Physics-Informed GNNs

GNN: Graph Neural Network

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4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 17

Oct 5, 2026cs.LG

Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow

Recent neural power-flow solvers, including emerging foundation models, achieve accurate voltage predictions, yet such accuracy does not necessarily imply physically consistent solutions. Even small complex voltage errors can yield large AC power-balance residuals. We study this accuracy-consistency gap across PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA on realistic 2224-bus Great Britain network (GBnetwork) scenarios, with cross-grid evaluation of GridSFM over 31 systems. Using a singular value decomposition (SVD) basis fitted to training AC power-flow solutions, we find that neural prediction errors contain substantial components outside the dominant solution subspace. To address this mismatch, calibrated solution-subspace projection (CSP) suppresses off-subspace prediction components after train-only bias calibration, reducing Mean PB by 67.0%, 37.8%, 40.5%, and 68.9% for PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA, respectively, relative to calibrated predictions, while improving voltage-magnitude accuracy in all four models. These results identify output-error geometry as an important factor in physics-consistent neural AC power flow. Code: https://github.com/Kimchangheon/neural-acpf-error-geometry

Changhun Kim, Timon Conrad, Redwanul Karim +7

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Institute of Electrical Energy Systems, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Physics-Informed GNNs Power Systems

Oct 4, 2026cs.LG

Physics-Augmented Graph Transformers for Patch-Antenna Forward and Inverse Design

Full-wave electromagnetic (EM) simulation enables accurate patch-antenna analysis but is computationally expensive for large-scale forward prediction and inverse design. We present a mesh-native, physics-augmented graph-learning framework that treats radiation-pattern prediction as signal reconstruction on an irregular surface mesh. For the forward problem, a GPS graph transformer is trained with Physics-Augmented Intermediate Supervision (PAIS), an auxiliary node-level objective that predicts complex surface currents, the physical intermediate linking geometry to radiation. PAIS improves multiple GNN backbones at no inference-time cost, while shuffled-current and non-physical controls show the gain comes from physical correspondence. Direction-conditioned decoding and a differentiable radiation-integral consistency loss further exploit this structure. On an 80,000-sample CST benchmark, GPS+PAIS reaches MSE 0.17 / PSNR 19.67, generalizes to a PCA split, and transfers zero-shot to canonical patches. For inverse design, surrogate-filtered diffusion beats nearest-neighbor retrieval by 32% relative MSE.

Avi Epstein, Snir Nehemia, Haim Suchowski +1

Tel Aviv University

Physics-Informed GNNs Graph Transformer Inverse Design

Oct 1, 2026cs.LG

Physics-Refined Spatiotemporal Forecasting on Open-Boundary Hydrologic Graphs

Spatiotemporal forecasting on hydrologic graphs is especially prone to instability in open-boundary systems, where the forecast domain exchanges fluxes with an unobserved exterior. In such systems, boundary nodes receive external forcing, e.g., upstream inflows in rivers or tidal signals in coastal regions, that is typically unavailable at prediction time. The absence of this information can compound errors as forecasts unfold in an autoregressive fashion, leading to inferior long-horizon performance. This paper dissects this instability issue by exploring two questions. 1) What boundary forcing enters the forecast domain when information beyond the boundary is missing? 2) How should this forcing propagate through the domain without incurring error amplification under autoregressive rollout? To address both, we propose a new computing framework comprising two key components. First, to compensate for the boundary forcing, our framework learns ghost node proxies from the boundary and interior nodes, striving to approximate unobserved external inputs. Second, to control error accumulation from these learned proxies, we leverage two physics refiners. In particular, one refiner enforces local consistency by aligning ghost proxies with their two-hop neighbors (i.e., boundary nodes and their immediate interiors). The other refiner enhances global stability by correcting the model forecasts through a physics-guided graph neural operator, reducing long-horizon numerical drift. Two real-world hydrologic graphs are employed for empirical evaluation. Comparative results show that our proposal enjoys higher prediction accuracy and long-horizon stability over both learning-based and physics-informed model competitors.

