Physics-Informed ML

ML: Machine Learning

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60 papers in the last four weeks, up 131% on the four weeks before. 0.6% of all new papers.

Jul 13Week of Sep 28

Latest papers 561

Oct 8, 2026hep-ph

Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery

Machine learning (ML) in high-energy nuclear physics (HENP) is entering a new stage in which physical knowledge is incorporated more directly into data analysis, simulation, and physics inference. This mini-review focuses on developments that have matured in the past several years. Whereas earlier applications emphasized event classification, pattern recognition, and surrogate models for selected observables, recent work has moved toward physics-integrated workflows: calibrated Bayesian extraction of QCD matter properties, dense-matter equation-of-state inference from heavy-ion and neutron-star data, generative event modeling, neural unfolding of weak physical signals, differentiable inverse solvers, gauge-equivariant and diffusion-based lattice-field samplers, and neural reconstruction of model functions in holographic QCD. We survey recent applications of ML in heavy-ion collisions, neutron-star physics, lattice QFT, and holographic or continuum QCD. The emphasis is not on ML architectures alone, but on how they enter concrete physics workflows, how physical constraints such as symmetries, conservation laws, causality, thermodynamic stability, and topology are imposed, and how uncertainty quantification and validation determine whether an AI-assisted result can support a reliable physics conclusion.

Xun Chen, Weiyao Ke, Yu-Gang Ma +2

School of Nuclear Science and Technology, University of South China, Hengyang 421001, China · INFN — Istituto Nazionale di Fisica Nucleare — Sezione di Bari, Via Orabona 4, 70125 Bari, Italy · Key Laboratory of Quark and Lepton Physics (MOE) & Institute of Particle Physics, Central China Normal University, Wuhan, Hubei 430079, China +6

High-Energy Physics Physics-Informed ML Scientific ML Physics-Informed Generative Modeling

Oct 8, 2026physics.comp-ph

Ghost tasking for parametrized Gaussian Processes solving linear differential equations

Physics-informed machine learning has gained significant attention in recent years. In regimes of limited data, parametrized Gaussian processes have become popular. Existing approaches, however, often face limitations, such as requiring parametrizable (also called controllable) systems or a large number of output tasks. In this work, we introduce a systematic procedure we call "ghost tasking", using auxiliary tasks to circumvent these limitations. We prove that such ghost tasks can render any non-parametrizable system effectively parametrizable, enabling algorithmic construction of parametrized Gaussian Processes while keeping the number of required tasks (i.e. output dimensions) and latent functions low. We find that ghost tasking performs especially well in an inverse problem setting, even with very few available data. We show the usage and power of ghost tasking in three experiments, providing systematic comparisons to the only other currently available method applicable to all experiments. We provide necessary syntax and explications for two computer algebra programs that compute parametrizations for systems with polynomial or rational coefficients. Our theoretical results extend to systems with meromorphic functions.

Johanna Moser, Christopher Albert, Sascha Ranftl

Gaussian Processes Physics-Informed ML

Oct 8, 2026cs.LG

Uncovering and Fixing Collider Bias in Bayesian PINNs

Bayesian physics-informed neural networks (B-PINNs) are a popular framework for parameter and state inference from sparse or noisy observations. They are commonly formulated via a collider structure, in which physical and trajectory parameters are assumed to be a priori independent and become coupled through virtual likelihoods on differential-equation residuals that enforce physical consistency. We show that this modeling choice can induce severe systematic bias in the posterior over physical parameters: even when the prior is favorably centered on the ground-truth parameters, the resulting posterior can drift away and concentrate far from them. As a remedy, we advocate a hierarchical chain model in which physics generates trajectories, which in turn generate observations. The chain model does not suffer from this posterior bias, but it poses a harder, so-called doubly intractable, inference problem due to a physics-dependent normalization constant. This challenge can be resolved by discretizing the underlying stochastic dynamics, after which the chain posterior can be sampled exactly with particle MCMC. We identify two distinct mechanisms characterizing the collider bias, derive analytical approximations of their magnitudes, and establish diagnostic criteria for predicting when standard B-PINNs remain reliable. Experiments confirm the predicted bias and show that the chain formulation successfully avoids it.

Michael Obermayr, Robert Peharz

TU Graz

Physics-Informed ML Bayesian Inverse Problems Hierarchical Bayesian Modeling

Oct 8, 2026cs.LG

Cova-PINN: Cross-Domain Conservation Physics-Informed Neural Network for Fluid-Solid Conjugate Heat Transfer in Complex Geometries

Multi-domain physics-informed neural networks (PINNs) flexibly model medium-specific representations to solve fluid--solid conjugate heat transfer (CHT). However, standard multi-domain PINNs enforce governing equations and interface conditions on separately sampled domain supports, which can yield plausible temperature fields but inaccurate end-to-end energy transfer and outlet temperatures. We propose Cova-PINN, a multi-domain PINN framework that aligns conservation support with thermal interaction paths in complex geometries. Cova-PINN jointly optimizes cross-domain composite control-volume balances at the local scale and paired-wall closure at the global exchanger scale. We evaluate Cova-PINN on four triply periodic minimal surface (TPMS) heat exchangers and a geometrically distinct DualMS design against CHT-specific, optimization-oriented, and complex-geometry PINN baselines under a common protocol. Relative to the closest baseline, MUSA-PINN-CHT, Cova-PINN reduces average outlet-temperature and device-level closure errors across the four TPMS topologies by

37.7\%

and

60.2\%

, respectively, while also improving full-field and heat-duty accuracy, with consistent gains on DualMS.

