The core problem the team set out to solve is generalization. In recent years, data-driven turbulence modeling has flourished: researchers train neural networks on high-fidelity simulation or experimental data, and the networks learn corrections to classical models such as the k-epsilon or Spalart-Allmaras closures. These learned models can dramatically improve accuracy—but usually only within the flow regime they were trained on. The reason is architectural. Most existing approaches use dense, monolithic networks in which every parameter participates in every prediction. Such networks tend to entangle the physics of different regimes into a single set of weights, so a model tuned to attached boundary layers may produce nonsense when asked about separated flow, and vice versa. The result is a patchwork of specialized models that engineers must manually select and swap as conditions change—an approach that is fragile, labor-intensive, and poorly suited to real-world applications where flows routinely traverse multiple regimes.

Liu and colleagues’ answer is a framework they call the factorized-gating mixture of experts, or FG-MoE. Mixture-of-experts architectures are not new to machine learning; they have powered large language models and other large-scale systems by dividing computation among specialized subnetworks, with a component called a router or gating network deciding which expert handles each input. What distinguishes FG-MoE is how it builds and controls its experts. Instead of one opaque router making high-dimensional decisions, the framework trains a set of regime-specific experts—each specializing in a distinct physical regime of turbulence—and blends their outputs using spatially varying probabilities. At every point in a flow field, the gating mechanism estimates how strongly each expert should contribute, producing a smooth, location-dependent combination rather than a hard switch between models.

The truly novel ingredient is the factorization of the gating function itself. Conventional routers are high-dimensional: they take the full set of local flow features and map them onto expert-selection probabilities through a dense layer, which is computationally expensive and notoriously difficult to interpret. FG-MoE replaces this monolithic router with a set of lightweight, physics-guided binary attributes—simple yes-or-no questions about the local flow state, such as whether a particular regime indicator is active. The overall gating probability is then approximated as a product of low-dimensional binary factor probabilities. This product-form decomposition slashes the complexity of the gating computation, because the network no longer has to learn an arbitrary mapping through a vast parameter space. Instead, it composes a handful of interpretable, physically motivated decisions into a final expert weighting.

Interpretability is not merely an aesthetic bonus here; it is central to why the approach matters for engineering. When a conventional neural network corrects a turbulence model, engineers often cannot tell why it made a particular prediction, which breeds distrust in safety-critical applications like aircraft certification or nuclear reactor design. With FG-MoE, the binary factors can be tied to recognizable flow physics, so the gating mechanism effectively explains itself: a given point in the flow is assigned to an expert because specific, legible conditions hold there. The authors argue that this transparency, combined with the reduced gating complexity, makes the framework a practical pathway for engineering turbulence modeling—one that decomposes complex turbulent flows into distinct physical regimes and then leverages the factorized gating strategy to keep the whole system interpretable, efficient, and scalable.

Scalability arrives in an unusually elegant form. In most machine learning systems, adding new capability means retraining the entire model, an expensive and disruptive process. FG-MoE is designed as a plug-and-play architecture: new experts can be added to the expert library without retraining the whole model. If engineers encounter a flow regime the current system handles poorly—say, a novel heat-transfer configuration in a gas turbine—they can train a dedicated expert for that regime and slot it into the existing framework, with the factorized gating mechanism automatically learning when to call on the newcomer. This modularity mirrors how human engineering knowledge actually accumulates: not by rewriting every textbook each time a new phenomenon is discovered, but by adding a chapter and cross-referencing it with the rest.

The evidence for the framework’s effectiveness comes from extensive numerical experiments spanning canonical benchmarks to complex, real-world engineering applications. Canonical cases—the well-instrumented standard flows that the turbulence community uses to judge models—allow head-to-head comparison against established baselines. The engineering applications then test whether the approach survives contact with the messy, multi-regime reality of industrial flows, where separation, reattachment, pressure gradients, and wall effects coexist in a single domain. Across this spectrum, the authors report that FG-MoE delivers consistently high-fidelity predictions across diverse flow regimes, in contrast to monolithic dense networks whose accuracy degrades sharply outside their training distribution. The consistency is the headline result: rather than excelling in one regime and failing in others, the expert-based system maintains its accuracy as the physics changes.

The implications reach across aerospace, energy, and environmental technology, the three domains the authors single out as being critically limited by turbulence model accuracy. In aerospace, better cross-regime turbulence prediction could sharpen estimates of drag, heat loads, and buffet onset, reducing the safety margins that currently inflate fuel consumption and design cost. In energy, gas turbines, wind farms, and fusion devices all involve flows that transition abruptly between regimes, and improved models could improve efficiency and reliability. In environmental applications, from urban wind comfort to pollutant dispersion, the ability to blend regime-specific knowledge smoothly across a domain could make simulations more trustworthy. Because the framework is modular and interpretable, it also offers a natural vehicle for incorporating new experimental or simulation data as it becomes available, without discarding the accumulated expertise encoded in existing experts.

