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.

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Latest papers 561

May 19, 2026cs.LG

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models

Physics-informed neural networks (PINNs) offer a mesh-free framework for solving partial differential equations (PDEs), yet training often suffers from gradient pathologies, spectral bias, and poor convergence, especially for problems with strong nonlinearity, sharp gradients, or multiscale features. We propose the Curriculum-Guided Gaussian Mixture Physics-Informed Neural Network (CGMPINN), which integrates Gaussian mixture modeling with dynamic curriculum learning. Specifically, a GMM is periodically fitted to the PDE residual distribution to quantify spatially varying learning difficulty. A smooth curriculum schedule progressively shifts training focus from easy to harder regions, while precision-based variance modulation suppresses unreliable clusters during early optimization. This dual curriculum is governed by a shared curriculum parameter and can be combined with self-adaptive loss balancing. We further establish theoretical guarantees, including sublinear convergence of the gradient norm for the induced time-varying loss, uniform equivalence between the curriculum-weighted and standard PDE losses, and a generalization bound with an explicit weighting-induced bias characterization. Experiments on six benchmark PDEs spanning elliptic, parabolic, hyperbolic, advection-dominated, and nonlinear reaction-diffusion types show that CGMPINN consistently achieves the lowest relative

L_2

and maximum absolute errors among all compared methods, reducing relative

L_2

error by up to 97.8% over the standard PINN at comparable cost. Our code is publicly available at https://github.com/Mathematics-Yang/CGMPINN.

Jianan Yang, Yiran Wang, Shuai Li +3

Xi’an Jiaotong University, Xi’an, China · College of International Business, Zhejiang Yuexiu University, Shaoxing, China · Shaoxing Key Laboratory of Intelligent Monitoring and Prevention of Smart Society, Shaoxing, China +1

PDE Solving Curriculum Learning Physics-Informed ML

May 18, 2026cs.CE

Physics-Informed Neural Networks for Radial Consolidation of Combined Electroosmotic, Vacuum and Surcharge Preloading Considering Smear Effects

This study develops a dimensionless multi-domain physics-informed neural network (PINN) framework for electro-osmotic radial consolidation considering smear effects and combined vacuum and surcharge loading. Three PINN-based models are investigated: a standard soft-constrained PINN (Std-PINN), a modified gated PINN (Mod-PINN), and a modified gated PINN with hard-constraint boundary encoding (Mod-HC-PINN). The models are evaluated against FEM reference solutions under four loading cases, including constant vacuum, exponential vacuum, exponential vacuum with ramp surcharge, and exponential vacuum with cyclic haversine surcharge. The results indicate that the gated architecture applied in Mod-PINN improves the resolution of steep pressure gradients near the cathode and smear-zone interface under constant vacuum loading. Under time-dependent loading, the soft-constrained Mod-PINN shows reduced accuracy because it must learn multiple competing objectives simultaneously. The Mod-HC-PINN mitigates this issue by embedding the cathode boundary and initial conditions into the output structure, thereby reducing the optimization burden and improving physical consistency. The Mod-HC-PINN achieves MAE values of 0.43, 0.41, and 0.27 kPa for the exponential vacuum, ramp surcharge, and cyclic surcharge cases, respectively. Sensitivity analyses further demonstrate that the proposed framework remains robust across practical ranges of network architecture, collocation density, and permeability contrast.

Dong Li, Yapeng Cao, Shuai Huang +4

a PhD, Department of Civil, Environmental, and Infrastructure Engineering, George Mason University, Fairfax, VA 22030, USA · b PhD, State Key Laboratory of Cryospheric Science and Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China; Laboratoire Navier/CERMES, École Nationale des Ponts et Chaussées, Institut Polytechnique de Paris, 77455 Marne-la-Vallée cedex 2, France · c PhD, State Key Laboratory of Tunnel Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China +3

Physics-Informed ML

May 18, 2026cs.LG

PH-Dreamer: A Physics-Driven World Model via Port-Hamiltonian Generative Dynamics

World models built on recurrent state space architectures enable efficient latent imagination, yet remain physically unstructured, producing dynamics that violate conservation and dissipative principles. We introduce a unified Port-Hamiltonian framework that remedies this through three synergistic mechanisms. First, we embed implicit physical priors into recurrent transitions by modeling projected latent evolution as action controlled energy routing governed by flow and dissipation, biasing the projected PH phase space toward a more compact and physically structured representation. Second, we develop a kinematics aware energy world model that estimates the Hamiltonian and power balance from proprioceptive observations, providing an explicit physical signal for thermodynamic reasoning. Third, leveraging these energy gradients, we establish an energy guided Actor-Critic that uses Lagrangian multipliers to regularize policy optimization toward lower energy and smoother control. Across visual control benchmarks, this paradigm not only attains superior asymptotic returns but also elevates internal simulator fidelity by establishing a tighter, lower variance alignment between imagined and real rewards, all while reducing latent phase space volume by 4.18-8.41%, energy consumption by up to 7.80%, and mean squared jerk by up to 9.38%.