Haoyang Jiang, Zhengui Wang, Shenghan Gao +3

William & Mary, Williamsburg, VA, USA · Virginia Institute of Marine Science, William & Mary, Gloucester Point, VA, USA · Florida Atlantic University, Boca Raton, FL, USA

Spatiotemporal Forecasting Physics-Informed GNNs Spatiotemporal GNNs

Sep 24, 2026eess.SY

GridSFM: A Foundation Model for Solving AC Optimal Power Flow

We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a

15

million parameter physics-inspired graph neural network pretrained across

54

topologies of

500

to

4{,}000

buses. Our model attains a

2.45\%

zero-shot generation-cost error on a

10{,}000

bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only

100

solved instances, GridSFM adapts to unseen grids up to

10{,}000

buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We prove that the resulting elastic feasible set is contractible, that the AC-OPF minimizers remain minimizers of the elastic problem above an explicit penalty threshold, and that projecting an approximate solution back onto the AC-OPF feasible set is well posed. We release all models, data, and code so that the community can build on a shared starting point for AC-OPF.

Luke Bhan, Weiwei Yang, Margaret Capetz +1

University of California, San Diego · Microsoft Research · University of Washington

Neural Surrogate Modeling Optimal Power Flow Physics-Informed GNNs Power Systems

Sep 10, 2026math.NA

A variational physics-informed graph neural network for heterogeneous solid mechanics

Stress localization in heterogeneous solids is governed by the bimaterial interface, where the displacement field remains

C^0

-continuous, while in-plane stresses jump due to the stiffness mismatch. Coordinate-based physics-informed neural networks (PINNs) represent this jump via a prescribed regularization width or a weighted interface penalty, making their accuracy sensitive to how phase-contrast changes are handled. This work presents a variational, label-free physics-informed graph neural network (PI-GNN) in which the heterogeneity is carried by the discretization rather than by the trial field. The solver operates on a conforming adaptive mesh graph, assigns constitutive behavior per element, and minimizes the discrete total potential energy as a single unweighted objective in which only first derivatives appear. The discrete energy on piecewise-linear elements coincides with the finite element (FE) Ritz functional. Dirichlet conditions are enforced by construction, with no penalty term, no interface weight, and no prescribed transition width. Using one fixed architecture, optimizer, and loss across small-strain elasticity and finite-strain Neo-Hookean hyperelasticity in two and three dimensions, the von Mises error remains below

3.58\%

across a stiffness-contrast sweep spanning

(E_{\mathrm{inc}}/E_{\mathrm{mat}}\in[10^{-2},10^{2}])

, where a strong-form PINN degrades to

5.58\%

, and its displacement error reaches

7.66\%

against

0.49\%

for the PI-GNN. A trained network halves the (

σ_{xx}

) error of an energy-based PINN (

5.01\%

versus

10.94\%

). Training cost exceeds a single FE solve by more than an order of magnitude, so the construction is a variationally consistent, penalty-free interface representation for parametric surrogates and inverse identification rather than a replacement for a one-off FE analysis.

Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar Annabattula

Mechanics of Materials Lab, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, Tamil Nadu, India

Neural PDE Solvers Structural Mechanics Physics-Informed ML Physics-Informed GNNs

Sep 2, 2026cs.LG

Mesh-Native Physics-Informed Graph Surrogates for TCAD-in-the-Loop Design Space Exploration

High-fidelity TCAD simulation of drift-diffusion transport remains the workhorse of emerging FinFET device design, but it is computationally expensive, especially for 3D structures where runtime escalates steeply with mesh complexity. This sharply limits multi-objective design space exploration. Existing machine-learning surrogates map a fixed set of design parameters to a few scalar device metrics, discarding the underlying physics and losing transferability across device geometries and families. A physics-informed graph attention network (GAT) surrogate is proposed. It operates directly on the tetrahedral TCAD mesh and predicts, at every mesh node, the electrostatic potential together with the electron and hole quasi-Fermi levels, the fundamental unknowns of the drift-diffusion system. Training combines a data loss with finite-volume current-continuity residuals, embedding carrier-transport physics into the objective. Operating on the mesh as a graph, the surrogate inherits size generalization: a model trained on few-fin meshes applies unchanged to substantially larger arrays, bounded at inference only by GPU memory. Per-node uncertainty from a deep ensemble drives an active-learning loop that screens large candidate pools in seconds and forwards only the most informative designs for full simulation. Benchmarked against Sentaurus Device on multi-fin tri-gate FinFETs, the surrogate reproduces the three drift-diffusion fields with sub-volt per-field RMSE and reaches a per-design throughput orders of magnitude higher than the full simulator. The advantage grows with device size: on large multi-fin arrays that are prohibitively slow to simulate directly, inference still completes in under a second per device, enabling Pareto-front exploration across device scales infeasible for direct TCAD sweeps.