There are, of course, caveats worth keeping in mind. The study is computational, resting on numerical experiments rather than new wind-tunnel measurements, and the quality of any data-driven turbulence model ultimately depends on the fidelity and breadth of its training data. The factorized gating relies on physics-guided binary attributes, which means someone must choose sensible regime indicators—a task that leans on domain expertise even as it reduces the burden on the learning algorithm. And while plug-and-play expansion avoids full retraining, each new expert still requires its own training data and validation. The published version of the paper is also an early-release, peer-reviewed accepted manuscript that the journal notes remains subject to further edits before the final Version of Record, so some details may be refined.

Even with those qualifications, the work represents a notable conceptual shift. For twenty years, data-driven turbulence modeling has largely pursued bigger, denser networks trained on ever-larger datasets, in the hope that raw capacity would yield universal closures. Liu, Luo, Zhang, and He make the opposite bet: that turbulence is best learned by dividing it—by training specialists, wiring them together through a gating mechanism that is deliberately simple, physically grounded, and mathematically factorized, and by making the whole assembly extensible. If the framework’s cross-regime performance holds up as it is tested against more industrial flows and, eventually, experimental data, the humble turbulence model may finally be on its way to becoming something engineers have long wanted: a system that knows which kind of chaos it is looking at, and admits it.

Subject of Research: Machine learning framework for cross-regime turbulence modeling using a factorized-gating mixture of experts

Article Title: Factorized-gating mixture of experts enables cross-regime turbulence modeling

Article References: Liu, H.-C., Luo, Q., Zhang, X.-L., & He, G. (2026). Factorized-gating mixture of experts enables cross-regime turbulence modeling. Communications Engineering. https://doi.org/10.1038/s44172-026-00802-5

Image Credits: AI Generated

DOI: 10.1038/s44172-026-00802-5

Keywords: turbulence modeling, mixture of experts, machine learning, fluid dynamics, aerospace engineering, neural networks, gating mechanism, data-driven modeling, flow regimes, interpretability, computational fluid dynamics, Chinese Academy of Sciences

The study, published in the Journal of Agriculture and Food Research, focused on suction-type pneumatic conveying, the vacuum-driven method most widely used in modern recirculating aquaculture systems to move feed from storage silos to fish tanks. While positive-pressure blowing systems have been studied extensively, suction conveying has received far less scientific attention, even though it dominates the aquaculture sector. The researchers, Hasan Ghafori and Sadegh Ataei, set out to close that gap with an unusually comprehensive experimental campaign covering twelve commercial pellet types spanning three species: rainbow trout, common carp, and sturgeon, each at four growth stages from pre-starter to fattening.

The physical test rig was a six-meter-long transparent Plexiglas pipeline with a 60-millimeter internal diameter, engineered for a conveying capacity of one ton per hour. A calibrated feeder valve dispensed pellets at mass flow rates ranging from 0.2 to 0.8 kilograms per second, while a variable-speed centrifugal blower pushed air velocities from 10 to 25 meters per second. Because the pipe was transparent, the team could watch the flow patterns directly, but they also backed up their eyes with instrumentation: digital manometers measured pressure drop at three points along the line, a high-precision differential pressure transmitter recorded instantaneous pressure fluctuations at the pipe midpoint, and a two-stage sieving procedure based on the ASABE S269.4 standard quantified mechanical damage by weighing the fines generated during each run.

One of the study’s most significant contributions is a quantitative method for classifying flow regimes, replacing the traditional reliance on visual observation with an objective statistical indicator. The researchers used the coefficient of variation of pressure fluctuations, calculated from 30-second recordings at 3 Hz, to draw hard numerical boundaries between four distinct flow regimes. When the coefficient stayed below 5 percent, the flow was classified as dilute phase, meaning pellets were fully suspended and moving uniformly. Values between 5 and 11 percent marked a transition zone, 11 to 16 percent signaled an unstable zone with a stationary layer at the pipe bottom and strand flow above, and values above 16 percent indicated dense phase, where plug-type flow and frequent particle collisions produce intense pressure fluctuations. These thresholds, validated against both visual observations and simulations, turn regime identification from an art into a reproducible measurement.

The experiments revealed a characteristic U-shaped relationship between air velocity and pressure drop for every pellet type. At low velocities in the dense phase, pressure drops were high, reaching 1100 to 1475 pascals per meter across species, but mechanical damage was minimal, between 1.2 and 4.2 percent, because pellets moved gently as slow-moving slugs. As velocity increased, pressure drop fell to a minimum at roughly 15 to 16 meters per second, the point of highest conveying efficiency, where flow was fully suspended and stable. Beyond that sweet spot, pressure drop climbed again and pellet damage rose sharply, reaching up to 8 percent for fragile pre-starter pellets at 25 meters per second, driven by increasingly violent impacts against walls and neighboring particles.

