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

Apr 26, 2026cs.LG

Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent diffusion framework designed to simultaneously resolve sparse-observation reconstruction and super-resolution. While existing physics-guided diffusion models typically rely on soft loss penalties or uninterpretable representations, our approach enforces physical compliance by constructing an inherently interpretable latent space. Specifically, we parameterize the latent variables directly as the coefficients and source terms of an assumed governing PDE. In doing so, LatentPDE is able to reliably reconstruct dynamics across highly disparate and structured data gaps. Empirical results on diverse configurations demonstrate that our model achieves high-fidelity recovery at any desired resolution while also tracking the underlying predictive uncertainty.

Valerie Tsao, Nathaniel Chaney, Manolis Veveakis

Department of Civil & Environmental Engineering, Duke University, NC, USA.

Physics-Informed Diffusion Models Sparse Recovery Latent Diffusion Models Physics-Informed ML Diffusion-Based Inverse Problems PDE Inverse Problems+1

Apr 26, 2026cs.LG

WISE-FM:Operation-Aware, Engineering-Informed Foundation Model for Multi-Task Well Design

Deploying machine learning models across diverse well portfolios requires generalisation to wells with design parameters outside the training distribution. Current data-driven approaches to virtual flow metering (VFM) and bottomhole estimation typically treat each well independently or ignore the influence of well design on operational behaviour. We present WISE (Well Intelligence and Systems Engineering Foundation Model), a design-aware, physics-informed multi-task model that integrates three complementary mechanisms: Feature-wise Linear Modulation (FiLM) and cross-modal attention to condition operational embeddings on well design parameters; multi-task learning for simultaneous prediction of flow rates, bottomhole conditions, and flow regime classification; and structural mass conservation with soft physics constraints derived from well engineering principles. Evaluation on the ManyWells benchmark (2000 simulated wells,

10^6

data points) demonstrates that design-aware models reduce VFM prediction error by up to

13\times

compared to design-unaware baselines, and that physics constraints reduce negative flow predictions by 65%. Flow regime classification achieves 97.7% bottomhole accuracy, providing continuous well integrity monitoring without additional sensors. The methodology transfers to real operational data from five Equinor Volve producers (oil rate

R^2 = 0.89

, bottomhole pressure

R^2 = 0.98

, water rate

R^2 = 0.97

). The trained model additionally serves as a fast surrogate for integrity-aware well design optimisation over a 24-dimensional design space, with more than

1000\times

speedup over drift-flux simulations. These results demonstrate that design awareness, physics enforcement, and multi-task learning are essential and complementary ingredients for foundation models intended to operate across large well portfolios.

Carine de Menezes Rebello, Anderson Rapello dos Santos, Idelfonso B. R. Nogueira

Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway · Petróleo Brasileiro S.A. (PETROBRAS), Wells/Well Engineering, Rio de Janeiro, Brazil

Surrogate Modeling Multi-Task Learning Physics-Informed ML

Apr 26, 2026quant-ph

An architectural capacity ceiling, not a barren plateau: why a fixed-encoding variational quantum circuit cannot fit the Lorenz-63 attractor

Variational quantum circuits train poorly on chaotic forecasting, usually blamed on barren plateaus (exponentially vanishing gradients). Using an exactly simulable four-qubit variational quantum physics-informed circuit fit to Lorenz-63, we show the barren-plateau explanation fails: the failure is an architectural capacity ceiling fixed by the circuit time-encoding, not its trainable depth. Four measurements support this. (i) A McClean-comparable gradient-variance estimator sits at the local-cost Haar/2-design scale 2^(-2n)=3.9e-3 at n=4; on structurally live parameters it decays about ninefold with depth then saturates there, large enough to train, not an exponential collapse. (ii) At a common budget of 200 optimiser iterations (600, in three stages, for layer-wise), gradient descent, layer-wise, and SPSA reach the same order of magnitude of loss, so no optimiser unlocks a better basin. (iii) The output-Jacobian rank saturates at 33 from five layers on, so depth buys no new output directions. (iv) A Fourier analysis explains why: the qubit-1 phase encoding acts on the initial |0> and is inert, so the maximum accessible frequency is 2.5/t_max=0.83 Hz, identical at every depth and about 4.4x below the narrowest Lorenz component bandwidth. The corrected band has dimension 1+2x5=11 per observable, and 3x11=33 equals the measured rank ceiling exactly, unifying the two diagnostics. A trained depth sweep agrees: mean loss improves with depth then flattens once the rank saturates. We correct our earlier preprint diagnosis, which compared unnormalised gradient norms to the McClean threshold, and place the advantage of fixed reservoirs and classical echo-state networks in architecture, not quantum mechanics.