Weizheng Zhang, Xunjie Xie, Hao Pan +1

Shandong University · Tsinghua University

Physics-Informed ML Neural PDE Solvers Computational Fluid Dynamics

Oct 7, 2026cs.LG

Gen-PINNs: Generative Adversarial Physics Informed Neural Networks for solving partial differential equations

Physics-Informed Neural Networks (PINNs) are a widely used data-free method for solving Partial Differential Equations (PDEs) using machine learning. With recent advances in Generative Adversarial Networks (GANs), adversarial learning has shown strong capabilities for modeling complex data-driven problems; however, the use of GANs in deterministic physics-informed PDE solutions remains limited. In this work, we first identify limitations of standard PINNs for solving PDEs, including spectral bias, loss imbalance, and optimizer stagnation. We then propose Generative Adversarial Physics-Informed Neural Networks (Gen-PINNs), a unified deterministic residual-adversarial framework designed to improve data-free solutions of PDEs with sharp or shock-front behavior. The generator learns the underlying PDE solution using dynamically weighted physics-informed loss components, while separate discriminators evaluate complementary PDE residual features against ideal zero-residual states. The framework further develops and adapts several methodological components, including a Fourier representation for resolving high-frequency spatial content, an orthonormal spectral diagnostic for quantifying frequency-dependent solution errors, and a modified gradient-based dynamic weighting system for physics, initial-condition, boundary-condition, and adversarial loss objectives. Gen-PINNs is tested against standard PINNs on nonlinear and higher-order PDEs, including the Burgers, Allen-Cahn, and Kuramoto-Sivashinsky equations. The results demonstrate substantial improvements in accuracy and convergence across sharp-front, stiff, and higher-order PDE solutions, highlighting the potential of deterministic residual-adversarial learning as an effective approach for solving challenging nonlinear PDEs.

Muhammad M. Akmal, Kamy Sepehrnoori, Michael J. Pyrcz

Hilderbrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin · Department of Earth and Planetary Sciences, The University of Texas at Austin

PDE Solving Physics-Informed ML Generative Adversarial Networks Adaptive Loss Weighting

Oct 7, 2026cs.LG

Physics-Aligned Electronic Ground-State Learning Improves Generalization

Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the cost-accuracy Pareto frontier by designing observable-agnostic electronic ground-state descriptor models (GSMs) with computational costs situated between MLIPs and Kohn-Sham density functional theory (KS-DFT). We align the learning objectives and architectures of GSMs with the governing equations of KS-DFT by enforcing physical constraints and removing optimization pressure on unphysical or irrelevant degrees of freedom. In our size-extrapolation experiments from QM9 to QM40, our combined contributions OrthoNormal-Loss (ON-Loss) and Grassmann Restricted Occupied-Orbital Training (GROOT) reach a 79.1% energy and 83.4% force mean absolute error (MAE) reduction over previous state-of-the-art density GSMs. For Hamiltonian GSMs, ON-Loss and Residual Optimal-gauge Conditioning-aware KS-Eq. Training (ROCKET) together reduce the energy and force MAEs of the strongest baseline by 99.8% and 95.9%, respectively. Using a self-consistency rejection criterion, we filter out extrapolation errors on QMugs, rejecting fewer than 0.4% of predictions while reaching an energy MAE of 0.07 mHa. Finally, we demonstrate the efficiency of label-free self-consistency fine-tuning, and transfer GSMs to reactive chemistry in Transition1x, reaching energy errors below chemical accuracy.

Eike S. Eberhard, Xaver Kainz, Viktor Kotsev +2

Technical University of Munich (TUM) · Munich Data Science Institute (MDSI) · Munich Center for Machine Learning (MCML) +1

Physics-Informed ML OOD Generalization Quantum Chemistry Computational Materials Science Molecular Property Prediction

Oct 7, 2026cs.LG

ProtocolMatch: Protocol-Dependent Model Selection for Scientific Dynamics Forecasting

Scientific dynamics forecasting is often framed as an architecture choice, although deployment is also determined by observed history, rollout feedback, compute budget, physical objective, and test distribution. We formulate protocol-dependent model selection and introduce ProtocolMatch, a compute-matched, validation-selected, and failure-preserving evaluation framework. On driven quantum-spin dynamics, we compare recurrent, patched-attention, causal-attention, and low-rank linear predictors across three independently generated datasets. The causal-attention--recurrence ordering reverses as the training set grows within a fixed two-spin task, while a linear predictor has the lowest mean error in the six-spin local-observable comparison. Restricting observed history worsens every refreshed-history view but improves every closed-loop view in the four-spin study. A latest-state MLP has lower error than persistence on every dataset under state refresh across all five cells, yet its closed-loop rank varies by system and includes finite explosive errors. Physical penalties improve targeted consistency without reliably improving prediction error, and in-distribution intervals lose most coverage after a driving-frequency shift. Thus scientific model selection should return a predictor with its protocol and report accuracy, physical validity, and shifted-distribution reliability separately.

Lu Wei, Yufeng Wang, Haibin Ling

Stony Brook University · Westlake University

Model Selection Physics-Informed ML Distribution Shift Robustness

Oct 7, 2026cs.LG

Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves

Physics-informed neural PDE solvers adapt their parameters to satisfy governing equations, yet their representational structure typically remains fixed throughout training. This rigidity is poorly matched to PDE solutions with strongly heterogeneous complexity across space and space--time, leaving capacity insufficient where the physics is difficult and redundant where it is simple. We introduce physics-informed neural plasticity, a paradigm in which the representation itself reshapes during optimization in response to unresolved physics. We instantiate this principle with Representation Capacity Adaptation for PDEs (ReCAP), a Gaussian-localized solver that dynamically redistributes capacity through local enrichment, residual-directed splitting, gate-based pruning, and function-aware merging. ReCAP uses responsibility-weighted error indicators and the geometry of residual energy to determine where and how to refine. To limit the disturbance introduced by splitting, we introduce quiet-child refinement, which initializes new components by transporting the parent representation while controlling instantaneous functional perturbation. We further establish conditional a posteriori reliability and structural-stability guarantees linking localized physics residuals to solution error and stable refinement. Across five challenging 3D and 4D PDE benchmarks against 11 physics-informed solvers, ReCAP achieves the lowest relative

L^2

error on every problem, reducing error by

10.7\%

--

27.5\%

relative to the strongest competing result. These results suggest that physics-informed solvers need not merely learn their parameters---they can learn how their representational capacity should be organized.

