Spatial transcriptomics has transformed how biologists study tissue. Instead of grinding up a sample and averaging gene activity across millions of cells, the technology measures gene expression at hundreds or thousands of discrete spatial spots, preserving the geography of the tissue. This lets researchers ask where particular gene programs are active, how cell types arrange themselves during development, and how disease disrupts the ordered architecture of an organ. A central computational task in this field is domain identification: grouping the spatial spots into coherent regions, such as the layered structure of the cerebral cortex, based on combined patterns of gene expression and physical adjacency. Get the domains right, and downstream analyses of cell types, developmental patterning, and pathology all become more meaningful.

Over the past several years, graph neural networks have become the dominant tool for this job. The idea is elegant. Represent each tissue spot as a node in a graph, connect neighboring spots with edges, and let the network learn representations that blend each spot’s gene expression profile with information flowing in from its spatial neighbors. Methods built this way, such as SpaGCN, consistently outperform older clustering approaches that consider expression alone. But the field has grown along a slightly troubling pattern: nearly every existing method represents the connection between two spots with a single scalar edge weight, typically a simple function of spatial distance, and no one had ever systematically evaluated whether that design choice matters. What if edges could carry richer descriptions? Would performance improve? Until now, the question had simply never been answered.

The new paper answers it by building an unusually capable system and then methodically taking it apart. The researchers call their model RMGAT, short for Relational Multi-Scale Graph Attention Network. Each spatial edge in RMGAT is described not by a single number but by an eight-dimensional learned feature vector, a level of relational detail that the authors state is new to spatial transcriptomics. The model’s training combines three objectives: a graph reconstruction loss that forces the learned representations to preserve the structure of the spatial network, an NT-Xent contrastive loss of the kind popularized by SimCLR that pulls together representations of similar spots and pushes apart dissimilar ones, and a self-expression decoder. On top of the network sits a post-processing pipeline called V30, which uses consensus clustering, Hungarian label alignment to keep cluster labels consistent, and spatial refinement to smooth the final domain maps.

To judge whether any of this machinery earns its keep, the team evaluated RMGAT on the standard benchmark in the field: twelve sections of the human dorsolateral prefrontal cortex, or DLPFC, a brain region whose cortical layers form a well-characterized pattern of tissue domains. They ran five independent random seeds on each section, producing sixty runs in total, and measured performance with the adjusted Rand index, or ARI, a standard statistic for comparing a computational clustering against expert anatomical labels. RMGAT achieved a mean ARI of 0.3422, with a standard deviation of 0.0402 and a 95 percent confidence interval running from 0.332 to 0.353. That lands the new model in the same territory as SpaGCN, which achieves roughly 0.36 on the same benchmark. In other words, RMGAT is competitive, but the raw performance number is not the real story.

The real story is the ablation study, and it is unusually careful. Rather than simply reporting that the full model performs well, the researchers systematically removed or replaced each of four components in turn: the graph attention mechanism, the contrastive learning objective, the eight-dimensional edge feature module built around an MLP, and the self-expression decoder. Critically, they paired each intervention with formal statistical testing across their sixty runs, treating design choices as hypotheses to be confirmed or rejected rather than as engineering folklore. The result is a rare thing in machine learning for biology: evidence-based guidance about which parts of a popular architecture actually matter.

One finding stood out above all the rest. When the authors replaced the graph attention mechanism, or GAT, with a plain graph convolutional network, or GCN, performance dropped by 0.028 ARI, a decrease that was statistically significant at p less than 0.0001. Graph attention differs from plain graph convolution in a crucial way: instead of treating every neighbor equally, attention lets each spot learn to weight its neighbors differently, attending more to some spatial relationships than others. The ablation result suggests that this adaptive weighting is doing real biological work, plausibly because tissue architecture is not uniform, and a spot at a boundary between two domains benefits from listening more carefully to neighbors on one side than the other. For the practitioners designing the next generation of spatial transcriptomics tools, this is the clearest takeaway in the paper: attention is not decoration, it is the load-bearing element.

The second finding is more nuanced. Contrastive learning showed a directional benefit, with removal costing 0.017 ARI at a p-value of 0.024 against the scalar-weight baseline. That is conventionally significant on its own, but the authors are careful to note that it does not survive a Bonferroni correction, the stringent multiple-testing adjustment that guards against false positives when many hypotheses are tested at once. Their recommendation is measured: contrastive learning appears helpful and is a reasonable choice, but the evidence stops short of proof. Meanwhile, the two components that most embody the complexity-adds-insight intuition, the eight-dimensional EdgeMLP that learns rich relational edge features and the self-expression decoder, were both essentially neutral, shifting ARI by only about 0.004 with p-values above 0.3. The elaborate edge representation the team built, the first of its kind in this application, provided no measurable advantage under their experimental conditions.

That null result deserves as much attention as the positive one, and the authors are transparent about its scope. The evaluation pipeline reduced input gene expression to fifty principal components, a standard dimensionality reduction step, and the authors explicitly frame their conclusions as holding at this PCA-50 input quality. It remains possible that richer edge features would matter more with higher-quality node inputs, or on benchmarks beyond the DLPFC. Science thrives on precisely this kind of boundary-drawing: knowing where a design principle applies is as valuable as knowing that it applies somewhere. The practical guidance that emerges is to invest in the quality of node features, meaning the gene expression representations themselves, rather than in edge feature complexity, and to prioritize attention-based architectures alongside, perhaps, contrastive learning.