Xueyu Luan, Chenwei Shi

School of Electronic and Information Engineering Tongji University Shanghai 200092, China · Shanghai Research Institute for Intelligent Autonomous Systems Tongji University Shanghai 200092, China

Dynamical Systems Reinforcement Learning Physics-Informed ML Latent World Models Port-Hamiltonian Systems Hamiltonian Dynamics+1

May 18, 2026cs.LG

UTOPYA: A Multimodal Deep Learning Framework for Physics-Informed Anomaly Detection and Time-Series Prediction

Anomaly detection in batch processes is hindered by transient dynamics, scarce fault labels, and reliance on single-modality sensor data. This work introduces UTOPYA (Unified Temporal Observation for Physics-Informed Anomaly Detection and Time-Series Prediction), a 15.2M-parameter multimodal framework that jointly addresses anomaly detection, time-series prediction, and phase classification in batch distillation by fusing eight data modalities through Feature-wise Linear Modulation (FiLM) conditioned cross-modal attention and gated fusion. A physics-informed regularisation scheme introduced in this work enforces temporal smoothness and thermodynamic monotonicity, while curriculum learning introduces training samples in order of physical difficulty. On the 119-experiment multimodal batch distillation dataset of Arweiler et al. (2026), UTOPYA achieves a window-level test AUROC of 0.832 and 0.874 under multi-signal experiment-level scoring, substantially outperforming four external baselines (PCA, autoencoder, Isolation Forest, and LSTM autoencoder) evaluated under identical conditions (+0.147 window-level AUROC over the best baseline). A multimodal ablation over 15~architectural configurations shows that static context via FiLM conditioning is the key enabler, lifting experiment-level multi-signal AUROC by +0.145 over the unimodal baseline (0.729 to 0.874). Separately, a training ablation across 14 design choices reveals that several widely-adopted techniques, including instance normalisation, Mixup, ensembling, test-time augmentation, and stochastic weight averaging, fail to improve or actively degrade generalisation in this data-scarce setting. These negative results expose a fundamental tension between smoothing-based regularisation and anomaly detection, providing practical guidance for multimodal process monitoring deployment.

Robson W. S. Pessoa, Julien Amblard, Alessandra Russo +1

aDepartment of Chemical Engineering, Norwegian University of Science and Technology2026 (NTNU), Trondheim, Norway · bDepartment of Computing, Imperial College London, London, United Kingdom

Multivariate Time Series Forecasting Industrial Anomaly Detection Multimodal Anomaly Detection Physics-Informed ML Multimodal Fusion Time-Series Anomaly Detection

May 18, 2026cs.LG

Physics-informed convolutional neural networks for fluid flow through porous media

Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly in intricate porous domains. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method uses a convolutional encoder-decoder architecture with skip connections to preserve spatial detail while extracting multi-scale features. Physical consistency is encouraged through a custom loss function combining velocity reconstruction with incompressibility, no-flow conditions inside solids, periodicity constraints, and agreement with the global tortuosity index. We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy. Several CNN backbones are evaluated to identify architectures providing accurate and robust predictions. The generalization ability of the trained model is tested on samples outside the training distribution, including changes in obstacle geometry, boundary conditions, porosity, and realistic porous structures. Finally, we demonstrate a practical use of the predicted velocity fields as initial conditions for Lattice-Boltzmann simulations. This warm-start strategy accelerates solver convergence, reducing the number of iterations in over 90% of tested cases.

Rafał Topolnicki, Paweł Dłotko, Maciej Matyka

Dioscuri Center in Topological Data Analysis, Institute of Mathematics, Polish Academy of Sciences, ul. ´Sniadeckich 8, 00-656, Warsaw, Poland · Institute of Experimental Physics, Faculty of Physics and Astronomy, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland · Institute of Theoretical Physics, Faculty of Physics and Astronomy, University of Wrocław, pl. M. Borna 9, Wrocław, 50-204, Poland +1

PDE Surrogate Modeling Physics-Informed ML Convolutional Neural Networks Computational Fluid Dynamics

May 17, 2026eess.SP

Hamiltonian-Inspired Attention Mechanism for Scalable RF Transmitter Fingerprinting

Radio-frequency (RF) fingerprinting identifies wire-less transmitters using hardware-induced imperfections present in baseband I/Q signals. However, deep learning models often degrade under receiver and channel distribution shifts, particularly as transmitter populations grow. This work proposes the Hamiltonian Transformer, a physics-informed attention architecture that enforces norm preserving value dynamics within each attention head using a learned skew-symmetric generator and a Störmer-Verlet leapfrog integration step. An additional phase-increment embedding exposes oscillator dynamics at the input layer. All experiments use non-equalized raw I/Q signals from the WiSig dataset under four protocols: same-day classification, cross-receiver generalisation, cross-day generalisation, and transmitter scaling up to 150 devices. The Hamiltonian Transformer achieves 99.12% accuracy under same-day conditions and 61.64% at 150 transmitters, consistently outperforming CNN and Transformer baselines across all scale points. A controlled ablation study identifies norm-preservation in the value update as the primary inductive bias driving the scaling advantage, with the phase increment embedding providing the single largest per-component improvement. These results indicate that embedding physics-informed structural priors into attention mechanisms is an effective approach to large-scale transmitter identification on raw wireless signals.

Chitraksh Singh, Monisha Dhanraj, Akram Sheriff

Frondeur Labs · Cisco Systems

Transformer Attention Physics-Informed ML Attention Mechanisms

May 16, 2026cs.CE

Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins

Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts through online parameter estimation under uncertainty. In many practical settings, however, this task is challenged by low observability, weak excitation, nonlinear dynamics, and noisy or biased measurements. In this work, we develop a new mathematical framework that integrates Weighted Flow Matching (WFM) generative modeling with physics-informed nonlinear filtering to enhance parameter estimation in DTs. WFM relies on dynamic reweighting of training samples, which guides the generative model toward parameter regimes most informative of the evolving system state. This generative component is tightly coupled with a physics-informed filtering architecture based on the Unscented Kalman Filter (UKF), yielding a unified DT framework that combines data-driven probability transport with physically consistent state and parameter estimation. The effectiveness of the new integrated framework is demonstrated within a spacecraft DT architecture, where stable moment of inertia estimation is achieved under uncertain and noisy sensing, with significant performance improvements over established approaches such as Extended Kalman Filtering (EKF) and Ensemble Kalman Filtering (EnKF). These results highlight the potential of weighted generative modeling as a core mechanism for real-time DT synchronization in operational and mission-critical systems.