Chun-Wun Cheng, Bingcheng Hu, Angelica I. Aviles-Rivero

Shanghai Normal University · YMSC, Tsinghua University

Neural PDE Solvers PDE Solving Physics-Informed ML Dynamic Neural Networks

Oct 6, 2026cs.LG

Domain-informed Adaptive Sampling for Generalizable PINNs in Metal Additive Manufacturing via Conditional Flow Matching

Accurate thermal modeling is essential in metal additive manufacturing (AM) for understanding the process-structure-property chain. Physics-informed neural networks (PINNs) offer effective surrogate thermal modeling by minimizing physics-based residual losses at collocation points. However, prior works typically rely on manually-crafted, static collocation sampling strategies, which are neither principled nor scalable across process conditions, hindering their generalization capability. In this work, we provide theoretical analysis through empirical risk minimization, showing that process condition-aware adaptive sampling is strictly more favorable than conventional static sampling for generalization. Building on this insight, we propose an adaptive sampling strategy within a two-stage framework: (1) a conditional Flow Matching model that learns approximate high-residual distributions across different process conditions, and (2) a mixed sampling strategy combining this distribution with a domain-informed base distribution to generate adaptive collocation points for refining the PINN predictor. Experiments on metal AM numerical benchmarks demonstrate that our method consistently outperforms state-of-the-art PINN baselines, achieving an average 62.1% reduction in relative

L_2

error under an identical collocation budget, by capturing process-dependent heat dissipation regions often overlooked in the literature. To the authors' knowledge, this is the first adaptive sampling strategy for PINNs in metal AM, contributing to the enhanced generalization and broader applicability.

Hyeonsu Lee, Jihoon Jeong

Wm Michael Barnes ’64 Department of Industrial and Systems Engineering Texas A&M University College Station, TX 77843, USA

Adaptive Sampling Physics-Informed ML PDE Surrogate Modeling Additive Manufacturing

Oct 5, 2026cs.LG

A Physics-Guided Transformer Framework for Electromigration Analysis in Multi-Segment Interconnects

As technology scales to smaller nodes, increasing current densities make electromigration (EM) one of the dominant reliability challenges in on-chip interconnects. Accurate transient stress analysis is needed to identify wires susceptible to EM degradation, but applying physics-based solvers across many interconnects remains computationally expensive. This paper proposes a physics-guided transformer framework for fast EM stress prediction in multi-segment interconnect lines. The framework converts each line into geometry- and DC-aware segment tokens and uses transformer attention to capture line-level context. A lightweight query decoder then predicts stress at selected locations and time instants. The model is trained with an objective that combines normalized supervised regression, linewise relative-

L_2

loss, and physics-guided continuity and terminal-flux terms. Experiments on IBM power grid benchmarks show that the proposed model achieves relative-

L_2

error below 8% and reaches up to 2459.68

\times

speedup compared with the matrix exponential~solver.

Pavlos Stoikos, Anuj Pathania, George Floros

Dept. of Electrical and Computer Engineering University of Thessaly, Greece · University of Amsterdam Amsterdam, The Netherlands · Dept. of Electronic and Electrical Engineering, Trinity College Dublin, Ireland

Neural Surrogate Modeling Transformer Physics-Informed ML

Oct 5, 2026math.NA

IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs

Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accurate and typically trained by non-convex optimization without error control. We propose IGA-KAN, which uses local Kolmogorov-Arnold networks, fitted in closed form, to improve the IGA solution instead of replacing it. An IGA Galerkin solve produces u_h; on every knot-vertex patch a Kolmogorov-Arnold ridge model is fitted to the strong form of the equation, the exact boundary data and u_h, and the models are blended by IGA hat functions. With fixed inner functions the fit is one batched linear least-squares problem, without optimizer, learning rate or initialization. An a posteriori safeguard, motivated by a maximum-principle bound, decides where local models are used, keeping the IGA solution elsewhere. On eight benchmarks with exact solutions, five from the literature and one also posed on a domain fitted to a brain slice from MRI, the method reduces the error of IGA, at an unchanged number of Galerkin unknowns, by factors of 4.2 to 90 in L^2 and 4.1 to 220 in H^1 on the reference meshes, and its L^2 error is 6 to 6x10^4 times smaller than that of the best Kolmogorov-Arnold network trained from scratch on the same equations with a fixed budget. In an inverse problem it recovers an unknown constant source from one noise-free observation 167 times more accurately than IGA. The gain is attributed to the superconvergence of local averages of the Galerkin solution.

Sima Naraghi, Kourosh Parand, Amirhossein Sadr +1

Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran · Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran · Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran +1

Neural PDE Solvers Kolmogorov-Arnold Networks Physics-Informed ML PDE Inverse Problems

Oct 5, 2026cs.LG

OCL-PDE: A Generative Framework for PDE Inverse Problems with Observation-Complementary Latents

Partial differential equation (PDE) inverse problems are often ill-posed, making fine-scale details difficult to recover. We address this problem by introducing a learned observation-complementary latent representation that preserves reconstruction-relevant information and is combined with the observation to reconstruct the unknown field. Building on this representation, we propose OCL-PDE, a generative framework that encourages the observation to guide large-scale structure and the latent to supply complementary fine-scale details. OCL-PDE is built on a physics-aware autoencoder (AE) and conditional Flow Matching, supporting inverse reconstruction as well as forward PDE prediction. Experiments demonstrate improved reconstruction accuracy and fine-detail recovery compared with the evaluated baselines.