There is a broader lesson here for computational biology at large. As deep learning methods multiply across genomics, imaging, and drug discovery, papers increasingly showcase novel architectures with impressive headline numbers but rarely interrogate which components drive the gains. This study offers a template for doing better: a systematic, statistically grounded dissection of a full pipeline, published open access under a Creative Commons license so that anyone can scrutinize and extend it. The work, supported by Anglia Ruskin University in Cambridge, demonstrates that negative results, honestly reported, can be as actionable as breakthroughs. For a field racing to decode the spatial grammar of tissues in health and disease, knowing that attention matters and that complexity for its own sake does not may save countless hours of computational effort and steer innovation toward the components that genuinely move the needle.

Subject of Research: A graph attention network and systematic ablation study for spatial transcriptomics domain identification

Article Title: RMGAT: a Relational Multi-Scale Graph Attention Network for spatial transcriptomics domain identification with systematic component ablation

Article References: RMGAT: a Relational Multi-Scale Graph Attention Network for spatial transcriptomics domain identification with systematic component ablation. (n.d.). https://doi.org/10.1186/s12859-026-06641-7

Image Credits: AI Generated

DOI: 10.1186/s12859-026-06641-7

Keywords: spatial transcriptomics, graph neural network, graph attention network, spatial domain identification, DLPFC, contrastive learning, ablation study, bioinformatics, cortical layers, machine learning, adjusted Rand index, gene expression

The core challenge the researchers set out to solve is a fundamental blind spot in existing machine learning approaches to mineral prospectivity modeling. Convolutional neural networks, the workhorses of modern image recognition, excel at spotting local patterns in voxelized 3D geological models, such as the geometry of a fault zone or the contact between an igneous intrusion and its host rock. But convolutional operations have inherently limited receptive fields, meaning they struggle to represent broader spatial relationships: the reach of a regional fault system, the alignment of intrusive bodies, or the distributed structural architecture that channels hydrothermal fluids across kilometers of crust. Graph neural networks can capture exactly those long-range relationships, yet they sacrifice detailed volumetric information. Neither approach alone, the authors argue, can fully characterize the multi-scale structure of a complex mineral system.

Their solution marries the two. The first branch of the hybrid model is a ResNet3D backbone enhanced with squeeze-and-excitation modules, which processes 7 by 7 by 7 voxel patches centered on each sampling location. The squeeze-and-excitation mechanism performs global average pooling over 3D feature maps and then recalibrates channel-wise responses through a small two-layer network, allowing the model to emphasize geological attributes most strongly associated with mineralization, such as Triassic host formations, diorite intrusions, and fault-related zones. The second branch is built on GATv2, a modern graph attention network, in which every sampling location becomes a node connected to its spatially nearest neighbors in a dynamically constructed K-nearest-neighbor graph. Attention weights, modulated by radial-basis distance encoding, let each node learn how much to trust information from its neighbors, effectively encoding coordinate-based spatial context that the convolutional branch cannot see.

Perhaps the most conceptually elegant component is the fusion mechanism that stitches these two branches together. Rather than averaging the two representations with fixed weights, the researchers introduce an entropy-guided adaptive gated fusion module. Each branch produces a probability prediction, and from that probability the team computes predictive entropy, a measure of how uncertain or ambiguous that branch is about a given location. Low entropy signals a confident branch; high entropy signals hesitation. The fusion gate reads these entropy values alongside measures of feature complementarity and dynamically adjusts the weighting alpha between the CNN embedding and the graph embedding, location by location. Where geology is locally complex and one branch falters, the other takes the lead. The authors are careful to note that this is a reliability-aware weighting scheme, not a full Bayesian uncertainty quantification framework, but it gives the model a self-correcting instinct that simple concatenation lacks.

Building the evidence base for such a model was a formidable undertaking in itself. The team integrated 1:50,000-scale geological maps, 86 mine-scale and regional cross sections, data from 489 boreholes, 26 audio-magnetotelluric interpreted profiles, and historical exploration reports. From these they constructed a 3D geological framework of the Anqing area, discretized into a voxel grid with 50-meter cubes, a resolution chosen as a compromise between geological fidelity and computational feasibility. The full prediction domain contained roughly 14.5 million valid voxels. For supervised training, the researchers extracted 4,253 voxels at known mineralized locations as positive samples and carefully selected 4,253 candidate negatives. Crucially, they avoided the easy trap of comparing ore against geologically irrelevant background: negative candidates were stratified by distance to known mineralization, from within 250 meters out to beyond 500 meters, and matched by geological signature, forcing the model to learn genuinely discriminative near-ore patterns. The authors candidly acknowledge that candidate negatives cannot be considered absolutely barren, since undiscovered mineralization may lurk within them.