Yasar Yanik, Himadri Basu, Ricardo G. Sanfelice +1

Department of Applied Mathematics, University of California, Santa Cruz, CA 95064, USA · Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA 95064, USA

Flow Matching Kalman Filtering Unscented Kalman Filtering Physics-Informed ML Digital Twins

May 16, 2026cs.LG

PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting

Time series forecasting under non-stationarity faces a fundamental tension between capturing stable representations and adapting to distribution shifts. Existing methods implicitly rely on static historical assumptions, leading to a critical failure mode we term Phase Amnesia, where models become blind to the evolving global context. To resolve this, we formalize non-stationary dynamics through three physical hypotheses: wold decomposition, dynamical phase evolution, and heteroscedastic manifold generation. These principles inspire PULSE, a physics-informed, plug-and-play framework adopting a Disentangle--Evolve--Simulate design philosophy. Specifically, PULSE utilizes phase-anchored disentanglement to resolve optimization interference caused by dominant trends, employs a Phase Router to actively generate future trajectories, and introduces Statistic-Aware Mixup (SAM) to ensure robustness against out-of-distribution volatility. Empirically, PULSE enables a simple MLP backbone to achieve state-of-the-art or highly competitive performance across 12 real-world benchmarks. This validates that a correct physics-informed inductive bias is far more critical than raw architectural complexity for non-stationary forecasting. The code is available at: https://github.com/Gemost/PULSE.

Yangyou Liu, Zezhi Shao, Xinyu Chen +3

College of Computer Science, Sichuan University, Chengdu, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · Institute of Artificial Intelligence, University of Central Florida, Orlando, USA +1

OOD Generalization Time Series Generation Non-Stationary Time Series Forecasting Physics-Informed ML

May 15, 2026cs.LG

Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure

Identifying latent state representations and dynamics is essential when direct modeling in observation space is infeasible, particularly under partial and high-dimensional observations. In such settings, representation learning and physics-aware modeling are inherently coupled. We study this problem for latent port-Hamiltonian systems, a structured class encompassing both conservative and dissipative dynamics. We propose a two-stage identify-then-project framework. First, a contrastive teacher learns continuous-time latent dynamics from partial observations. Then, a student projects the identified teacher representation and dynamics onto a port-Hamiltonian submanifold via a learned affine chart, yielding a physically consistent realization. As a conceptual counterfactual, we also consider a single-stage variant that jointly learns latent identification and port-Hamiltonian structure, but find it to be less reliable, motivating the proposed two-stage teacher-student framework. We show theoretically that affine projection is the natural bridge between the affine gauge of contrastive latent identification and the port-Hamiltonian systems. Empirically, we demonstrate that the proposed two-stage approach preserves the teacher's dynamics while enforcing physical structure, and performs more reliably than the single-stage alternative, particularly in dissipative regimes and high-dimensional visual settings.

Peilun Li, Kaiyuan Tan, Daniel Moyer +1

Department of Computer Science Vanderbilt University Nashville, TN 37235

Contrastive Learning Latent Dynamics Modeling System Identification Physics-Informed ML State Representation Learning Port-Hamiltonian Systems+1

May 15, 2026cs.CR

GenAI-FDIA: Physics-Informed Generative Models for False Data Injection Attacks

Training and evaluating false data injection attack (FDIA) detectors for power systems is constrained by data scarcity. Operational grid measurements are commercially sensitive, and hand-crafted attacks fail to capture complex distributional structures imposed by network physics. We present \textsc{GenAI-FDIA}, a framework benchmarking a pool of

P{=}20

architectures for physics-compliant FDIA synthesis, spanning Wasserstein GANs, MMD-VAEs, normalising flows, diffusion models, and cross-family hybrids. These are evaluated across three IEEE testbeds (14-bus DC, 30-bus DC, and 14-bus AC) under a 60/20/20 chronological split using data-driven Bad Data Detection (BDD) threshold calibration. Our empirical results verify that these models generate high-fidelity attacks, with all architectures achieving evasion rates of

ε_{\text{BDD}} \ge 86.6\%

on the 14-bus network; additionally, limiting an attacker's topological knowledge induces a measurable degradation in stealthiness (

p \le 0.0022

). Crucially, we identify a previously unreported failure mode: applying affine physics projections directly in normalised feature spaces critically displaces the attack vector, collapsing BDD evasion from

{\sim}55\%

to

<\!2\%

on the 30-bus testbed. We resolve this via a novel inference-time harmoniser, restoring full stealthiness (

ε_{\text{BDD}}{=}100\%

) across all physics-informed variants without retraining. Finally, we isolate a covariance-collapse phenomenon (

κ\approx {-}0.076

) within advanced hybrid architectures and rectify it through 50-epoch warm-up schedules (

κ\to 0.785

,

Δ\text{MMD}={-}3.1\%

). Ultimately, \textsc{GenAI-FDIA} delivers a robust recovery blueprint applicable to any physics-constrained generative model deployed for power-system security.

Mohammad A. Razzaque, Muta Tah Hira

School of Computing, Engineering and Digital Technologies, Teesside University, UK · Smartifier Ltd, Stockton-on-Tees, UK

Cyber-Physical Systems Physics-Informed Generative Modeling False Data Injection Attacks Synthetic Data Generation Cybersecurity Physics-Informed ML+1

May 15, 2026cs.LG

Hypothesis-driven construction of mesoscopic dynamics

Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including global well-posedness, asymptotic stability, unique factorization identifiability, and discrete energy dissipation, applicable to all spatio-temporal evolution equations within this hypothesis class prior to all learning stages. Data from each problem instance is then used to guide the identification of members within our hypothesis class, giving rise to accurate, robust and interpretable dynamical models. We empirically validate this framework on both data from continuum PDE models as a check, and on data arising from microscopic chain models for which exact meso-scale models are unknown. The proposed approach not only acts as an effective dynamics learner, but also offers vital interpretable diagnostics of the underlying physics.