Ding Yang, Chuqi Chen, Chang Ma +1

Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong · Department of Mathematics, University of Michigan, Ann Arbor, USA · Department of Materials, The Hong Kong University of Science and Technology, Hong Kong +1

Physics-Informed Generative Modeling PDE Operator Learning Physics-Informed ML PDE Inverse Problems

Oct 5, 2026cs.LG

Parameter Estimation in Machining Dynamics with Regenerative Delay and Nonsmooth Friction using Physics-Informed Neural Networks

A multi-domain eXtended Physics-Informed Neural Network (XPINN) framework is developed for nonsmooth Delay Differential Equations (DDEs). This is the first implementation to demonstrate the efficacy of partitioning the temporal domain into subdomains of integer multiples of the characteristic time delay and progressively training the associated subnetworks while freezing previously learned parameters. The efficacy of the proposed framework is demonstrated using a machining dynamics model that incorporates both regenerative and nonsmooth frictional effects. Results demonstrate that the proposed multi-domain XPINN framework leads to better solution reconstruction in DDEs and improved parameter estimation compared to a generic PINN (SPINN) formulation. The proposed method works particularly well for extended temporal domains and non-constant history functions. The robustness of inverse XPINN (I-XPINN) is also assessed using reference data contaminated with Gaussian measurement noise. Results indicate that I-XPINN remains resilient to measurement noise and the physics-informed constraints guide the network toward accurately recovering the underlying dynamics. This demonstrates, for the first time, the potential of the proposed framework for reliable parameter identification in DDEs characterised by nonsmoothness and large time delays.

Meiyazhagan Jaganathan, Vikram Pakrashi, Aasifa Rounak

UCD Centre for Mechanics, Dynamical Systems and Risk Laboratory, School of Mechanical and Materials Engineering, University College Dublin, D04 V1W8, Dublin, Ireland

Dynamical Systems Parameter Estimation Physics-Informed ML

Oct 4, 2026cs.AI

R1A-PC: Physics-Guided Electromagnetic Inversion of Three-Dimensional Human Point Clouds in Complex Static Environments

Recovering three-dimensional human geometry from electromagnetic measure?ments in a complex static environment is difficult because strong multipath responses from walls, floors, and other objects obscure the weak target per?turbation. We propose R1A-PC, a physics-guided method that reconstructs a 2048-point human cloud from paired complex fields measured with and without the target. Complex background subtraction emphasizes target-induced ampli?tude and phase changes, while the background field remains available as an environmental condition. A frequency-balanced discrete Born adjoint produces a three-dimensional spatial knowledge map. At each of two bounded deformation stages, the decoder combines complex measurement features, background fea?tures, and multiscale physical features queried at the current point coordinates; the second stage queries again after the first coordinate update. We analyze the residual of paired subtraction, the weighted normal-operator structure of the raw adjoint, and the feasible set of the predicted cloud. In a held-out background generated by full-wave simulation under a fixed acquisition geometry, R1A-PC obtains a squared Chamfer distance of 0.001434 m2 and an F-score of 0.963080 at 0.05 m. Compared with TopNet, the Chamfer distance decreases by 70.28%. Removing physical guidance or background subtraction increases the Chamfer distance by 242.06% or 241.18%, respectively. Experiments across background layouts and poses support the complementary roles of paired subtraction and position-dependent adjoint features.

Xudong Yuan, Ruyun Xu, Jingtai Yang +1

School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun, China.

3D Reconstruction Point Cloud Surface Reconstruction 3D Human Reconstruction Physics-Informed ML Inverse Problems

Oct 4, 2026cs.LG

Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation

Physics-informed neural network (PINN) training minimizes a weighted combination of partial differential equation (PDE), boundary-condition, and initial-condition losses. Because adaptive methods modify these weights during training, their weighted total losses are not always directly comparable. We compare fixed-weight PINN, gradient-normalized PINN (GNPINN), and a rule-based adaptive controller (AgenticPINN) under matched settings on a heat-equation benchmark and a simplified Czochralski-oriented thermal-fluid problem. In the crystal-growth MLP experiment, adaptive control reduced the PDE residual from the order of

10^{-5}

to

10^{-6}

, while the boundary-condition loss increased from the order of

10^{-5}

to

10^{-2}

. On the heat-equation benchmark, GNPINN achieved the lowest relative

L_2

field error (0.054), whereas AgenticPINN obtained the smallest PDE residual but a relative

L_2

error of 1.368. Gaussian-process surrogates were additionally evaluated using case-wise holdout tests on corrected Czochralski CFD parameter sweeps. The temperature-field error for the temperature sweep was approximately 6%, whereas the axial-velocity error for the crystal-rotation sweep was approximately 42%. These findings show that adaptive control can improve equation satisfaction while weakening other physical constraints. PINN training should therefore be evaluated using separate PDE, boundary-condition, and solution-error metrics rather than weighted total loss alone.

Niruta Chapagain, Rohit Raj, Bertwin Kurisinkal Shine +1

University of Europe for Applied Sciences Potsdam, Germany · Vienna, Austria · Technische Universität Chemnitz Chemnitz, Germany +1

Neural PDE Solvers PDE Surrogate Modeling Adaptive Loss Weighting Physics-Informed ML

Oct 1, 2026cs.AI

Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering

The rapid maturation of artificial intelligence (AI) and machine learning (ML) has catalyzed a profound shift in how chemical engineering problems are formulated, analyzed, and solved. Advances in computing, data availability, and learning algorithms have enabled AI/ML methods to impact applications spanning atomic-scale simulations, materials and catalyst discovery, transport and thermodynamics, separations, process systems engineering, and industrial operations. This article provides a perspective on recent methodological developments and representative applications, emphasizing how AI/ML tools are being integrated with first-principles models to address challenges of predictive accuracy, data scarcity, extrapolation, interpretability, and model lifecycle management. Across domains, a unifying trend is the move away from purely black-box approaches toward hybrid and physics-informed frameworks that explicitly respect conservation laws, thermodynamic consistency, and known structural constraints. These approaches not only improve robustness and reliability, but also enable meaningful human-AI collaboration by providing information at an appropriate level of abstraction for the task and decision context. We conclude that AI and ML are not replacing the core principles of chemical engineering; rather, they are amplifying them. As the field advances toward increasingly autonomous, adaptive, and sustainable systems, the thoughtful integration of AI/ML with first-principles understanding and domain expertise will be essential to realizing their full potential across both research and industrial practice.