When the full hybrid model was put to the test, the numbers spoke loudly. On the validation set it achieved an area under the precision-recall curve of 0.942 and an area under the receiver operating characteristic curve of 0.964, with roughly 93 percent accuracy and an F1 score of about 0.92. The comparisons were unforgiving: the GAT-only model managed an AUROC of 0.918, the CNN-only variant 0.844, and classical machine learning baselines such as logistic regression, random forests, and histogram gradient boosting languished with AUPRC values of only 0.59 to 0.61. The fusion model also proved robust across decision thresholds, holding an F1 near 0.92 across a wide range before degrading at extreme values, and it converged faster and more smoothly than either single branch. Embedding visualizations using principal component analysis and t-SNE showed the hybrid model producing far cleaner separation between mineralized and barren classes than the CNN alone, evidence that the graph module was genuinely integrating spatial adjacency information.

Turning a cloud of raw probabilities into something an exploration geologist can actually use required a further layer of engineering. The full-domain probability volume was smoothed, thresholded conservatively at 0.76, cleaned with binary morphological operations, and segmented using 3D connected-component analysis, volume filtering, vertical-continuity filtering, and geological-association screening. This pipeline suppressed isolated, overconfident voxels and retained spatially coherent bodies. The final output comprised five distal prediction targets, T1 through T5, none overlapping known mineralization, plus a sixth reference target supported by known mineralization that demonstrated the workflow could recover familiar ore-controlling geology. Maximum probabilities of the targets ranged from 0.916 to 0.978, and target-level mean entropy values between 0.343 and 0.431 provided a relative reliability index for ranking them.

The geological stories behind the individual targets are telling. Target T1, the largest, sits several hundred meters from the reconstructed Triassic host body and within a kilometer of diorite, but roughly 5.49 kilometers from known mineralization, making it a distal hypothesis rather than a near-mine extension. Target T2, the most distant at about 12.62 kilometers from known ore, overlaps only a sliver of Triassic-related rock and is flagged for caution given its weak intrusive association. Targets T3 and T5, by contrast, show stronger direct geological support, overlapping or abutting both the Triassic host rock and the diorite body, precisely the intrusive-host interaction that generates skarn copper mineralization. Target T4 overlaps the Triassic body within about 187 meters of diorite. The team stresses that all five remain predictive exploration hypotheses requiring independent geological, geophysical, and drilling validation before they can be called discoveries.

The study’s honesty about its own limitations may prove as influential as its results. The authors explicitly warn that validation metrics derive from a random-stratified sample-level split that cannot fully eliminate spatial autocorrelation, that the batch-wise KNN graph is a local approximation rather than a fixed full-region graph, and that the entropy-based fusion should not be read as full Bayesian uncertainty. Predictive entropy maps, displayed in plan view and in vertical cross sections, are offered as relative reliability guides for target ranking, not absolute confidence statements. In a field where high validation scores are too often mistaken for exploration certainty, this leakage-aware, uncertainty-conscious workflow sets a standard. If the hybrid voxel-and-graph vision of the subsurface holds up under the drill bit, the era of AI-guided mineral discovery in deeply concealed terrains may have quietly begun beneath the rice paddies of Anhui Province.

Subject of Research: Hybrid 3D CNN and graph attention deep learning for mineral prospectivity modeling in the Anqing skarn copper district

Article Title: A Hybrid 3D CNN-GAT Framework with Entropy-Guided Adaptive Fusion for 3D Mineral Prospectivity Modeling

Article References: Chen, C., Zhang, M., Wang, X., Wang, L., & Li, X. (2026). A Hybrid 3D CNN-GAT Framework with Entropy-Guided Adaptive Fusion for 3D Mineral Prospectivity Modeling. Natural Resources Research. https://doi.org/10.1007/s11053-026-10780-2

Image Credits: AI Generated

DOI: 10.1007/s11053-026-10780-2

Keywords: mineral prospectivity mapping, deep learning, 3D geological modeling, graph attention network, convolutional neural network, predictive entropy, skarn copper deposit, Anqing, exploration targeting, uncertainty quantification, ResNet3D, Yangtze River Metallogenic Belt

The challenge the researchers set out to solve is deceptively simple to describe but notoriously difficult in practice. Industrial systems spend nearly all of their time operating normally, with genuine faults appearing only in fleeting moments. As the authors illustrate, a factory that malfunctions for just five seconds in a day produces a dataset in which normal data overwhelmingly dominates, creating severe class imbalance that cripples conventional binary classification approaches. Signals in these environments also tend to be erratic rather than seasonal, making them hard for machine learning models to segment and learn. Rather than trying to classify each moment as normal or abnormal, the team adopted a prediction-based strategy: train the model exclusively on normal data to forecast future sensor values, then flag anomalies whenever reality diverges sharply from prediction.

Architecturally, the framework stacks three complementary components. At its core sits a three-layer bidirectional gated recurrent unit, or Bi-GRU, which processes sequences of sensor readings in both forward and backward directions. The GRU itself is a streamlined variant of the recurrent neural network that tamed the vanishing gradient problem through reset and update gates, requiring fewer parameters than the better-known LSTM and therefore training faster and generalizing more easily. By making the network bidirectional, the researchers allowed it to interpret the full context at every point in a sequence, capturing complex temporal dependencies and converging more quickly during training thanks to gradients flowing from both directions. A residual skip connection further eased gradient flow through the deep stack.