Zhuoyuan Li, Aiqing Zhu, Qianxiao Li

Institute for Functional Intelligent Materials, National University of Singapore · Department of Mathematics, National University of Singapore

Latent Dynamics Modeling Nonlinear System Identification Physics-Informed ML

May 15, 2026cs.LG

Variational Autoregressive Networks with probability priors

Monte Carlo methods are essential across diverse scientific fields, yet their efficiency is frequently hampered by critical slowing down-a sharp increase in autocorrelation times near phase transitions. Although deep learning approaches, such as neural-network-based samplers, have been proposed to alleviate this issue, they face another serious problem: the difficulty of training the models. This difficulty partially stems from the overly general nature of original machine-learning architectures, which often ignore underlying physical symmetries and force networks to relearn them from scratch. In this paper, we demonstrate that incorporating physical priors into the model significantly enhances performance. Building upon existing strategies that integrate spin-spin interactions, we propose a framework that utilizes a prior probability distribution as a starting point for training. Our results for the Ising model, as well as for the Edwards-Anderson spin glass model, suggest that moving away from `blank slate' models in favor of physics-informed priors reduces the training burden and facilitates the simulation of larger system sizes in discrete spin models.

Piotr Białas, Piotr Korcyl, Tomasz Stebel +1

Institute of Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland · Institute of Theoretical Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland · Doctoral School of Exact and Natural Sciences, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland

Autoregressive Generation Physics-Informed ML Variational Inference

May 15, 2026cs.LG

When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective

Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral bias, stiffness, and poor accuracy on high-frequency or multiscale solutions. Adversarial training based on generative adversarial networks (GANs) has recently gained surprisingly strong empirical results in improving training, but the underlying mechanisms remain elusive. To this end, we propose a new analysis framework for adversarially trained PINNs, based on the key observation of how the discriminator in GANs can influence the training dynamics of PINNs. The framework first provides a much needed theoretical grounding to why and when adversarial training is effective in PINNs, then presents a unified analysis of GANs variants in such training, and finally leads to a new, practical, efficient training algorithm for PINNs. Empirical results demonstrate that our method can significantly reduce the pathology of PINNs training, thereby providing better models with superior performances, often several magnitudes more accurate than alternative methods.

Yuan-dong Cao, Chi Chiu SO, Jun-Min Wang +1

School of Mathematics and Statistics, Beijing Institute of Technology, China · Department of Computer Science & UCL AI Centre, University College London, UK · School of Professional Education and Executive Development The Hong Kong Polytechnic University, China

Adversarial Training PDE Surrogate Modeling Physics-Informed ML Generative Adversarial Networks

May 14, 2026cs.LG

Curriculum Learning of Physics-Informed Neural Networks based on Spatial Correlation

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN training still suffers from high-dimensional non-convex loss landscapes, imbalanced multiobjective constraints, and ineffective information propagation. Existing curriculum learning and causality-guided strategies improve training stability, but mainly focus on temporal or parametric progression, lacking explicit treatment of spatial information propagation and inter-region consistency. Moreover, they are not directly applicable to boundary value problems (BVPs) with strong spatial coupling. To address this issue, we propose a spatially correlated curriculum learning framework for PINNs. To the best of our knowledge, this is the first work to address PINN training difficulties from the perspective of spatial coupling among subregions. First, spatial causal weights guide information from near-boundary regions inward, reducing optimization failures and spurious convergence. Second, a low-frequency information bridge enforces pseudo-label-based consistency across spatially separated regions, suppressing global low-frequency drift. Third, a region-adaptive reweighting strategy adjusts subregion losses to reduce local residuals and recover high-frequency details. Experiments on PDE benchmarks show that, under comparable computational cost, the proposed method alleviates training failures and improves solution accuracy. The code is available at https://github.com/pigofmomo/CurriculumLearningPINN.

Xujia Chen, Xinyue Hu, Letian Chen +2

Department of Automation, Tsinghua University, Beijing 100084, P.R. China

PDE Solving Curriculum Learning Physics-Informed ML

May 14, 2026cs.CV

Training-Time Optical Priors for Wireless Capsule Endoscopy Classification: Hemoglobin-Aware Input Fusion with Cross-Vendor Evaluation

Gastrointestinal cancers cause approximately 3.4 million deaths annually, and early small-bowel lesions are easily missed at wireless capsule endoscopy (WCE). RGB-trained WCE classifiers conflate hemoglobin contrast with bile staining and illumination falloff, limiting sensitivity to small-vessel vascular findings such as Lymphangiectasia. We introduce a physics-informed framework that injects an analytic, Monte-Carlo-inspired hemoglobin prior into a standard classifier purely at training time -- to our knowledge the first use of an explicit optical light-transport prior in WCE classification. On Kvasir-Capsule (47,238 frames, 43 patients, 11 evaluable classes; patient-disjoint split) we evaluate, across six seeds against an RGB-only EfficientNet-B0 baseline, a five-channel input-fusion variant feeding the prior alongside RGB, a distillation variant that runs on plain three-channel RGB at inference, and a three-stream extension adding a temporal Transformer and an autoencoder-residual stream; we replicate across ResNet-18 and ConvNeXt-Tiny and assess cross-vendor zero-shot transfer on the public Galar cohort. Input fusion lifts cross-seed macro-AUC from 0.760 to 0.783 (5/6 seeds positive); distillation reaches 0.773; the three-stream model reaches 0.804 (+0.044 over baseline, paired DeLong p < 0.0001). Lymphangiectasia AUC rises from 0.238 to 0.337, sign-consistent across all six seeds. A four-variant ablation reveals a parameterization-mechanism boundary: only the spatial-channel form lifts. Cross-vendor zero-shot on Galar retains about 60% of the lift. The distillation variant deploys on plain RGB with a free interpretability heatmap, and we release GalKva-2026, a paired cross-vendor benchmark.