Michael Baldea, Linda J. Broadbelt, Marianthi G. Ierapetritou +17

McKetta Department of Chemical Engineering and Oden Institute for Chemical Engineering and Sciences, The University of Texas at Austin, Austin, TX 78731, USA · Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA · Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE 19716, USA +13

Scientific ML Physics-Informed ML

Oct 1, 2026cs.CV

PhysDEM: Physics-Defined Energy-Matching Diffusion for Spatiotemporal Field Generation under Scarce Measurements

Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a distribution over complete fields. This limits conventional data-driven diffusion models that rely on full-field datasets. We introduce PhysDEM, a physics-defined diffusion framework that combines governing equations with spatially sparse observations to generate multiple plausible fields. First, we construct a Gibbs target by reweighting a measurement-conditioned Gaussian reference with PDE residual energy. Second, we derive an exact conditional-mean identity that reduces denoising to supervised learning of the standardized energy-induced mean correction. Third, a physics-displacement probability flow cancels Gaussian reference terms and enables amortized sampling with changing measurements through Gaussian conditioning, without retraining. Experiments on synthetic PDE systems and real-world-informed applications demonstrate that PhysDEM supports coherent field recovery and efficient sampling while maintaining stable diagnostics under tested noise levels, illustrating its practical value for field assessment. To our knowledge, PhysDEM is the first physics-defined diffusion model enabling amortized spatiotemporal field inference without preassembled full-field datasets.

Zhenyu Liang, Yining Huang, Yubo Zhao +1

HKUST · UT Austin

Physics-Informed Diffusion Models Physics-Informed Generative Modeling Diffusion Model Sampling Physics-Informed ML Diffusion-Based Inverse Problems PDE Inverse Problems

Sep 30, 2026cs.CV

PACT: End-to-End Learning of Human Pose, Contacts, and Forces from Video

Human motion, environmental contacts, and interaction forces are governed by common physical laws, yet existing approaches typically separate visual pose reconstruction from contact and force estimation. This separation limits joint reasoning and can propagate errors between stages. We introduce PACT, an end-to-end model that jointly learns to estimate human pose, contacts and contact forces from monocular video. Our approach augments a human reconstruction foundation model with learnable contact-force tokens and a temporal transformer that integrates visual features with world-space motion. Joint prediction heads refine human poses and estimate contacts and forces, while physics-based supervision encourages consistency between the reconstructed motion and interaction forces. To address the scarcity of force annotations, we develop a data annotation pipeline that combines contact labeling with physics-based motion and force optimization, producing training supervision from synthetic and real-world videos. We also introduce a real-world climbing benchmark ForceWall with climbing videos and corresponding ground-truth contact forces obtained from the force sensors. Experiments demonstrate state-of-the-art contact and force estimation, outperforming staged reconstruction approaches and generalizing to interactions beyond the training distribution. These results support end-to-end joint learning as an effective approach to recovering human motion and physical interactions from video.

Rikhat Akizhanov, Yangsong Zhang, Nikolai Kaliazin +5

MBZUAI · ETH Zürich · EPFL

Human Pose Estimation 3D Human Reconstruction Physics-Informed ML Human-Object Interaction

Sep 30, 2026hep-ph

PINNing the pion: conformal deep learning for $F_π(s)$ and the $(g-2)_μ$ hadronic contribution

Extracting the pion electromagnetic form factor

F_π(s)

through phenomenological curve-fitting models introduces model dependence, unphysical artefacts, and kinematic inconsistencies. We introduce a Physics-Informed Neural Network (PINN) embedded in a conformal

z

-plane that constructs

F_π(s)

directly from first principles across spacelike and timelike domains: charge normalisation and Schwarz reflection are enforced by construction, while Cauchy-Riemann analyticity, dispersion relations, Watson's theorem, and perturbative QCD asymptotics enter through the loss functional. Thus, the fundamental S-matrix principles dictate the form factor's behaviour while data act as constraints. Mapping the cut complex plane onto the unit disk bounds the Hessian norm and prevents Neural Tangent Kernel spectral starvation, two known failure modes of deep-learning optimisation. Besides

e^+e^-

scattering data, we also incorporate

τ

-decay data through a switch that isolates the pure isovector form factor natively, bypassing model-dependent isospin-breaking pre-corrections. The network organically yields an interior zero-free form factor, while the framework tests experimental tensions around the

ρ(770)

peak against analyticity and dispersion constraints. We obtain model-independent estimates of the pion charge radius,

\langle r_π^2 \rangle = 0.435 \pm 0.008_{\text{stat}} \pm 0.007_{\text{cali}}

fm

^2

, the second-sheet pole parameters,

m_ρ^{\text{pole}} = 761.72\pm 1.04

MeV and

Γ_ρ^{\text{pole}} = 135.99 \pm 1.20

MeV, and the two-pion contribution to the muon anomalous magnetic moment,

a_μ^{ππ} = (506.48 \pm 2.02_{\text{stat}} \pm 1.70_{\text{cali}}) \times 10^{-10}

.