Leonid Popryho, Ayoub Sadeghi, Inna Partin-Vaisband

University of Illinois Chicago · Chicago, IL, USA

PDE Surrogate Modeling Physics-Informed ML Physics-Informed GNNs

Jul 22, 2026physics.flu-dyn

Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields

Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, the FVM-loss model achieves an all-field normalized root-mean-square error (nRMSE) of 2.3-2.8%. It demonstrates close agreement with the CFD references, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model outperforms the supervised baseline in terms of accuracy, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.

Tianyu Li, Zhiwei Cao, Qingang Zhang +3

Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, Singapore. · School of Future Technology, Fuzhou University, Fuzhou, China. · College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore. +2

Neural Surrogate Modeling Graph Neural Networks PDE Solving Physics-Informed ML Physics-Informed GNNs Computational Fluid Dynamics

Jul 6, 2026cs.LG

MeGA-MP: Metric Graph Advection Message Passing -- A Physics-Informed Message Passing Operator for Advection-Dominated Metric Graphs

Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes. Examples include utility networks such as water distribution systems or gas networks, electrical grids, and traffic flow networks. Such systems are naturally modeled as metric graphs, where edges correspond to one-dimensional Euclidean subspaces connected at vertices. Metric graphs are independent of an underlying global Euclidean space, limiting direct application of typical PINNs and operator-learning methods. Especially transport dynamics like advection require a methodology able to capture antisymmetric and long-range dependencies on graphs, which is itself a challenge. We propose a novel physics-informed message passing operator that encodes linear advection on metric graphs as an inductive bias. In the purely advective setting, the operator provably recovers the exact dynamics up to a theoretically derived discretization error without any training. Combined with trainable components like MLPs, our message passing operator extends to realistic advection-reaction dynamics in water distribution systems, where we achieve superior performance compared to baselines and zero-shot generalization across different graph topologies.

Janine Strotherm, Luca Hermes, André Artelt +1

Bielefeld University

Graph Representation Learning PDE Solving Message Passing Neural Networks Physics-Informed GNNs Physics-Informed Neural Operators

Jun 18, 2026cs.LG

Physics-Guided Dual-Stream Heterogeneous Graph Neural Network for Predicting Full-Field Structural Response of Stiffened Panels

Iterative design and optimization of large, complex structures require fast and accurate prediction of stress, displacement, and other fields. Finite element analysis (FEA) is computationally expensive for this task. Existing neural network surrogates often struggle with varying topologies and complex boundary conditions. This study proposes the novel Dual-Stream Heterogeneous Graph Neural Network (DS-HGNN) for full-field stress and displacement prediction in thin-walled structures, demonstrated on box beams made of stiffened panels. DS-HGNN operates on panel-level heterogeneous graph representations and introduces physics-guided edge states initialized from edge types, spatial information, and boundary kinematics. These states are updated through dual-stream message passing that separates longitudinal and transverse structural information while allowing cross-stream exchange. Geometry and loading effects are incorporated through Feature-wise Linear Modulation (FiLM)-conditioned 1-D spectral convolutions, and physical fields are reconstructed using a spectral-bypass low-rank readout. The model is evaluated on stiffened panel datasets with different geometries, boundary kinematics, loading conditions, and material nonlinear responses. DS-HGNN achieves the lowest stress and displacement RMSE compared with six benchmark heterogeneous graph neural network models. It also reaches comparable accuracy to the strongest benchmark models using 19%-38% fewer training samples. A targeted evaluation further shows that DS-HGNN captures yield and post-yield stress features.