Chengshuai Yang, Lei Xing, Keyaan Zawad Alam +4

Department of Biomedical Engineering, University of Texas Southwestern Medical Center, 5323 Harry Hines Blvd, Dallas, 75390, TX, USA · Department of Radiation Oncology, Stanford University, Stanford, 94305, CA, USA · Coppell High School, Coppell, TX, USA +4

Endoscopy Medical Image Classification Physics-Informed ML

May 14, 2026eess.SY

Randomized Atomic Feature Models for Physics-Informed Identification of Dynamic Systems

We present a physics-informed framework for system identification based on randomized stable atomic features. Impulse responses are represented as random superpositions of stable atoms, namely damped complex exponentials associated with poles sampled inside a prescribed disk. Identification is then cast as a convex regularized least-squares problem with optional linear, second-order-cone, and KYP constraints. The approach generalizes random Fourier and random Laplace features to the damped, nonstationary regime relevant to engineering systems while retaining modal interpretability and scalable finite-dimensional computation. The main analytic point is an operator-theoretic Disk-Bochner viewpoint: positive measures over stable poles generate positive-definite kernels with a radius-dependent shift defect, while a converse scalar disk moment representation for an arbitrary kernel is characterized by subnormality of the canonical shift. We prove this statement, establish an RKHS-to-l1 embedding, show that sampled poles induce a valid finite atomic gauge, discuss random-feature convergence, and state sparse-recovery guarantees conditionally on the restricted-eigenvalue properties of the realized disk-Vandermonde or input-output design matrix. We also connect the normalized transfer function problem to Nevanlinna-Pick interpolation and LFT set-membership. The framework directly encodes stability margins, modal localization, DC-gain bounds, monotonicity, passivity, relative degree, settling-time targets, and time/frequency-domain error bounds. Numerical comparisons illustrate how physically meaningful priors can compensate for poor excitation and improve constrained impulse-response recovery in an under-informative data setting.

Rajiv Singh, Mario Sznaier, Lennart Ljung

∗The MathWorks Inc., 1 Apple Hill Drive, Natick, MA 01760 USA · ∗∗ECE Dept., Northeastern University, Boston, MA 02115, USA · ∗∗∗Div. of Automatic Control, Linköping University, Sweden

Random Feature Methods System Identification Kernel Methods Physics-Informed ML

May 13, 2026cs.LG

Uncertainty-Aware Prediction of Lung Tumor Growth from Sparse Longitudinal CT Data via Bayesian Physics-Informed Neural Networks

This work studies lung tumor growth prediction from sparse and irregular longitudinal computed tomography (CT) observations with measurement variability. A Bayesian physics-informed neural network is developed by combining Gompertz growth dynamics with low-dimensional Bayesian inference in the log-volume domain. The framework employs a two-stage inference strategy combining maximum a posteriori (MAP) estimation and Hamiltonian Monte Carlo (HMC) sampling to estimate posterior predictive distributions and uncertainty intervals. The method was evaluated on longitudinal data from the National Lung Screening Trial (30 patients). Results show that the model captures heterogeneous tumor growth patterns while maintaining reasonable prediction accuracy under limited observations. Compared with deterministic modeling approaches, the proposed approach additionally provides calibrated uncertainty estimates. The inferred posterior parameter correlations were consistent with expected biological growth behavior. The proposed framework achieved a cohort-level log-space RMSE of approximately 0.20 together with well-calibrated 95% credible interval coverage across 30 patients. These findings suggest that Bayesian physics-informed modeling may be useful for uncertainty-aware tumor growth assessment when only limited longitudinal follow-up scans are available.

Lingfei Kong, Haoran Ma

Department of Mathematics, Vanderbilt University, Nashville, TN, USA · John A. Paulson School of Engineering and Applied Science, Harvard University, Allston, MA, USA

Medical Image Analysis Longitudinal Medical Image Analysis Oncology Physics-Informed ML Uncertainty Calibration Regression Prediction Intervals

May 13, 2026physics.chem-ph

Physics-Guided Concentration Inference from Resistance Transients in a Mixed-Phase SnO-SnO $_2$ Carbon Monoxide Sensor with p-n Switching

This work presents a physics-guided machine-learning framework for carbon monoxide concentration inference from experimentally measured resistance transients of a mixed-phase SnO-SnO

_2

material gas sensor exhibiting temperature-dependent p-n switching behavior. Cycle-level transient responses are represented through physically interpretable descriptors and complemented by compact fast Fourier transform (FFT) and discrete wavelet transform (DWT)-based summaries. Using leakage-aware grouped cross-validation, we study both multi-class concentration classification and continuous concentration regression for the p-type and n-type sensing regimes separately. Across both regimes, fused features provide the strongest overall performance, while the physics-guided descriptor block remains highly competitive, indicating that the dominant concentration information is already encoded in physically meaningful transient dynamics. The p-type branch shows the best concentration-class discrimination, with the fused Random Forest classifier reaching approximately

96.5\%

accuracy, whereas the n-type branch yields the best quantitative concentration estimation, with the fused Random Forest regressor achieving an MAE

\approx 1.48

ppm and an R

^2

\approx 0.992

. These results reveal a clear dual-regime behavior: p-type sensing is particularly favorable for classification, whereas n-type sensing is more favorable for high-fidelity regression. More broadly, the study demonstrates that leakage-aware, cycle-level, physics-guided machine learning can extend conventional gas-sensing analysis beyond single-response metrics while preserving physical interpretability

Sani Biswas, Preetam Singh, Amit Kumar Gangwar

Centro de Modelamiento Matem´atico, Universidad de Chile & IRL 2807 - CNRS, Santiago, Chile · CSIR-National Physical Laboratory, Dr. K.S. Krishnan Marg, New Delhi, 110012, India · Department of Chemical Engineering, Biotechnology and Materials, FCFM, Universidad de Chile, Santiago, Chile and ANID - Millenium Science Initiative, Millenium Nuclei of Advanced MXenes for Sustainable Applications (AMXSA), Santiago, Chile