Tushar Pandey

Texas A&M University, College Station, TX 77843, USA

Variational Quantum Circuits Physics-Informed ML Quantum Circuit Trainability Chaotic Time-Series Prediction

Apr 26, 2026cs.RO

QuietWalk: Physics-Informed Reinforcement Learning for Ground Reaction Force-Aware Humanoid Locomotion Under Diverse Footwear

Humanoid robots operating in human-centered environments (e.g., homes, hospitals, and offices) must mitigate foot--ground impact transients, as impact-induced vibration and noise degrade user experience and repeated impacts accelerate hardware wear. However, existing low-noise locomotion training often relies on kinematic proxy objectives or fragile force sensors, and footwear-induced changes in contact dynamics introduce distribution shifts that hinder policy generalization.We present QuietWalk, a physics-informed reinforcement learning framework for ground-reaction-force-aware humanoid locomotion under diverse footwear conditions. QuietWalk employs an inverse-dynamics-constrained physics-informed neural network (PINN) to estimate per-foot vertical ground reaction forces (GRFs) from proprioceptive signals, and integrates the frozen predictor into the RL training loop to penalize predicted impact forces without requiring force sensors at deployment.On a held-out real-robot dataset, enforcing inverse-dynamics consistency reduces vertical GRF prediction errors by 82%-86% compared with a purely supervised predictor and improves the coefficient of determination from 0.39/0.67 to 0.99/0.99 for the left/right feet. On hardware at 1.2 m/s (barefoot; averaged over four floor materials), QuietWalk reduces mean A-weighted noise level by 7.17 dB and peak noise level by 4.98 dB under a consistent recording setup. Cross-footwear experiments (barefoot, skate shoes, athletic sneakers, and high heels) across multiple surfaces further demonstrate robust adaptation to footwear-induced contact variations.

Hanze Hu, Luying Feng, Silu Chen +6

Humanoid Robot Locomotion Robot Locomotion RL for Legged Locomotion Physics-Informed ML Physics-Informed RL Robust RL

Apr 26, 2026cs.LG

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

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

α

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

k

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

Ru Geng, Panayotis Kevrekidis, Yixian Gao +2

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

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

Apr 26, 2026cs.LG

When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions

Physics-informed neural networks (PINNs) provide a promising machine learning framework for solving partial differential equations, but their training often breaks down on challenging problems, sometimes converging to physically incorrect solutions despite achieving small residual losses. This failure, we argue, is not merely an optimization difficulty. Rather, it reflects a fundamental weakness of the empirical PDE residual loss, which can admit trivial or spurious solutions during training. From this perspective, we revisit pseudo-time stepping, a technique that has recently shown strong empirical success in PINNs. We show that its main benefit is not simply to ease optimization; instead, when combined with collocation-point resampling, it helps reveal and avoid spurious solutions. At the same time, we find that the effectiveness of pseudo-time stepping depends critically on the choice of step size, which cannot be tuned reliably from the training loss alone. To overcome this limitation, we propose an adaptive pseudo-time stepping strategy that selects the step size from a finite-difference surrogate of the local residual Jacobian, yielding the largest step permitted by local stability without per-problem tuning. Across a diverse set of PDE benchmarks, the proposed method consistently improves both accuracy and robustness. Together, these findings provide a clearer understanding of why PINNs fail and suggest a practical pathway toward more reliable physics-informed learning. All code and data accompanying this manuscript are available at https://github.com/sifanexisted/jaxpi2.

Sifan Wang, Shawn Koohy, Yiping Lu +1

Institute for Foundations of Data Science, Yale University · Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania · Industrial Engineering & Management Science, Northwestern University

PDE Solving Physics-Informed ML

Apr 26, 2026cs.LG

Interpretable Physics-Informed Load Forecasting for U.S. Grid Resilience: SHAP-Guided Ensemble Validation in Hybrid Deep Learning Under Extreme Weather