Mayank Goel, Subhadip Mitra, Monalisa Patra

Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India

High-Energy Physics Physics-Informed ML

Sep 30, 2026cs.LG

Physics-Informed Method of Group Data Handling: Adaptive Construction of Functional Representations with an Application to the Navier-Stokes Equations

Physics-informed computational methods usually optimize parameters within a functional representation whose structure is fixed in advance. This work proposes a Physics-Informed Method of Group Data Handling (PI-GMDH), in which representations of coupled physical fields are progressively constructed during solution. Candidate functional directions are evaluated through the first variation of the complete physical and observational objective, introduced in packages, and followed by block-coordinate damped Gauss-Newton coefficient optimization. The framework is demonstrated with tensor-product Chebyshev functions on the incompressible Navier-Stokes equations using a two-dimensional time-dependent Taylor-Green benchmark. Under the tested configuration, adaptive PI-GMDH reached validation and held-out test losses of 5.299e-19 and 5.296e-19 with 204, 201, and 175 active functions for u, v, and p. Complete degree-by-degree and all-terms PI-GMDH variants, together with selected PINN and KAN reference configurations, are used to examine the effect of structural construction policy. The results show that, for this controlled synthetic benchmark, selective progressive construction can provide a favorable combination of accuracy, representation size, and wall-clock time. The comparison is illustrative rather than a claim of universal superiority over alternative physics-informed approaches.

Mykhailo Minin

JSC KIEP, Kyiv, Ukraine

Neural PDE Solvers Physics-Informed ML Computational Fluid Dynamics

Sep 29, 2026cs.AI

PE-EK-PINN: Physics Embedding with Evolving Kernel for Scalable Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) embed governing equations into deep learning, but enforce them only through loss residuals, leaving highly oscillatory wave behavior to be discovered by optimization. As a result, methods that achieve relative

L_2

errors below

10^{-3}

on standard manufactured Helmholtz benchmarks can fail on practical radiation problems involving singular excitations, absorbing boundaries, and wave fields spanning tens of wavelengths. Architectural physics embedding addresses this limitation by factorizing the field into analytically derived oscillatory kernels and learnable envelopes. However, the kernel dictionary must be manually constructed and scales with the number of elementary units, growing exponentially with the depth of hierarchically structured systems such as antenna arrays and metasurfaces. We propose PE-EK-PINN (Physics Embedded with Evolving Kernels), which treats physics kernels as reusable learned representations rather than fixed analytical inputs. A converged subsystem field is frozen and promoted to an evolved kernel, whose transformed copies are reused to represent higher-level configurations without deriving new governing equations. The resulting hierarchy makes the peak number of active kernels independent of system size and reduces cumulative training cost from

O(N)

to

O(\log N)

. Experiments on dipole arrays, composite line-source geometries, and cross arrays demonstrate the dramatic training cost reduction, while achieving a reduced or comparable relative

L_2

error. One notable example is PE-EK-PINN solves a

256

-dipole array more than 30 times faster than direct PE-PINN.

Huiwen Zhang, Feng Ye, Chu Ma

Department of Electrical & Computer Engineering Madison, WI, 53706, USA

Neural PDE Solvers Physics-Informed ML

Sep 28, 2026math.NA

GAC-PINN: Geometry-Adaptive and Constraint-Enhanced Physics-Informed Neural Networks

For systems with steep gradients, sharp interfaces, or severe spatio-temporal coupling, Physics-informed neural networks (PINNs) suffer from spectral bias, geometric inflexibility, and boundary constraint conflicts, which undermine accuracy and convergence. To overcome these issues, we propose a geometry-adaptive and constraint-enhanced PINN (GAC-PINN). The framework comprises four components: a gradient-driven adaptive grid mapping (AGM) for diffeomorphic point concentration with Jacobian regularization, an adaptive bandwidth hard-constraint ansatz with spatially-varying boundary transition widths, a Gaussian Fourier feature mapping as a spectral preconditioner to further enhance high-wavenumber representation, and an operator-aware router that automatically selects the appropriate hard-constraint construction based on whether the governing PDE contains temporal derivatives. An AGM callback mechanism and a three-stage training strategy ensure stable coordination. Benchmarks including the viscous Burgers equation, a sharp-peaked 2D Poisson problem, and the Allen-Cahn phase-transition equation show that GAC-PINN attains relative (L^2) errors of ((1.747\pm 0.450)\times 10^{-4}), ((2.868\pm 0.947)\times 10^{-5}), and ((1.756 \pm 0.712)\times 10^{-3}), respectively, consistently outperforming the baselines. Ablation studies further reveal that AGM alone yields a substantially lower error than residual-based adaptive refinement (RAR), while RAR becomes beneficial only when combined with FFM, demonstrating a context-dependent module interaction. Convergence analysis verifies rapid error reduction and saturation with increasing resolution, establishing a practical adaptive framework for high-fidelity simulation of problems with localized sharp features in applied mechanics and computational physics.

Yanxin Zhang, Yong Zhang, Houbiao Li

University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

Neural PDE Solvers Physics-Informed ML

Sep 28, 2026physics.flu-dyn

Physics-Informed Neural Networks for Depth-Averaged Avalanche Dynamics

Accurate prediction of avalanche motion is essential for hazard assessment in mountainous terrain. This study develops and evaluates a physics-informed neural network (PINN) framework for the Savage-Hutter model of depth-averaged granular flow, progressing from 1D analytical verification to 2D experimental validation. First, three 1D problems of increasing complexity were verified against the analytical solution: height prediction with prescribed velocity, velocity prediction with prescribed height, and coupled prediction of both fields using the conservative formulation. The decoupled tests accurately reconstructed the spatio-temporal evolution of each field when the other was prescribed. The coupled formulation learned both fields without prescribed data, achieving mean height and velocity RMSEs of 0.043 and 0.079 in non-dimensional units. A hyperparameter sensitivity study evaluated the effects of network depth, width, collocation density, learning rate, and epochs. The framework was then extended to 2D and validated against laboratory experiments of a cylindrical granular pile collapsing on an inclined plane, with TITAN2D providing numerical comparisons. Purely physics-based training converged to the trivial zero solution; augmenting the loss with 10 sparse training points from final deposit profiles produced a physics-informed, data-assisted hybrid framework. Peak flow depth, depth-averaged velocity, RMSE, and wetted-area IoU evaluated global and local agreement. Global height RMSE ranged from 2.7 to 6.7 mm across four experimental cases, while mean wetted-area IoU ranged from 69 to 81 %, demonstrating consistent performance across variations in pile mass and slope angle.