Temporal modeling alone, however, ignores a crucial truth about industrial plants: sensors do not operate in isolation. Boilers, turbines, valves, pumps, and tanks interact through physical process flows, and an anomaly at one component often propagates to its neighbors. To capture this spatial dimension, the team wired a graph neural network into the predictive model. The graph’s adjacency matrix was not learned from statistical correlations, which the authors caution can introduce spurious edges when anomalies are rare, but instead derived directly from the piping and instrumentation diagrams of the testbed. Each entry in the matrix encodes whether a direct process-flow path exists between two sensors or actuators, embedding physically grounded causal pathways into the model’s structure from the outset.

On top of this structural backbone, the researchers layered a graph attention network, or GAT, a relatively recent architecture that has proven exceptionally powerful for graph-structured data. Unlike graph convolution, which applies uniform weights to all neighboring nodes, the attention mechanism learns normalized coefficients that quantify the relative influence of each connected sensor. Through multi-head attention, the model can simultaneously attend to multiple aspects of each node’s neighborhood, stabilizing learning and enriching feature extraction. The attention weights multiply the input data before it reaches the bidirectional GRU, ensuring that the temporal model processes information in alignment with the underlying system topology. Crucially, these weights are also interpretable, allowing operators to see exactly which sensor relationships drive detection decisions.

The experimental platform was anything but a toy. The team evaluated the framework on the HAI 21.03 dataset, recorded at one sample per second from 79 sensors and actuators spanning a hardware-in-the-loop industrial control system testbed that replicates steam turbine generation and pumped-storage hydroelectric power. The testbed comprises four integrated processes: a boiler process handling heat transfer through water, a turbine process simulating rotating machinery, a water treatment process moving water between reservoirs, and a hardware-in-the-loop simulation layer synchronizing the whole, built on real industrial controllers from Emerson, GE, and Siemens. The test set contained 50 simulated attack scenarios, of which five were reserved for validation and 45 for final evaluation, with anomalies making up just 2.23 percent of the data.

The results demonstrated clear benefits from each design decision. Among unidirectional models, the plain LSTM baseline fared worst, while GRU-based models with graph neural network modules led the field with an F1 score of 0.912. Switching to bidirectional architectures pushed performance further: Bi-LSTM+GNN and Bi-GRU+GNN achieved F1 scores of 0.879 and 0.924 respectively, with the GE-BiGRU configuration emerging as the best overall performer. The gains were especially pronounced in sensitivity and time-series-aware precision, metrics that directly reflect missed-detection risk and operator alarm burden in continuous monitoring. Notably, the bidirectional extension added negligible computational cost, with even the most expensive variant requiring less than half a millisecond per sample, comfortably within the one-second budget imposed by the testbed’s sampling rate.

Perhaps the most striking finding concerns interpretability. The attention weights learned by the GAT revealed three exceptionally strong sensor connections, and each corresponded precisely to documented actuator-sensor pairs in the plant’s feedback control loops: a flow control valve linked to return-tank water levels, a level control valve linked to tank level measurements, and an auto speed demand linked to turbine RPM. These same channel pairs coincided with the primary targets of the testbed’s attack scenarios and exhibited markedly elevated prediction errors during attack intervals. In practical terms, this means operators can trace fault-propagation paths through the plant, identifying, for example, that a valve malfunction is likely when an anomaly coincides with abrupt changes in the relationship between a flow control valve and downstream water levels. Such insights can inform troubleshooting and preventive maintenance strategies.

The authors are candid about limitations. The adjacency matrix is constructed statically from simulator configuration documents and remains fixed during training, so topology changes such as adding or removing sensors would require full retraining, an expensive prospect in continuously operating plants. The evaluation also relies on simulator-based data, which, despite incorporating genuine industrial controllers, cannot fully reproduce sensor degradation, environmental variability, or adaptive adversarial attacks seen in the field. The team notes that sensitivity values remained below 0.75 across most models, reflecting a threshold selection procedure that balances precision and recall rather than minimizing missed detections; in safety-critical deployments where a missed fault costs far more than a false alarm, operators might weight recall more heavily. Future work will pursue dynamic graph construction, broader benchmark evaluation, and latency optimization for resource-constrained edge devices.

Even with these caveats, the study marks a meaningful advance in the race to secure critical infrastructure. By learning what normal looks like, exploiting the physical topology of the plant, and explaining its own reasoning through attention weights, the GE-BiGRU framework offers a blueprint for anomaly detection systems that are simultaneously accurate, efficient, and transparent. As power grids, water treatment facilities, and transportation networks grow ever more interconnected through the Internet of Things, tools that can spot a five-second anomaly buried in a sea of normal data, and tell engineers exactly where to look, may prove indispensable to keeping the lights on.

Subject of Research: A graph neural network and bidirectional GRU framework for detecting anomalies in multivariate time-series data from power generation cyber-physical systems.