Accurate short-term electricity load forecasting is a cornerstone of U.S. grid reliability; however, prevailing deep learning models remain opaque, limiting operator trust during extreme weather. A unified, interpretable, physics-informed ensemble framework is proposed, integrating a Convolutional Neural Network (CNN) branch for local feature extraction and a Transformer branch for long-range dependency modeling; the branches are fused through a validation-optimized weighted ensemble and regularized by a physics-informed loss derived from the piecewise parabolic temperature-demand relationship of the Electric Reliability Council of Texas (ERCOT) system. Post-hoc interpretability is provided through SHapley Additive exPlanations (SHAP) with the DeepExplainer backend, yielding global and event-level attributions. Using eight years of ERCOT hourly load data (2018-2025) fused with Automated Surface Observing System (ASOS) records from three Texas stations, the framework achieves 713 MW MAE, 812 MW RMSE, and 1.18% MAPE on the test window. For Hampel-flagged extreme events, MAPE falls by 20.7% relative to its Transformer branch and by 40.5% relative to its CNN branch; an ablation confirms that the parabolic and ramp constraints drive a 14.7% RMSE reduction. SHAP analysis reveals a regime shift: temperature dominates under normal operation, whereas wind speed and precipitation become more influential during cold fronts and heatwaves.

Md Abubakkar, Sajib Debnath, Md. Uzzal Mia

Dept. of Computer Science, Midwestern State University, Dallas, TX, USA · O&M Analytics, AES Clean Energy, The AES Corporation, Louisville, CO, USA · Dept. of Information and Communication Engineering, Pabna University of Science and Technology, Bangladesh

Hybrid CNN-Transformer Architectures Time Series Forecasting Physics-Informed ML Electricity Load Forecasting Power Systems

Apr 25, 2026cs.LG

GeoCert: Certified Geometric AI for Reliable Forecasting

Forecasting systems in science must be accurate, physically consistent, and certifiably reliable. Most existing models address prediction, constraint enforcement, and verification separately, limiting scalability and interpretability. We introduce GeoCert, a geometric AI framework that unifies forecasting, physical reasoning, and formal verification within a single differentiable computation. GeoCert formulates forecasting as evolution along a hyperbolic manifold, where negative curvature induces contraction dynamics, intrinsic robustness, and logarithmic-time certification. A hierarchical constraint architecture separates universal physical laws from domain-specific dynamics, enabling certified generalization across energy, climate, finance, and transportation systems. GeoCert achieves state-of-the-art accuracy while reducing computational cost by 97.5% and maintaining better certification rates. By embedding verification into the geometry of learning, GeoCert transforms forecasting from empirical approximation to formally verified inference, offering a scalable foundation for trustworthy, reproducible, and physically grounded scientific AI.

Regina Zhang, Zongru Li, Honggang Wen +4

Department of Biomedical Informatics & Data Science, Yale University, US · School of Computing and Data Science, Nanyang Technological University, Singapore. · Department of Computer Science, The University of Hong Kong, Hong Kong SAR +1

Neural Network Verification Time Series Forecasting Physics-Informed ML Certified Robustness

Apr 25, 2026physics.flu-dyn

Physics-Informed Temporal U-Net for High-Fidelity Fluid Interpolation

Reconstructing high-fidelity fluid dynamics from sparse temporal observations is quite challenging, mainly due to the chaotic and non-linear nature of fluid transport. Standard deep learning-based interpolation methods often tend to regress to the mean, which results in spatial blurring and temporal strobing, especially noticeable around the observed anchor frames where transitions become discontinuous. In this work, we propose a novel Temporal U-Net architecture that integrates a VGG-based perceptual loss along with a Physics-Informed Bridge to overcome these issues. By introducing time-weighted feature blending and enforcing a parabolic boundary condition defined by t(1 - t), the model ensures smooth transitions while also maintaining perfect consistency at the endpoints. Experimental results on multi-channel RGB fluid data show that our method clearly outperforms standard models, both in terms of structural fidelity and texture preservation. In particular, the model achieves a Mean Absolute Error of 0.015, compared to 0.085 for a standard L1 baseline. Further Spatial Power Spectral Density (PSD) analysis reveals that the model is able to retain high-frequency turbulent details that are usually lost in deterministic reconstructions.

Eshwar R. A., Nevin Mathew Thomas, Nehal G +1

Department of Computer Science Engineering, PES University - Electronic City Campus, Bangalore 560100, India.