Pradyumn Singh Sikarwar, Vishal Sharma, Gaurav Bhutani

School of Mechanical and Materials Engineering, Indian Institute of Technology Mandi, India

Neural PDE Solvers Physics-Informed ML

Sep 28, 2026cs.AI

PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs

Physical trajectories contain more than snapshots of a system: they also reveal how its states evolve under governing conditions. However, representation learning for parametric partial differential equations (PDEs) has largely relied on reconstruction-based objectives that emphasize recovering observed physical fields. In this paper, we investigate predictive representation pretraining as an alternative to reconstruction-based learning. We find that predictive representations preserve rich physical information, yet this advantage alone does not ensure accurate field evolution. Based on these observations, we introduce PDE-JEPA for parametric PDE dynamics. Specifically, we first train an encoder using a masked-latent prediction to capture the underlying regularities of PDE dynamics. To explicitly adapt the pretrained representation toward a more dynamics-aligned state space, we then introduce a geometry projector that aligns latent trajectory geometry with the evolution geometry of physical fields. Finally, building on this geometry-aligned latent space, we further develop a physics-structured latent predictor that decomposes the dynamics into parameter-independent evolution and parameter-dependent response components. Extensive experiments on nine widely used PDE benchmarks demonstrate that our framework outperforms existing state-of-the-art methods by an average of 33.4% in-distribution, while achieving an average improvement of 51.4% when extrapolating to unseen governing parameters. The project page is available here.

Zhentao Tan, Jianrong Zhang, Ruijie Quan +1

Zhejiang University.

Latent Dynamics Modeling Joint-Embedding Predictive Architecture PDE Surrogate Modeling Predictive Representation Learning Physics-Informed ML

Sep 27, 2026cs.LG

When Known Physics Helps Neural PDE Models: Residual Constraints Out-Regularize Generic Priors for Nonlinear Dynamics

Neural PDE surrogates increasingly incorporate structural priors, yet it is often unclear whether their gains arise from physics-specific information or simply from regularization and training choices. We evaluate several such priors under a common protocol against a matched from-scratch neural operator baseline. Our central result is that a known-equation residual consistently outperforms the best generic regularizer at equal tuning budget. At fixed capacity this benefit appears across linear and nonlinear PDEs, but a capacity sweep reveals a sharp distinction: the advantage persists and grows for Burgers, KdV, and Allen-Cahn, while collapsing toward or below parity for linear heat and advection-diffusion. Thus, the durable value of the residual is specific to nonlinear operators. We further falsify a pre-registered hypothesis that the benefit is activated only by data sparsity: the residual remains advantageous even under full supervision. Its usefulness does, however, have a clear boundary. Under grid under-resolution, nonlinear coarse fields no longer satisfy the naive governing-equation residual, and enforcing it becomes actively harmful. In contrast, cross-family pretraining and in-context conditioning fail to outperform the strong from-scratch baseline in the regime studied. Together, these results identify when known physics provides non-redundant information to neural PDE models, when it does not, and when enforcing it introduces bias.

Zahra Farazpay, Aniruddha Bora

Department of Physics Louisiana Tech University Ruston, LA, USA · Department of Computer Science Texas State University San Marcos, TX, USA

PDE Surrogate Modeling Physics-Informed ML Physics-Informed Neural Operators Neural Operators

Sep 27, 2026cs.LG

PI-NOMT: Physics-Informed Neural Optimal Mass Transport for Brain Fluid Dynamics

Recovering hidden transport mechanisms from sparse spatiotemporal observations is a fundamental inverse problem in scientific machine learning. In brain tracer imaging, dynamic contrast-enhanced MRI (DCE-MRI) provides time-resolved measurements of tracer concentration, while the underlying velocity and source mechanisms governing tracer propagation remain unobserved. We formulate this problem as physics-informed latent-state inference, in which the transport field itself is the primary object of inference rather than an auxiliary variable used only to reconstruct observed densities. We propose Physics-Informed Neural Optimal Mass Transport (PI-NOMT), a framework that represents density, velocity, and source as continuous neural fields and combines a continuous neural density teacher, recursive differentiable advection--diffusion--source rollout, unbalanced optimal-transport regularization, and governing-equation supervision. Physical laws act as structural priors that constrain the space of admissible transport mechanisms, while observed tracer dynamics provide evidence for estimating the latent transport state. We evaluate PI-NOMT on a synthetic benchmark with known ground-truth transport and on DCE-MRI sequences from nine control rats. On the synthetic benchmark, PI-NOMT accurately recovers the prescribed velocity field, including its magnitude, direction, and integrated trajectories, rather than merely reconstructing endpoint densities. Across the nine rat datasets, the framework yields sub-percent local endpoint error, consistent physical speed scales, and low post-training PDE and incompressibility residuals. These results support physics-informed latent-state inference as a general framework for recovering hidden transport mechanisms from observed dynamic scalar fields.

Mehmet Emin Acar, Vahit Bugra Yesilkaynak, Helene Benveniste +1

Istanbul Technical University, Faculty of Computer and Informatics Engineering, AI and Data Engineering Department, Istanbul, Turkiye · Yale University, School of Medicine, New Haven, CT, USA

Physics-Informed ML PDE Inverse Problems Optimal Transport

Sep 27, 2026cs.LG

From Grey-Box to Green-Box: When can Physics-Informed Machine Learning Reduce Carbon Footprints in Structural Health Monitoring?