Physics-Informed ML

May 13, 2026cs.LG

MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning

Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons. We propose MPINeuralODE, which combines a soft physics-informed residual with a Multiple-Initial-Condition (MIC) multiple-shooting curriculum whose ingredients are structurally complementary: the physics term anchors the vector-field magnitude on the support that MIC enlarges. We evaluate along three axes: out-of-sample error, long-horizon stability, and Hamiltonian drift, which together expose whether the learned dynamics recover the underlying vector field. On Lotka-Volterra, MPINeuralODE achieves the lowest out-of-sample and long-horizon MSE among data-driven methods, with a 24% reduction over the baseline Neural ODE, while essentially matching the PINN ablation on Hamiltonian drift.

Lake Yang, Antonio Malpica-Morales, Frank Ioannis Papadakis Wood +1

Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom

Neural Network Generalization System Identification Physics-Informed ML Neural ODEs

May 13, 2026cs.LG

Unified generalization analysis for physics informed neural networks

Physics-Informed Neural Networks (PINNs) and their variational counterparts (VPINNs) are neural networks that incorporate physical laws, making them useful for scientific problems. Existing generalization analyses for PINNs and VPINNs remain limited, often requiring restrictive assumptions such as stability conditions or linear ellipticity. In this paper, we derive generalization bounds for neural networks that involve differentiation with respect to input variables, covering PINNs and VPINNs under a unified framework. We apply Taylor expansion to represent nonlinear differential operators as linear operators on a high-dimensional space, enabling the use of Koopman-based analysis and showing that high-rank networks can generalize well even in settings involving differential operators. We also show that the nonlinearity of the differential operator exponentially enlarges the bound, highlighting its significant impact on generalization.

Yuka Hashimoto, Tomoharu Iwata

1. NTT, Inc. · 2. RIKEN AIP

Neural Network Generalization Physics-Informed ML Generalization Bounds

May 13, 2026cs.LG

StampFormer: A Physics-Guided Material-Geometry-Coupled Multimodal Model for Rapid Prediction of Physical Fields in Sheet Metal Stamping

Traditional sheet metal forming relies on time-consuming and expensive Finite Element Analysis (FEA) for design validation, a process that significantly prolongs design cycles. While surrogate models offer faster iteration, current approaches have limitations: scalar-based methods cannot capture comprehensive field-based FEA results, while existing image-based models often ignore the critical role of material properties by focusing solely on geometry. To address this gap, we develop a physics-guided deep learning framework, namely StampFormer, which simultaneously uses component geometry and material stress-strain responses to predict FEA outcomes. The StampFormer framework uses three core components to process data. A Material-Augmented Geometric Network (MAGN) first fuses geometric and material data. This information is then integrated at various levels by a Hierarchical Material Embedding Injection Unit (HMEIU) before being processed by the primary network backbone, an adapted Swin-UNet. We evaluated our model on the stamping of a crossmember panel with two simulation datasets for steel and aluminium panels, and results demonstrate that StampFormer provides high-fidelity predictions of critical physical fields - including thinning, major strain, minor strain, plastic strain, and displacement - in under a second. Compared with ground truth FEA, our model achieved an average relative error of less than 8.5% on the four 2D fields and a mean squared error of less than 1.2 mm2 for the 3D displacement field. In summary, we introduce a practical and efficient framework that integrates multimodal information, namely geometry and material properties, to provide fast and accurate predictions, enabling designers to perform real-time manufacturability assessments.

Jiajie Luo, Mohamed Mohamed, Osama Hassan +8

Neural Surrogate Modeling Surrogate Modeling Physics-Informed ML Multimodal Fusion

May 12, 2026cs.RO

Few-Shot Physics-Informed Neural Network for Shape Reconstruction of Concentric-Tube Robots

Modeling concentric tube robots (CTRs) involves complex nonlinear continuum mechanics, and despite recent progress, physics-based models often lack an accurate representation of the experimental setups. To overcome these limitations, deep neural network-based models have been explored as alternatives with superior accuracy; however, they often overlook known mechanics, require large training datasets, and typically discard shape estimation of the robot. We present a physics-informed neural network (PINN) for kinematic modeling of a 6-DoF CTR with three pre-curved tubes that embeds the Cosserat rod differential equations and learns from few-shot observational data, balancing physics priors with data-driven fitting. PINN enables full-state estimation of shape, twist angle, torsional strain, bending moment, and orientation. Benchmark tests show a mean shape error below 1% of the robot length and accurately recovered other kinematic states, outperforming a purely physics-based Cosserat rod model baseline while using a minimal training set. The resulting model is also computationally efficient and robust, making it well-suited for real-time control applications.

Navid Feizi, Filipe C. Pedrosa, Rajni V. Patel +1

Canadian Surgical Technologies and Advanced Robotics (CSTAR), London Health Sciences Centre (LHSC), and with the Department of Electrical and Computer Engineering, Western University, London, Ontario, Canada

Robotics Physics-Informed ML Robot State Estimation

May 12, 2026cs.LG

Identifying the nonlinear string dynamics with port-Hamiltonian neural networks

Hybrid machine learning combines physical knowledge with data-driven models to enhance interpretability and performance. In this context, Port-Hamiltonian Systems (PHS), which generalize Hamiltonian mechanics to describe open, non-autonomous dynamical systems, have been successfully integrated with neural networks under the name Port-Hamiltonian Neural Networks (PHNNs). While the ability of PHNNs to identify Hamiltonian ordinary differential equation (ODE) systems has already been demonstrated, their application to learning Hamiltonian partial differential equation (PDE) systems remains largely unexplored. This limitation restricts their use in musical acoustics, where instruments are typically modeled as distributed parameter systems governed by PDEs. In this work, we demonstrate how to learn the nonlinear string dynamics from data in a physically-consistent framework through a PHNN extension to PDEs. By constructing structured neural network architectures based on PHS, we can recover both the Hamiltonian governing the string and the dissipation affecting it. This approach outperforms baseline, non-physics-informed methods in terms of both accuracy and interpretability. Numerical experiments using synthetic data demonstrate the ability of the proposed PHNN model to identify and emulate the nonlinear dynamics of the system.