Article Title: Graph-enhanced bidirectional GRU for anomaly detection in power generation environments

Article References: Kwon, D., Kang, Y., Lee, J., Nam, Y., Won, J., Kim, K. K., Kim, D. D., & Park, C. (2026). Graph-enhanced bidirectional GRU for anomaly detection in power generation environments. Data Mining and Knowledge Discovery, 40(6), Article 102. https://doi.org/10.1007/s10618-026-01262-3

Image Credits: AI Generated

DOI: 10.1007/s10618-026-01262-3

Keywords: anomaly detection, graph neural networks, graph attention network, bidirectional GRU, cyber-physical systems, power generation, industrial control systems, multivariate time series, cybersecurity, deep learning, fault diagnosis, HAI dataset

The study, led by Dezhi Zhi and colleagues at Northeast Forestry University in Harbin, China, tackles a problem that has grown acute as spatial transcriptomics has swept through plant science. Spatial transcriptomics allows researchers to measure gene expression across intact tissue sections, preserving the physical layout of cells within a leaf, root, or stem. That spatial context is exactly what plant biologists need to understand how vascular stem cells, epidermal cells, and meristematic pools coordinate their behavior. But the raw data alone does not reveal which of the thousands of possible ligand–receptor combinations are actually at work in a given tissue.

Existing tools for inferring cell–cell communication were largely built for animal single-cell data, where physical proximity is a reasonable proxy for signaling potential. In plants, that assumption breaks down. Cell walls, plasmodesmata, and the intricate local architecture of tissues mean that spatial adjacency is a weak and sometimes misleading indicator of effective communication. On top of this, plant ligand–receptor resources are complicated by massively expanded gene families, mappings derived from sequence homology rather than direct experiment, and highly uneven levels of experimental validation across candidate pairs.

PlantCCC approaches the problem as a graph-learning challenge. The framework takes a plant ligand–receptor database as its candidate search space and then builds a directed heterogeneous graph that connects cells, genes, and candidate communication edges. Rather than treating every neighboring cell pair as equally likely to exchange signals, PlantCCC applies expression-gated spatial weighting, a mechanism that scales the influence of spatial proximity according to whether the relevant genes are actually expressed. This allows the model to distinguish between cells that merely coexist in a tissue region and cells whose molecular profiles suggest an active signaling relationship.

The architecture combines several techniques from modern deep learning. Residual spatial expression enhancement sharpens the gene expression profiles of individual cells using information from their spatial neighborhoods. Spatially aware multi-head graph attention lets the model weigh different neighbors differently when aggregating information, while self-supervised contrastive learning helps the framework learn robust representations without requiring labeled training examples of true interactions. Together, these components allow PlantCCC to score candidate ligand–receptor edges in a way that integrates expression, spatial adjacency, and tissue context simultaneously.

To test whether the framework could separate genuine signaling from mere coincidence, the researchers constructed a semi-synthetic benchmark using an Arabidopsis leaf single-cell Stereo-seq dataset as a realistic spatial background. Into this background they injected known interaction components, creating TRUE pairs that contained a genuine communication signal, alongside CONFOUNDER pairs that showed tissue co-localization alone. PlantCCC successfully distinguished the two categories, demonstrating that it can detect an injected interaction component rather than simply rewarding pairs of cells that happen to occupy the same neighborhood. The framework also remained comparatively robust under dropout perturbation, a common artifact in single-cell and spatial data in which genes are spuriously recorded as unexpressed.

The researchers then applied PlantCCC to real biological questions, beginning with poplar stem datasets. Because a curated ligand–receptor resource for poplar was not directly available, the team derived a candidate set for Populus through homology mapping from Arabidopsis entries. Despite this added layer of uncertainty, PlantCCC prioritized candidate ligand–receptor axes that were consistent with the known architecture of the poplar stem, including the organization of meristematic cell pools within the secondary vascular tissue, and with prior experimental evidence for the corresponding signaling modules.

As an independent validation, the team turned to a publicly available 10x Genomics Visium HD dataset of Arabidopsis thaliana, using Arabidopsis PlantPhoneDB entries as the candidate search space. PlantPhoneDB is a manually curated pan-plant database of ligand–receptor pairs, and grounding the analysis in its experimentally supported entries gave the results a firmer biological footing. Once again, the top-ranked candidate communication axes aligned with tissue architecture, spatial expression patterns, and established knowledge of plant signaling pathways, suggesting that the framework’s rankings reflect genuine biology rather than computational artifacts.

The significance of this work extends beyond a single algorithm. Plant development depends on countless short-range peptide signals and receptor kinases: the CLAVATA pathway limits stem cell proliferation in shoot meristems, the PXY–CLE41 pair controls the rate and orientation of vascular cell division, FERONIA-mediated signaling maintains cell-wall integrity during salt stress, and peptide hormones such as phytosulfokine regulate cell expansion. Tools that can reliably prioritize which of these candidate axes are active in a specific tissue, at a specific developmental stage, could accelerate the discovery of new regulatory mechanisms in wood formation, defense responses, and organ development.

PlantCCC is also designed with interpretability and reproducibility in mind. The study analyzed four publicly available spatial transcriptomic datasets, and all implementation code and analysis scripts are openly available in a GitHub repository, covering everything from data preprocessing and homology mapping to model training, inference, and visualization. For a field where computational results can be difficult to reproduce, this openness lowers the barrier for other laboratories to apply the framework to their own crops, forest trees, or model species. As spatial transcriptomics continues to drive a new era in plant research, frameworks like PlantCCC offer a way to move from maps of where genes are expressed to mechanistic hypotheses about how plant cells actually coordinate their lives.

Subject of Research: A computational framework for inferring ligand–receptor cell–cell communication from plant spatial transcriptomics data.