Yuecheng Cai, Jasmin Jelovica

Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada · Department of Civil Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada

Neural Surrogate Modeling Graph Neural Networks Structural Mechanics Heterogeneous GNNs Physics-Informed GNNs

Jun 10, 2026cs.LG

Physics-Aware Auxiliary Losses Improve Out-of-Distribution Generalization of a GNN Synthesizability Filter

Machine-learning drug-discovery pipelines increasingly rely on generative models that propose molecules far from the data used to train downstream synthesizability filters. Existing filters (SAScore, SCScore, RAscore, DeepSA) are purely statistical and degrade in exactly this out-of-distribution (OOD) regime. We ask whether cheap, closed-form physical priors, used as auxiliary supervision on a graph neural network (GNN), improve OOD generalization. We add two auxiliary losses to a GINE backbone: a topological complexity regression supervised by the Bertz index, and a strain-energy soft penalty supervised by MMFF94 force-field energy. On a 65,177-molecule corpus (HIV, Tox21, COCONUT) labeled by SAScore thresholds we reproduce a strong in-distribution baseline, then evaluate a 4-way ablation (baseline / +complexity / +strain / +both) on a single-source OOD split (train on drug-like HIV+Tox21, test on COCONUT natural products), repeated over 5 seeds with paired bootstrap confidence intervals. All three physics-aware variants give a small but statistically significant OOD improvement over the baseline (mean OOD AUC 0.9774): +complexity Delta = +0.0060 (95% CI [+0.0023, +0.0102]), +strain Delta = +0.0032 ([+0.0008, +0.0052]), +both Delta = +0.0066 ([+0.0038, +0.0093]); every interval excludes zero, and the combination is best. The variants are indistinguishable in-distribution, so the effect is visible only under OOD evaluation. We are explicit that the effects are modest, and we report a cautionary methodological finding: a single-seed version of this experiment produced a qualitatively different (non-monotone) story that did not survive multi-seed evaluation.

Riya Bisht, Dhruv Agarwal

Graph Neural Networks OOD Generalization Physics-Informed ML Molecular Property Prediction Physics-Informed GNNs

Jun 9, 2026cs.CE

Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks

Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.

Manuel Ricardo Guevara Garban, Yves Chemisky, Étienne Prulière +3

Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, Talence, France · Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, Talence, France · Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, 09599, Germany +2

Neural Surrogate Modeling Structural Mechanics Physics-Informed ML Physics-Informed GNNs Spatiotemporal GNNs

May 19, 2026cs.LG

Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments

Dental aerosol procedures produce sub-50 micrometre nuclei that can remain airborne for long periods in enclosed clinics, creating pathways for airborne pathogen transmission. Reynolds-Averaged Navier-Stokes (RANS) simulations with Euler-Lagrange particle tracking capture this transport accurately but require very long run times per scenario, which precludes real-time clinical decision support in 3D. We present the Eulerian-Lagrangian Graph Interaction Network (ELGIN), a physics-informed graph surrogate that jointly predicts carrier-flow dynamics on the OpenFOAM polyhedral mesh and the per-parcel motion of the polydisperse spray cloud. ELGIN couples a multi-head Graph Transformer with Jacobi-preconditioned learnable pressure projection and a turbulence-closure head to a sigmoid-gated Lagrangian Interaction Network through differentiable inverse-distance mesh-parcel coupling, and advances parcels with a symplectic Stormer-Verlet integrator. A four-stage physics-informed curriculum stabilises 260-step autoregressive rollouts without gradient explosion. A parameter sweep with foam-extend 4.1 OpenFOAM reactingParcelFoam across clinically relevant ventilation rates and handpiece spray speeds provides CFD ground truth. This article reports a single-case demonstration in which both ELGIN and a Lagrangian-only baseline (M0) are trained and evaluated on Sweep_Case_03 of a twenty-case sweep; full 16/2/2 retraining is in progress and will replace all reported metrics. On this case, ELGIN tracks the foam-extend particle cloud much more closely than M0: mean parcel displacement error falls from 19.56% to 16.20% of room width and cloud radius-of-gyration error from 9.85% to 6.58%. A 26-second rollout completes in ~64 s on a 4 GB GPU, approximately 37x faster than the foam-extend reference pipeline, toward per-appointment infection-risk screening once the multi-case checkpoint is in place.