Maximino Linares, Guillaume Doras, Thomas Hélie

1IRCAM, 1, place Igor-Stravinsky, 75004, Paris, France · 2Sorbonne Université, 4, place Jussieu, 75005, Paris, France · 3CNRS, 3 rue Michel-Ange, 75016, Paris, France

Dynamical Systems Nonlinear System Identification Hamiltonian Neural Networks System Identification Physics-Informed ML

May 12, 2026cs.LG

OceanCBM: A Concept Bottleneck Model for Mechanistic Interpretability in Ocean Forecasting

Extreme ocean phenomena are challenging not only to predict but to diagnose, as accurate forecasts alone do not reveal the underlying physical drivers. While recent machine learning approaches achieve strong predictive skill, they remain largely opaque and provide limited guarantees of fidelity to ground-truth physics. We introduce OceanCBM, the first concept bottleneck model (CBM) for spatiotemporal prediction and mechanistic interrogation of ocean dynamics. OceanCBM uses mixed supervision to predict mixed layer heat content, a key precursor of marine heatwaves, while routing information through an intermediate layer of prescribed concepts derived from geophysical fluid dynamics and a 'free' concept. This design imposes soft physical structure without over-constraining the model, and the free concept both regularizes concept predictions and captures residual physical processes. Across ensemble initializations, we show that mixed supervision yields consistent mechanistic representations, whereas prediction-only and prescription-only baselines learn highly variable latent structures despite similar predictive performance. OceanCBM achieves interpretable, physically grounded representations without sacrificing skill, explicitly characterizing the interpretability-performance trade-off.

Sanah Suri, Kieran Ringel, Maike Sonnewald

Department of Computer Science University of California, Davis Davis, CA 95616 · University of Washington, Seattle, WA, USA. · NOAA Geophysical Fluid Dynamics Laboratory, Princeton, NJ, USA.

Concept Bottleneck Models Mechanistic Interpretability Physics-Informed ML Spatiotemporal Forecasting

May 12, 2026physics.optics

Bin Latent Transformer (BiLT): A shift-invariant autoencoder for calibration-free spectral unmixing of turbid media

The accurate recovery of constituent-level optical properties from integrating sphere measurements is a central analytical challenge in pharmaceutical analysis, food science, and biomedical diagnostics. Neural network autoencoders can extract spectrally resolved absorption and scattering coefficients for each constituent without prior knowledge, but their fully connected encoders bind learned features to absolute wavelength indices, causing accuracy loss under spectrometer calibration drift or hardware exchange. This work introduces the Bin Latent Transformer (BiLT)-Autoencoder, in which the dense encoder is replaced by a cross-attention scanner: 16 learnable probe vectors query a convolutional feature map, aggregating morphological spectral information independently of absolute wavelength position. A physics-constrained linear decoder with enforced absorption/scattering separation and a three-phase curriculum augmentation strategy complete the architecture. On a liquid phantom benchmark (intralipid and two ink absorbers; 496 samples), the model achieves

R^2 = 0.979

and

0.975

for

μ_a(λ)

and

μ_s'(λ)

, respectively, on held-out test spectra, maintaining

R^2 > 0.90

for

μ_a

and

R^2 \approx 0.99

for

μ_s'

across the full tested shift range of

\pm 10

spectral bands. The model generalises to a simulated spectrometer with a broader instrument line shape (

{\approx}24

nm FWHM) without retraining, retaining

R^2 \approx 0.96

and

0.974

for the two channels. Attention map analysis reveals a physically interpretable two-component probe strategy: sparse anchor probes at absorption-edge wavelengths combined with a diffuse, SNR-driven ensemble at the high-transmittance long-wavelength region, which recruits additional probes dynamically under noise to provide implicit spectral averaging.

Martin Hohmann

Institute of Photonic Technologies (LPT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Konrad-Zuse-Straße 3/5, 91052 Erlangen, Germany

Autoencoders Transformer Attention Physics-Informed ML Spectral Methods

May 11, 2026cs.LG

Physics-Informed Teacher-Student Ensemble Learning for Traffic State Estimation with a Varying Speed Limit Scenario

Physics-informed deep learning (PIDL) neural networks have shown their capability as a useful instrument for transportation practitioners in utilizing the underlying relationship between the state variables for traffic state estimation (TSE). Another efficient traffic management approach is implementing varying speed limits (VSLs) on transportation corridors to control traffic and mitigate congestion. However, the existing training architecture of PIDL in the literature cannot accommodate the changing traffic characteristics on a freeway with VSL. To tackle this challenge, we propose a novel framework integrating teacher-student ensemble training with PIDL neural networks for TSE under VSL scenarios. The physics of flow conservation law is encoded locally in the teacher models by PIDL, and the student model uses a multi-layer perceptron classifier (MLP) to identify traffic characteristics and selects the ensemble member of PIDL neural networks for TSE. This integrated framework provides a natural solution for capturing the heterogeneity of VSL and accurately addressing the TSE problem. The case study results validate the proposed ensemble approach, demonstrating its superior performance in TSE compared to other popular baseline methods, as indicated by relative L2 error.