Species and growth stage mattered enormously. Pre-starter pellets, which are crushed and compacted into small diameters, suffered the worst damage, between 2.8 and 3.1 percent even at the gentle velocity of 10 meters per second, while robust fattening pellets lost only 0.7 to 0.8 percent under the same conditions. Sturgeon pellets, with the highest bulk densities at 590 to 650 kilograms per cubic meter, consistently demanded the most fan power, up to 677 watts at 25 meters per second, while common carp pellets, the lightest and most free-flowing, entered the dilute phase at lower velocities and showed the lowest pressure drops overall. These differences, rooted in measurable properties such as pellet diameter, sphericity, terminal velocity, and drag coefficient, were carefully characterized using digital calipers, a vertical wind tunnel, and universal testing machine measurements of Poisson’s ratio, shear modulus, and friction coefficients.

To capture the physics that experiments alone cannot resolve, the team built a coupled computational fluid dynamics and discrete element method simulation. The gas phase was solved with the standard k-epsilon turbulence model in ANSYS FLUENT, while each pellet’s translational and rotational motion was tracked with Newton’s second law, using the Hertz-Mindlin contact model for particle interactions and the Gidaspow drag model for gas-solid coupling. Crucially, the pellets were not treated as indestructible spheres: a Bonded Particle Model represented each pellet as an assembly of sub-particles connected by breakable bonds, so that fracture occurred whenever impact energy exceeded the pellet’s specific fracture energy, calibrated against single-particle impact tests that measured critical breakage velocities between 16.1 and 19.8 meters per second. A particle replacement model then swapped fractured pellets for fragments, allowing the simulation to compute breakage ratios under every operating condition.

The simulations validated well against experiments, with relative errors of 10.5 to 15.7 percent for pressure drop and 2.50 to 3.23 percent for particle velocity across the full operating range. But full CFD-DEM runs are computationally expensive, which limits their usefulness for the rapid, repeated evaluations that real optimization demands. To overcome this, the researchers trained a surrogate artificial neural network on 480 data points, combining 384 simulation-derived records with 96 experimental measurements. The network, a multi-layer perceptron with an 8-20-12-4 architecture, dropout regularization, and batch normalization, predicts four key outputs at once: pressure drop, average particle velocity, mechanical damage, and power consumption. It achieved a coefficient of determination above 0.96 across all outputs, with test-set mean absolute errors of roughly 12.8 pascals per meter for pressure drop and 0.32 percent for damage, while cutting computation time by several orders of magnitude.

Interpretability analyses confirmed that the network had learned genuine physics rather than statistical artifacts. SHAP analysis identified inlet air velocity as the dominant input, followed by mass flow rate and pellet type, together explaining over 70 percent of predictive variance. Sobol variance-based sensitivity analysis with 65,536 quasi-Monte Carlo samples echoed this ranking, assigning total-order indices of about 0.51 to air velocity for pressure drop and 0.47 for mechanical damage. Even more impressively, the model held up under out-of-distribution testing: when challenged with eight extrapolated scenarios, including air velocities up to 30 meters per second and flow rates outside the training envelope, relative errors stayed below 9.1 percent, defining a reliable operating boundary of 8 to 28 meters per second and 0.1 to 1.0 kilograms per second.

The practical upshot is a set of design guidelines that aquaculture engineers can act on immediately, with an important caveat. For most pellet types, the dilute-phase window around 15 to 16 meters per second offers the best multi-objective compromise: minimum pressure drop, fully suspended stable flow, and acceptable damage. When pellet integrity is the overriding priority, as with fragile pre-starter feeds, controlled dense-phase operation near 10 meters per second minimizes breakage despite higher pressure drop and blockage risk, while the unstable zone should always be avoided. The authors stress that all quantitative boundaries come from a six-meter laboratory pipeline, so industrial installations with longer runs, bends, and higher throughputs will need further validation before these numbers become set-points. Still, the framework itself, experiments feeding simulations feeding an interpretable AI surrogate, offers a template for making one of aquaculture’s most invisible losses visible, measurable, and ultimately controllable.

Subject of Research: Hybrid CFD-DEM and machine learning modeling of mechanical damage and flow regimes in pneumatic conveying of aquaculture feed pellets

Article Title: Hybrid CFD-DEM and ANN modeling of pneumatic conveying of aquaculture feed pellets: Flow regimes, mechanical damage, and performance optimization

Article References: Hybrid CFD-DEM and ANN modeling of pneumatic conveying of aquaculture feed pellets: Flow regimes, mechanical damage, and performance optimization. (n.d.). https://doi.org/10.1016/j.jafr.2026.103285

Image Credits: AI Generated

DOI: 10.1016/j.jafr.2026.103285

Keywords: pneumatic conveying, aquaculture, fish feed pellets, CFD-DEM, artificial neural network, flow regimes, mechanical damage, pressure drop, SHAP analysis, Sobol sensitivity, suction conveyor, feed conversion ratio