Takshak Shende, Viktor Popov

Department of Mechanical Engineering, University College London (UCL), London, United Kingdom · Ascend Technologies Ltd, Southampton, United Kingdom

PDE Surrogate Modeling Physics-Informed ML Physics-Informed GNNs Spatiotemporal GNNs Computational Fluid Dynamics

May 4, 2026cs.RO

Learning Equivariant Neural-Augmented Object Dynamics From Few Interactions

Learning data-efficient object dynamics models for robotic manipulation remains challenging, especially for deformable objects. A popular approach is to model objects as sets of 3D particles and learn their motion using graph neural networks. In practice, this is not enough to maintain physical feasibility over long horizons and may require large amounts of interaction data to learn. We introduce PIEGraph, a novel approach to combining analytical physics and data-driven models to capture object dynamics for both rigid and deformable bodies using limited real-world interaction data. PIEGraph consists of two components: (1) a \textbf{P}hysically \textbf{I}nformed particle-based analytical model (implemented as a spring--mass system) to enforce physically feasible motion, and (2) an \textbf{E}quivariant \textbf{Graph} Neural Network with a novel action representation that exploits symmetries in particle interactions to guide the analytical model. We evaluate PIEGraph in simulation and on robot hardware for reorientation and repositioning tasks with ropes, cloth, stuffed animals and rigid objects. We show that our method enables accurate dynamics prediction and reliable downstream robotic manipulation planning, which outperforms state of the art baselines.

Sergio Orozco, Tushar Kusnur, Brandon May +2

Brown University, Providence, RI · Robotics and AI (RAI) Institute, Cambridge, MA · General Motors

Deformable Object Manipulation Robotic Manipulation Equivariant GNNs Physics-Informed ML Physics-Informed GNNs Deformable Object Simulation

Apr 26, 2026cs.LG

Hamiltonian Graph Inference Networks: Joint structure discovery and dynamics prediction for lattice Hamiltonian systems from trajectory data

Lattice Hamiltonian systems underpin models across condensed matter, nonlinear optics, and biophysics, yet learning their dynamics from data is obstructed by two unknowns: the interaction topology and whether node dynamics are homogeneous. Existing graph-based approaches either assume the graph is given or, as in

α

-separable graph Hamiltonian network, infer it only for separable Hamiltonians with homogeneous node dynamics. We introduce the Hamiltonian Graph Inference Network (HGIN), which jointly recovers the interaction graph and predicts long-time trajectories from state data alone, for both separable and non-separable Hamiltonians and under heterogeneous node dynamics. HGIN couples a structure-learning module -- a learnable weighted adjacency matrix trained under a Hamilton's-equations loss -- with a trajectory-prediction module that partitions edges into physically distinct subgraphs via

k

-means clustering, assigning each subgraph its own encoder and thereby breaking the parameter-sharing bottleneck of conventional GNNs. On three benchmarks -- a Klein--Gordon lattice with long-range interactions and two discrete nonlinear Schrödinger lattices (homogeneous and heterogeneous) -- HGIN reduces long-time energy prediction error and trajectory prediction error by six to thirteen orders of magnitude relative to baselines. A symmetry argument on the Hamiltonian loss further shows that the learned weights encode the parity of the underlying pair potential, yielding an interpretable readout of the system's interaction structure.

Ru Geng, Panayotis Kevrekidis, Yixian Gao +2

School of Mathematics and Statistics, Changchun University, Changchun, 130022, China · Department of Mathematics and Statistics, University of Massachusetts, Amherst, 01003, MA, USA · Department of Physics, University of Massachusetts, Amherst, 01003, MA, USA +2

Dynamical Systems Graph Structure Learning Graph Neural Networks Graph Representation Learning System Identification Physics-Informed ML+2

Apr 17, 2026cs.LG

Zero-Shot Scalable Resilience in UAV Swarms: A Decentralized Imitation Learning Framework with Physics-Informed Graph Interactions