Archie J. Huang, Dongdong Wang, Shaurya Agarwal +3

Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Canada · Urban Artificial Intelligence Laboratory, University of Florida, Gainesville, USA · Department of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, USA

Ensemble Learning Traffic Flow Estimation Physics-Informed ML Teacher-Student Learning

May 11, 2026cs.LG

GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms

Scientific methods are developed for classes of problems, so knowledge transfers across structurally related cases. Language-model agents can execute scientific workflows, but their problem--method relationships remain implicit, so each new problem restarts the search and little of what worked transfers. We introduce GRAFT--ATHENA, which makes this problem-to-method map explicit as an expandable probabilistic structure of admissible problems, methods, and their dependencies. Graph factorization keeps the substrate tractable, and semantic fingerprints measure similarity, so experience guides related problems. As a result, the framework matched or exceeded expert baselines, attaining near-machine-precision losses in physics-informed learning, reproducing clinically consistent blood-rheology trends, and developing a high-order hypersonic-flow solver for the Apollo Command Module that matched experimental measurements within

1.8\%

. It also proposed a certified regularization for ill-posed in vivo brain-flow reconstruction, developed a spectrally convergent physics-informed architecture, and established machine-checked universal-approximation theorems for two widely used architectures. Scientific structure enables cumulative and verifiable agentic discovery.

Juan Diego Toscano, Zhaojie Chai, George Em Karniadakis

Division of Applied Mathematics, Brown University, Providence, 02912, RI, USA

AI Agents for Scientific Discovery Automated Algorithm Discovery Physics-Informed ML Self-Improving Agents Autonomous Research Agents

May 11, 2026cs.CV

CausalGS: Learning Physical Causality of 3D Dynamic Scenes with Gaussian Representations

Learning a physical model from video data that can comprehend physical laws and predict the future trajectories of objects is a formidable challenge in artificial intelligence. Prior approaches either leverage various Partial Differential Equations (PDEs) as soft constraints in the form of PINN losses, or integrate physics simulators into neural networks; however, they often rely on strong priors or high-quality geometry reconstruction. In this paper, we propose CausalGS, a framework that learns the causal dynamics of complex dynamic 3D scenes solely from multi-view videos, while dispensing with the reliance on explicit priors. At its core is an inverse physics inference module that decouples the complex dynamics problem from the video into the joint inference of two factors: the initial velocity field representing the scene's kinematics, and the intrinsic material properties governing its dynamics. This inferred physical information is then utilized within a differentiable physics simulator to guide the learning process in a physics-regularized manner. Extensive experiments demonstrate that CausalGS surpasses the state-of-the-art on the highly challenging task of long-term future frame extrapolation, while also exhibiting advanced performance in novel view interpolation. Crucially, our work shows that, without any human annotation, the model is able to learn the complex interactions between multiple physical properties and understand the causal relationships driving the scene's dynamic evolution, solely from visual observations.

Nengbo Lu, Minghua Pan

Guilin University of Electronic Technology · Guilin, China

Dynamic Scene Reconstruction Video Prediction Physics-Informed ML Physical Reasoning in Video

May 11, 2026cs.CV

VeloGauss: Learning Physically Consistent Gaussian Velocity Fields from Videos

In this paper, we aim to jointly model the geometry, appearance, and physical information of 3D scenes solely from dynamic multi-view videos, without relying on any physical priors. Existing works typically employ physical losses merely as soft constraints or integrate physical simulations into neural networks; however, these approaches often fail to effectively learn complex motion physics. Although modeling velocity fields holds the potential to capture authentic physical information, due to the lack of appropriate physical constraints, current methods are unable to correctly learn the interaction mechanisms between rigid and non-rigid particles. To address this, we propose VeloGauss, designed to learn the physical properties of complex dynamic 3D scenes without physical priors. Our method learns the velocity field for each Gaussian particle by introducing a Physics Code and a Particle Dynamics System, and ultimately incorporates Global Physical Constraints to ensure the physical consistency of the scene. Extensive experiments on four public datasets demonstrate that our method outperforms achieves state-of-the-art performance in both Novel View Interpolation and Future Frame Extrapolation tasks.

Nengbo Lu, Bin Zhao

Guangxi Key Laboratory of Robot Intelligent Perception and Control, School of Artificial Intelligence, Guilin University of Electronic Technology, Guilin, 541004, China

3D Gaussian Splatting Dynamic Scene Reconstruction Novel View Synthesis Video Prediction Physics-Informed ML

May 11, 2026cs.LG

PhysEDA: Physics-Aware Learning Framework for Efficient EDA With Manhattan Distance Decay

Electronic design automation (EDA) addresses placement, routing, timing analysis, and power-integrity verification for integrated circuits. Learning methods -- attention (Transformer) and reinforcement learning (RL) -- have recently emerged on EDA tasks, yet face two common bottlenecks: vanilla attention's quadratic complexity limits scaling, and data-scarce models overfit statistical noise and amplify weak long-range correlations against the underlying physics. We observe that EDA tasks share a physical prior -- pairwise electrical and routing interactions decay exponentially along Manhattan distance -- and integrate it as a unified inductive bias into both architecture and training. We propose PhysEDA, comprising two components Physics-Structured Linear Attention (PSLA) folds the separable Manhattan decay into the linear-attention kernel as a multiplicative bias, reducing complexity from quadratic to linear; Potential-Based Reward Shaping (PBRS) constructs a physical potential from the same kernel, providing dense reward signal under sparse RL while preserving the optimal policy via the policy-invariance theorem. Across three EDA scenarios -- decoupling-capacitor placement, macro placement, and IR-drop prediction -- PhysEDA improves zero-shot cross-scale transfer by 56.8% and achieves 14x inference speedup with 98.5% memory savings on 100x100 grids; PBRS adds another 10.8% in sparse-reward DPP.

Zetao Yang

School of Mathematics and Statistics Beijing Institute of Technology Beijing, China

Efficient Neural Network Inference Reward Shaping Electronic Design Automation Linear Attention Physics-Informed ML Sparse-Reward RL