Article Title: PlantCCC prioritizes context-specific candidate ligand–receptor communication patterns in plant spatial transcriptomics

Article References: Zhi, D., Wang, L., Guan, X., Chen, W., & Chen, K. (2026). PlantCCC prioritizes context-specific candidate ligand–receptor communication patterns in plant spatial transcriptomics. Plant Molecular Biology, 116(5), Article 93. https://doi.org/10.1007/s11103-026-01758-y

Image Credits: AI Generated

DOI: 10.1007/s11103-026-01758-y

Keywords: spatial transcriptomics, plant cell–cell communication, ligand–receptor pairs, graph attention network, graph contrastive learning, PlantPhoneDB, Arabidopsis thaliana, poplar stem, expression-gated spatial weighting, heterogeneous graph, PlantCCC, plant signaling

The framework operates within a Pythagorean fuzzy multi-scale information system, a setting designed for situations in which different decision makers grade their assessments at different levels of granularity. One expert might rate a transportation option simply as poor, fair, or excellent, while another provides a finely tuned linguistic scale with seven or nine gradations. The researchers first deploy a recursive scale-expansion mechanism that converts these heterogeneous Pythagorean fuzzy evaluations into representations at different levels of granularity. Pythagorean fuzzy sets extend ordinary fuzzy logic by assigning each element both a membership degree and a non-membership degree whose squares must sum to no more than one, giving evaluators more room to express hesitation. The recursive mechanism ensures that opinions expressed at coarse scales can be consistently compared and merged with those expressed at fine scales without discarding information in the process.

What distinguishes the new framework from earlier consensus models is its refusal to treat decision makers as identical rational agents. Decades of behavioral economics research, most famously the work of Daniel Kahneman and Amos Tversky, have shown that real people distort probabilities, fear losses more than they value equivalent gains, and weigh unlikely events in systematically biased ways. The team captures this heterogeneity through a hybrid behavioral model that combines cumulative prospect theory with rank-dependent utility. Cumulative prospect theory describes how individuals evaluate gains and losses relative to a reference point, weighting outcomes by a distorted probability function, while rank-dependent utility transforms cumulative probabilities in a rank-ordered fashion. Merging the two yields five psychological parameters for each decision maker: sensitivity to gains, sensitivity to losses, a loss-aversion coefficient, and two curvature parameters describing probability distortion in the gain and loss domains.

Estimating these parameters is far from trivial, and the paper devotes a detailed appendix to the problem. The authors designed a structured questionnaire of nineteen binary choices, each pitting a sure outcome against a probabilistic lottery, following the standard elicitation paradigm in behavioral decision theory. Participants switch preferences at points that reveal their certainty equivalents for various lotteries, and those switching points allow the researchers to back out each parameter. Gain sensitivity, for example, is estimated from the ratio of the probability weighting at even odds to the logarithm of the normalized certainty equivalent, while the loss-aversion coefficient follows from the indifference gain and loss identified in a mixed gamble. Probability-weighting curvatures are fitted by least squares across probability levels ranging from one percent to eighty percent. The team notes that this choice-based approach reduces the cognitive burden on respondents and improves the reliability of the resulting estimates compared with direct questioning.

Once every decision maker carries a psychological profile vector, the framework clusters participants hierarchically according to the similarity of their estimated parameters. This step recognizes that a risk-seeking optimist and a loss-averse pessimist will interpret the same fuzzy evaluation in profoundly different ways, and that consensus mechanics should account for those differences rather than averaging them away. The clustering partitions the large group into subgroups of psychologically like-minded members, each of which can then be managed with its own consensus strategy. Within each subgroup, social network analysis takes over: by mapping who trusts, consults, or influences whom, the method computes degree-centrality weights that identify the most connected and persuasive individuals. Feedback and opinion adjustment are targeted at those influential members, amplifying the effect of each intervention without forcing every participant to revise their views repeatedly.

The second layer of the framework coordinates the subgroups themselves, and this is where machine learning enters the picture. A regularized graph attention network learns adaptive weights for the different clusters, attending more strongly to subgroups whose current positions matter most for closing the consensus gap. Graph attention networks compute weights dynamically from the structure and content of the network rather than fixing them in advance, which makes them well suited to the shifting landscape of a consensus process as opinions evolve across iterations. Crucially, the authors add a regularization term that penalizes excessive weight concentration, preventing the model from pouring all its attention into one dominant cluster and neglecting the tail of smaller groups whose agreement is still needed. The result is an inter-group negotiation that adapts its weighting scheme as the discussion progresses while remaining numerically stable.

To demonstrate the machinery in action, the researchers applied the framework to a real-world class of problem: selecting a low-carbon urban transportation scheme. Such decisions are ideal testbeds because they involve large panels of stakeholders, from traffic engineers to environmental planners, who naturally differ in both the precision of their assessments and their tolerance for risk about future costs and emissions. When the authors benchmarked their method against five representative group decision-making approaches, the double-layer framework reached the prescribed consensus threshold in fewer inter-group iterations and with lower total adjustment cost, meaning that experts had to modify their opinions less aggressively to reach collective agreement. The method also preserved more of the original evaluation information, an important consideration since forcing coarse or over-smoothed judgments erodes the very expertise that large panels are convened to harvest.