Large-scale Unmanned Aerial Vehicle (UAV) failures can split an unmanned aerial vehicle swarm network into disconnected sub-networks, making decentralized recovery both urgent and difficult. Centralized recovery methods depend on global topology information and become communication-heavy after severe fragmentation. Decentralized heuristics and multi-agent reinforcement learning methods are easier to deploy, but their performance often degrades when the swarm scale and damage severity vary. We present Physics-informed Graph Adversarial Imitation Learning algorithm (PhyGAIL) that adopts centralized training with decentralized execution. PhyGAIL builds bounded local interaction graphs from heterogeneous observations, and uses physics-informed graph neural network to encode directional local interactions as gated message passing with explicit attraction and repulsion. This gives the policy a physically grounded coordination bias while keeping local observations scale-invariant. It also uses scenario-adaptive imitation learning to improve training under fragmented topologies and variable-length recovery episodes. Our analysis establishes bounded local graph amplification, bounded interaction dynamics, and controlled variance of the terminal success signal. A policy trained on 20-UAV swarms transfers directly to swarms of up to 500 UAVs without fine-tuning, and achieves better performance across reconnection reliability, recovery speed, motion safety, and runtime efficiency than representative baselines.

Huan Lin, Lianghui Ding

Institute of Image Communication and Network Engineering, School of Integrated Circuits, Shanghai Jiao Tong University, Shanghai 200240, China

Multi-Robot Systems Swarm Robotics Adversarial Imitation Learning Imitation Learning Multi-Robot Coordination Physics-Informed ML+2

Apr 16, 2026cs.LG

G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes

Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network. However, pixel-based convolutions are restricted to static, uniform Cartesian grids, making them ill-suited to following evolving localized structures in an efficient manner. Graph neural networks (GNNs) naturally handle irregular spatial discretizations, but existing graph-based physics-aware deep learning (PADL) methods have difficulty handling extreme nonlinear regimes. To address these limitations, we propose Graph PARC (G-PARC), which uses moving least squares (MLS) kernels to approximate spatial derivatives on unstructured graphs, and embeds the derivatives of governing partial differential equations into the network's computational graph. G-PARC achieves better accuracy with 2-3x fewer parameters than MeshGraphNet, MeshGraphKAN, and GraphSAGE, replacing the traditional encoder-processor-decoder framework with analytically computed differential operators. We demonstrate that G-PARC (1) generalizes across nonuniform spatial and temporal discretizations; (2) handles moving meshes required for structural deformation; and (3) outperforms existing graph-based PADL methods on nonlinear benchmarks including fluvial hydrology, planar shock waves, and elastoplastic dynamics. By embedding explicit physical operators within the flexibility of GNNs, G-PARC enables accurate modeling of extreme nonlinear phenomena on complex computational domains, moving PADLbeyond idealized Cartesian grids.

Jack T. Beerman, Tyler J. Abele, Mehdi Taghizadeh +6

School of Data Science, University of Virginia, Charlottesville, VA 22903, United States · Department of Engineering Systems and Environment, University of Virginia, Charlottesville, VA 22903, United States · Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22903, United States +1

Neural PDE Solvers PDE Surrogate Modeling Physics-Informed ML Physics-Informed GNNs Spatiotemporal GNNs

Sep 26, 2025cs.LG

Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator

Physics-informed graph neural networks (PIGNNs) have emerged as fast AC power-flow solvers that can replace the classic NewtonRaphson (NR) solvers, especially when thousands of scenarios must be evaluated. However, current PIGNNs still need accuracy improvements at parity speed; in particular, the soft constraint on the physics loss is inoperative at inference, which can deter operational adoption. We address this with PIGNN-Attn-LS, combining an edge-aware attention mechanism that explicitly encodes line physics via per-edge biases to form a fully differentiable knownoperator layer inside the computation graph, with a backtracking line-search-based globalized correction operator that restores an operative decrease criterion at inference. Training and testing use a realistic High-/Medium-Voltage scenario generator, with NR used only to construct reference states. On held-out HV cases consisting of 4-32-bus grids, PIGNN-Attn-LS achieves a test RMSE of 0.00033 p.u. in voltage and 0.08 deg in angle, outperforming the PIGNN-MLP baseline by 99.5% and 87.1%, respectively. With streaming micro-batches, it delivers 2-5x faster batched inference than NR on 4-1024-bus grids.

Changhun Kim, Timon Conrad, Redwanul Karim +6

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Institute of Electrical Energy Systems, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Efficient Neural Network Inference Graph Attention Networks Physics-Informed ML Physics-Informed GNNs Power Systems