronics Engineers: the IEEE 123-bus, 141-bus and 295-bus distribution networks, which represent increasingly large and realistic grid scenarios. They pitted GGDDEA-MFWM against five competing algorithms, including SRK-DDEA, TT-DDEA, MS-DDEO, CL-DDEA and BDDEA-LDG, each representing a different state-of-the-art strategy for data-driven evolutionary optimization. The evaluation went beyond simple performance comparisons. The team applied Wilcoxon statistical tests to verify that the observed advantages were statistically significant rather than artifacts of random variation, and they conducted ablation studies, systematically removing each of the three core strategies to confirm that all of them contributed essentially to the algorithm’s performance.

The results showed that the new algorithm achieved superior topology optimization for power loss reduction across the benchmark systems, with statistically significant performance advantages over all five competitors. The ablation studies were particularly telling: removing any one of the three core components, the multi-feature surrogate modeling, the dynamically weighted model integration or the graph-guided recombination strategy, degraded performance, demonstrating that the pieces work together as an integrated whole rather than as interchangeable tricks. For utilities, the practical implication is that an algorithm like this could, in principle, continuously adjust network switching as conditions change, reducing losses that today are simply accepted as the cost of doing business.

The broader context makes the work timely. Distribution networks worldwide were designed for one-way power flows from centralized plants to passive consumers. Rooftop solar, electric vehicles, battery storage and smart buildings are turning them into dynamic, bidirectional systems, and operators need tools that can keep pace. Data-driven evolutionary optimization has emerged as a powerful framework for such problems because it can search enormous combinatorial spaces without requiring exact analytical models, using learned surrogates to stand in for expensive simulations. The Yangzhou team’s contribution is a careful engineering of that framework for the specific physics and constraints of power distribution, from radiality requirements to the shifting importance of voltage, current and topological features.

Challenges remain before such algorithms move from benchmark feeders to live grids. Real networks carry measurement noise, unbalanced loads and protection coordination requirements that the clean IEEE test systems do not fully capture, and the researchers note that data will be made available on request, inviting further scrutiny and replication. The work was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangsu Province. Still, the study offers a concrete demonstration that machine-learned surrogates, intelligently fused and guided by the graph structure of the grid itself, can tame one of power engineering’s hardest combinatorial problems. As grids grow more complex and the margin for waste shrinks, algorithms that can rewire the network in seconds rather than hours may become as essential as the wires themselves.

Subject of Research: Data-driven evolutionary optimization of distribution network reconfiguration using graph-guided surrogate modeling

Article Title: Graph-guided data-driven evolutionary algorithm with multi-feature weight-fused modeling for distribution network reconfiguration optimization

Article References: Zhao, R., Kang, J., Yang, L., Fu, L., Liu, C., Jiang, C., & Shi, Y. (2026). Graph-guided data-driven evolutionary algorithm with multi-feature weight-fused modeling for distribution network reconfiguration optimization. Cluster Computing, 29(13), Article 745. https://doi.org/10.1007/s10586-026-06552-5

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06552-5

Keywords: distribution network reconfiguration, evolutionary algorithm, surrogate modeling, radial basis function, power loss reduction, smart grid, renewable energy integration, graph-guided optimization, IEEE test feeders, multi-feature fusion, SLSQP, Cluster Computing