The team went beyond a single demonstration, subjecting the framework to both ablation studies and sensitivity analyses. In the ablation experiments, removing or disabling individual components—such as the behavioral clustering, the social-network-based influence weighting, or the regularization of the attention network—degraded performance, confirming that each element contributes measurably to the overall result. The sensitivity analyses varied key parameters across plausible ranges and found that the outcomes remained stable, suggesting that the method is not a fragile artifact of carefully tuned settings but a robust procedure that practitioners could realistically deploy. That robustness matters, because consensus models that only work under idealized conditions rarely survive contact with the noisy, deadline-driven environments of municipal planning and corporate strategy.

The implications extend well beyond transportation policy. Any setting in which many stakeholders with vague, multi-granularity information and divergent risk attitudes must converge—health technology assessment, disaster response planning, infrastructure investment, environmental regulation—could benefit from a consensus mechanism that respects both the uncertainty of the data and the psychology of the people. By uniting Pythagorean fuzzy mathematics, behavioral economics, social network analysis, and graph neural networks in a single coherent architecture, the Shanxi University team has sketched a template for what next-generation group decision support might look like: models that do not pretend humans are perfectly rational, information is perfectly comparable, or influence is perfectly flat, but instead build those imperfections into the mathematics of agreement itself. The work was supported by the Humanities and Social Sciences Research Project of the Ministry of Education of China, and the article is available open access.

Subject of Research: Group decision-making with multi-scale fuzzy information and behavioral preferences

Article Title: A double-layer consensus framework for group decision-making with multi-scale fuzzy information and behavioral preferences

Article References: Chai, M., Fan, J., Lu, J., Wu, M., Cheng, R., & Chen, R. (2026). A double-layer consensus framework for group decision-making with multi-scale fuzzy information and behavioral preferences. Complex & Intelligent Systems. https://doi.org/10.1007/s40747-026-02492-0

Image Credits: AI Generated

DOI: 10.1007/s40747-026-02492-0

Keywords: group decision-making, Pythagorean fuzzy sets, consensus framework, cumulative prospect theory, rank-dependent utility, social network analysis, graph attention network, behavioral preferences, multi-scale information system, loss aversion, machine learning, low-carbon transportation

The physical mechanism most widely invoked to explain particle adhesion is adiabatic shear instability. During impact, the periphery of the particle experiences extreme strain rates, often exceeding ten to the seventh per second. When thermal softening locally outpaces strain hardening, a narrow shear band forms, concentrating deformation and heat into a thin region at the particle-substrate interface. This localized softening promotes the formation of material jets and enables metallurgical bonding between surfaces that would otherwise rebound elastically. The Johnson-Cook constitutive model, which couples strain, strain-rate, and temperature effects into a single flow stress description, is the standard framework for capturing this behavior in finite element simulations, and its parameters directly shape how the response surface varies across the process parameter space.

Single-particle finite element models, such as the spherical particle on a cylindrical substrate configuration used in this study, have become the canonical tool for interrogating these mechanisms. The geometry chosen here, a forty-micrometer-radius aluminum particle striking an aluminum substrate of two hundred fifty micrometer radius and depth, reflects the typical scale of cold spray powder feedstock and allows the impact event to be resolved with sufficient mesh refinement to capture the deformation gradients near the contact zone. Normal incidence is assumed, which is a reasonable first approximation since most particles in a cold spray jet strike the substrate at or near perpendicular orientation, although oblique impacts and particle-particle interactions in real deposits introduce additional complexity that single-particle studies deliberately set aside.

The five output targets selected for prediction capture complementary aspects of the impact response. Maximum equivalent plastic strain quantifies the severity of deformation, which correlates with the extent of interfacial contact area development and hence with bonding likelihood. Average contact plastic strain provides a more spatially averaged measure of deformation at the interface. Maximum temperature indicates whether adiabatic heating approaches the softening regime necessary for jetting. Maximum von Mises stress characterizes the mechanical loading experienced by the material, relevant to residual stress development and potential substrate damage. The deformation ratio, finally, describes the geometric flattening of the particle, a quantity experimenters can measure directly in cross-sectioned deposits, making it a useful bridge between simulation and experimental validation.

The choice of particle velocity, particle temperature, and friction coefficient as the three input parameters reflects their dominant roles in governing impact outcomes. Velocity controls the kinetic energy available for plastic work and is widely regarded as the single most influential cold spray parameter, with critical velocities below which particles rebound and above which they bond. Particle temperature, set by the gas temperature in the spray nozzle, pre-softens the material and lowers the energy barrier for deformation. The friction coefficient at the interface, though harder to control experimentally, governs tangential restraint and energy dissipation during sliding contact, influencing jet formation and the distribution of plastic strain around the contact periphery.

The surrogate modeling strategy adopted in this work addresses a persistent bottleneck in process simulation. A single resolved finite element impact simulation can require substantial computational resources, and exploring a three-dimensional parameter space at useful resolution demands hundreds or thousands of such runs. Once trained, a surrogate model evaluates new process conditions in milliseconds, enabling optimization studies, sensitivity analyses, and inverse design tasks that would be intractable with direct simulation. The practical value of the surrogate, however, depends entirely on its accuracy across the operating envelope, which is precisely where the choice of machine learning architecture becomes consequential.