Machine learning plays an increasingly vital role in engineering, but the corresponding increase in compute time is not without environmental cost. Physics-informed machine learning or "grey-box" models have been developed to overcome some of the limitations of traditional black-box learners, utilising the physical insight that an engineer would have about the structure they are modelling and have shown promising results in the structural engineering field among many others. This work explores whether an additional advantage could be a reduced environmental impact, considering the relationship between training data quantity and training time, linking this duration to carbon emissions from computing. In a structural health monitoring context, four physics-informed machine learning approaches - spanning Gaussian processes and neural networks - are evaluated: residual modelling, input augmentation, hybrid modelling, and constrained learning. The emissions for training each of the models to reach a given error threshold is compared, and in most examples, shown to be lower for the physics-informed models (with input augmented models being an exception). This reduction in training emissions further compounds the environmental savings achieved by collecting and storing less data. Although promising results, we cannot expect a silver bullet and the case studies demonstrate that a trade-off is needed between the increased complexity that comes from introducing physics into a machine learner, against the gain from reduced training data requirements.

Daisy R. Bradley, Nathan A. Hinchliffe, Daniel J. Pitchforth +2

Dynamics Research Group, University of Sheffield, Sheffield, UK

Energy-Efficient ML Physics-Informed ML Data-Efficient Learning Structural Health Monitoring

Sep 27, 2026cs.LG

The limits of exactness: On the failure of automatic differentiation in physics-informed machine learning

Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it the computational backbone of physics-informed machine learning. Yet exactness in the mathematical sense is not the same as fidelity to the physics. Here I argue that a derivative can be numerically perfect and still be the wrong derivative for the problem at hand, because AD, by construction, has no notion of the physical structure a solution must obey. Convection and its associated directionality, diffusion, and dispersion are only the most visible instances of a much longer list that spans all branches of computational science and engineering, including conservation, thermodynamic consistency, symmetry, symplectic structure, positivity, monotonicity, and boundedness. Recognizing this broader gap reframes how the field should build the next generation of PDE-driven neural surrogates.

Ameya D. Jagtap

Aerospace Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA

Automatic Differentiation PDE Surrogate Modeling Scientific ML Physics-Informed ML

Sep 23, 2026eess.IV

Physics-Guided Multi-Objective Deep Learning for Ultrasound RF Data Interpolation in Resource-Constrained Imaging

Ultrasound imaging increasingly targets portable, point-of-care, and wearable settings where constraints on power, bandwidth, and hardware complexity often necessitate sparse data acquisition in spatiotemporal scanning. However, image reconstruction using the sparse data can introduce insufficient phase information in coherent beamforming process, resulting in grating-lobe artifacts that degrade imaging contrast resolution. We present a physics-guided, data-driven framework for sparse-to-dense radio-frequency (RF) reconstruction that aligns training with downstream image formation. Our approach trains an end-to-end interpolation network using a hybrid supervision scheme that combines an RF-domain and a beamforming-domain loss with exponential moving average (EMA) to stabilize the multi-objective training. To improve generalization under variable acquisition layouts, we also introduce a random-skip masking strategy that varies sparsity patterns during training so a single model can handle diverse decimation factors and irregular channel configurations. We evaluate the framework on a held-out test set using the mean structural similarity index measure (SSIM) between reconstructed and ground-truth beamformed images. Across decimation factors

\times 2

to

\times 13

, the best-performing configuration maintains mean SSIM around 0.95. Overall, the results show consistent gains in RF reconstruction and post-beamforming image quality across diverse acquisition conditions. This approach enables robust, high-quality ultrasound imaging at resource-constrained settings by allowing more sparse scanning in spatiotemporal domain.

Luoyuan Zhang, Yiyang You, Ananya Tandri +4

University of North Carolina at Chapel Hill, Chapel Hill, NC, USA · Johns Hopkins University, Baltimore, MD, USA

Physics-Guided Image Restoration Image Reconstruction Ultrasound Imaging Physics-Informed ML

Sep 23, 2026cs.LG

Physics-Informed Self-Supervised Learning for Joint Wire Calibration and Interaction Position Reconstruction in Multi-Wire Parallel Plate Avalanche Counters

Scientific instruments require accurate calibration to convert detector signals into reliable physical observables. Conventional calibration procedures typically rely on dedicated calibration measurements, analytical response models or labelled reference data, limiting their ability to adapt to changing operating conditions and detector aging. We present a physics-informed self-supervised learning framework that jointly performs wire calibration and interaction position reconstruction in Multi-Wire Parallel Plate Avalanche Counters (MWPPACs) without requiring labelled position measurements or dedicated calibration runs. The method formulates detector calibration as a latent optimization problem in which global wire gains and event-wise interaction positions are estimated simultaneously using supervision derived exclusively from detector geometry and charge-energy consistency constraints. A detector-independent neural network reconstructs sub-wire interaction positions from local charge distributions, eliminating the need to assume analytical induction profiles by learning the detector response directly from experimental data. The end-to-end differentiable framework enables continuous detector self-calibration while improving the uniformity and accuracy of position reconstruction. Experimental evaluation on the entrance MWPPAC tracking detectors of the VAMOS++ magnetic spectrometer demonstrates stable convergence, improved spatial homogeneity and enhanced position resolution. Beyond the detector studied, the method establishes a general framework for physics-informed self-supervised calibration of scientific instruments and is a step toward autonomous intelligent instrumentation capable of continuous adaptation during operation. In this paradigm, detector calibration is no longer a prerequisite for an experiment but an integral part of the measurement process itself.

Antoine Lemasson, Maurycy Rejmund

GANIL, CEA/DRF - CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France.

Self-Supervised Learning Physics-Informed ML