The central representational innovation of the study is the treatment of each simulation sample as a node in a k-nearest-neighbour graph constructed in feature space, rather than as an isolated feature vector. In conventional feedforward networks, each training example is processed independently, and any information about the similarity between neighboring process conditions is implicit only in the aggregate statistics of gradient descent. By contrast, graph neural networks explicitly pass messages along edges connecting similar samples, allowing each node’s prediction to be conditioned on the responses of its parametric neighbors. For a physical system like cold spray impact, where the response surface is smooth and continuous in the vicinity of any given operating point, this inductive bias aligns naturally with the structure of the underlying data-generating process.

The comparative results carry a clear message about which architectural assumptions suit this problem. GraphSAGE-style spatial aggregation and the geometric attention network both achieved coefficients of determination above 0.93 for most targets, with the attention model reaching 0.97 for maximum plastic strain. These architectures share a common principle: they aggregate information from spatially proximate neighbors in feature space, weighting that information either uniformly or through learned attention coefficients. The attention mechanism’s slight edge is physically sensible, since the velocity-dominated nature of the response means that neighbors at different velocities carry unequal informational value, and attention weights can adaptively emphasize the most relevant ones.

The comparatively poor performance of the Chebyshev spectral graph convolution network and the topologically augmented multilayer perceptron, including negative R-squared values on several targets, is instructive rather than merely negative. Spectral methods operate through polynomial approximations of the graph Laplacian, which excel at multi-scale feature extraction when the graph structure itself carries meaningful community or frequency information. For a k-nearest-neighbour graph built from a relatively smooth parametric dataset, the spectral structure may be too weak or too sensitive to the choice of graph construction to provide a useful signal. Similarly, persistent homology descriptors encode global topological features of the point cloud, such as connected components and loops across scales, which may be largely uninformative for a response surface governed by local parametric gradients rather than by global shape features.

Negative R-squared values deserve particular emphasis for readers less familiar with regression diagnostics. A negative coefficient of determination indicates that the model’s predictions are worse than simply predicting the mean of the training data for every input. This is not a marginal failure but a categorical one, signaling that the architecture has failed to extract any generalizable input-output relationship from the training set. In surrogate modeling applications, such failures typically arise from an inductive bias mismatched to the data structure, or from architectures whose capacity is poorly matched to the available training set size, rather than from noise in the underlying simulation data, which is deterministic in this case.

The velocity-dominated character of the input-output relationships, confirmed by the three-dimensional feature space visualizations and two-dimensional contour projections, is consistent with decades of experimental cold spray research. Deposition efficiency, critical velocity, and coating quality all vary steeply with particle velocity, while temperature and friction act as secondary modulators. A surrogate model that respects this hierarchy, as the attention-based spatial aggregation evidently does, can allocate its representational capacity where the response varies most sharply. This interpretability of model performance in terms of constitutive physics is one of the study’s more valuable contributions, since it transforms an empirical architecture comparison into a statement about the physics of the process itself.

Several limitations frame the scope of these findings. The dataset derives from a single material system, aluminum on aluminum, with a single particle size and normal impact geometry, so extrapolation to dissimilar material pairs, oblique impacts, or multi-particle interactions remains untested. The friction coefficient is treated as a fixed input parameter, whereas in reality interfacial friction evolves with temperature, pressure, and surface state during the impact itself. Furthermore, the surrogate learns from simulation data and inherits any idealizations embedded in the finite element model, including the constitutive parameters of the Johnson-Cook model and the assumed contact behavior. Experimental validation against measured deformation ratios or deposition efficiencies would strengthen confidence in the surrogate’s predictions beyond the simulation domain.

Nevertheless, the framework points toward practical applications in cold spray process development. A validated surrogate could accelerate the identification of operating windows that maximize interfacial plastic strain while keeping substrate stresses within acceptable limits, or support real-time process control where nozzle gas conditions are adjusted in response to measured particle velocities and temperatures. The graph-based representation could also be extended to incorporate additional parameters, such as particle size distributions, substrate preheating, or nozzle standoff distance, as further node features, provided the training dataset is expanded accordingly through continued automated simulation campaigns.

More broadly, the study contributes to a growing recognition in computational materials science that the structure imposed on training data can matter as much as the choice of model family. Where physical responses vary smoothly across a parametric space, encoding that continuity directly into the learning architecture, as graph-based neighborhood aggregation does, provides a form of physics-informed bias that improves both accuracy and data efficiency. For solid-state deposition processes, and potentially for other impact-dominated manufacturing problems with expensive simulations and smooth response surfaces, this representational insight may prove as consequential as the specific performance numbers reported.

Subject of Research: Application of geometric and topological deep learning to predict thermo-mechanical performance in cold spray deposition process modeling

Article Title: Geometric and topological deep learning for predicting thermo-mechanical performance in cold spray deposition process modeling

Article References: Mishra, A. (2026). Geometric and topological deep learning for predicting thermo-mechanical performance in cold spray deposition process modeling. Discover Informatics, 1(1), Article 13. https://doi.org/10.1007/s44564-026-00012-3

Image Credits: AI Generated

DOI: 10.1007/s44564-026-00012-3

Keywords: cold spray deposition, geometric deep learning, graph neural network, GraphSAGE, finite element simulation, Johnson-Cook model, topological data analysis, graph attention network, thermal spray coating, additive manufacturing, surrogate modeling, supersonic particle impact