U-Net Video Frame Interpolation Physics-Informed ML Convolutional Neural Networks Computational Fluid Dynamics

Apr 24, 2026cs.LG

Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen

In this paper, we propose a Physics-Informed Neural Network framework for time-dependent simulations of pollution propagation originating from moving emission sources. We formulate a robust variational framework for the time-dependent advection-diffusion problem and establish the boundedness and inf-sup stability of the corresponding discrete weak formulation. Based on this mathematical foundation, we construct a robust loss function that is directly related to the true approximation error, defined as the difference between the neural network approximation and the (unknown) exact solution. Additionally, a collocation-based strategy is introduced to speed up neural network training. As a case study, we investigate pollution propagation caused by snowmobile traffic in Longyearbyen, Spitsbergen, supported by detailed in-field measurements collected using dedicated sensors. The proposed framework is applied to analyze the effects of thermal inversion on pollutant accumulation. Our results demonstrate that thermal inversion traps dense and humid air masses near the ground, significantly enhancing particulate matter (PM) concentration and worsening local air quality.

Leszek Siwik, Maciej Sikora, Natalia Leszczyńska +7

AGH University of Krakow, Faculty of Computer Science, Al. Mickiewicza 30, Kraków, 30-059, Poland · Medical University of Silesia-Katowice, Faculty of Medical Sciences, ul. Poniatowskiego 15, Katowice, 40-055, Poland · The University Centre in Svalbard, Longyearbyen, Box 156 N-9171, Longyearbyen, Norway +4

Neural PDE Solvers Air Quality Prediction Physics-Informed ML Computational Fluid Dynamics

Apr 24, 2026cs.RO

Information-Theoretic Geometry Optimization and Physics-Aware Learning for Calibration-Free Magnetic Localization

Wireless localization of permanent magnets enables occlusion-free guidance for medical interventions, yet its practical accuracy is fundamentally limited by two coupled challenges: the poor observability of conventional planar sensor arrays and the simulation-to-reality (Sim-to-Real) gap of learning-based estimators. To address these issues, this article presents a unified framework that combines information-theoretic sensor geometry optimization with physics-aware deep learning. First, a rigorous Fisher Information Matrix (FIM)-based evaluation framework is established to quantify geometry-induced observability limitations. The results show that a staggered split-array topology provides a substantially stronger observability foundation for localization while remaining compatible with practical external deployment. Second, building on this optimized sensing configuration, we propose Phy-GAANet, a calibration-free estimator trained entirely on hardware-aware synthetic data. By incorporating Physics-Informed Features (PIF) for saturation modeling and Geometry-Aware Attention (GAA) for preserving cross-layer vector structure, the network effectively bridges the Sim-to-Real gap. Extensive real-world experiments demonstrate state-of-the-art performance, achieving a position error of 1.84 mm and an orientation error of 3.18 degrees at a refresh rate exceeding 270 Hz. The proposed method consistently outperforms classical Levenberg--Marquardt solvers and generic convolutional baselines, particularly in suppressing catastrophic outliers and maintaining robustness in challenging near-field boundary regions. Beyond the proposed network, the FIM-guided analysis also provides a framework for sensor geometry design in magnetic localization systems under practical deployment constraints.

Wenxuan Xie, Yuelin Zhang, Qingpeng Ding +4

Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong.

Sim-to-Real Transfer Wireless Localization Physics-Informed ML

Apr 23, 2026cs.LG

Transferable Physics-Informed Representations via Closed-Form Head Adaptation

Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the learning process, PINN models have demonstrated the ability to learn physical outcomes reasonably well. However, current PINN approaches struggle to predict or solve new PDEs effectively when there is a lack of training examples, indicating they do not generalize well to unseen problem instances. In this paper, we present a transferable learning approach for PINNs premised on a fast Pseudoinverse PINN framework (Pi-PINN). Pi-PINN learns a transferable physics-informed representation in a shared embedding space and enables rapid solving of both known and unknown PDE instances via closed-form head adaptation using a least-squares-optimal pseudoinverse under PDE constraints. We further investigate the synergies between data-driven multi-task learning loss and physics-informed loss, providing insights into the design of more performant PINNs. We demonstrate the effectiveness of Pi-PINN on various PDE problems, including Poisson's equation, Helmholtz equation, and Burgers' equation, achieving fast and accurate physics-informed solutions without requiring any data for unseen instances. Pi-PINN can produce predictions 100-1000 times faster than a typical PINN, while producing predictions with 10-100 times lower relative error than a typical data-driven model even with only two training samples. Overall, our findings highlight the potential of transferable representations with closed-form head adaptation to enhance the efficiency and generalization of PINNs across PDE families and scientific and engineering applications.

Jian Cheng Wong, Isaac Yin Chung Lai, Pao-Hsiung Chiu +3

Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore · National University of Singapore (NUS), Singapore · Indian Institute of Technology Goa (IIT Goa), India +1

Representation Learning PDE Solving Physics-Informed ML

Apr 23, 2026cs.LG

A Green-Integral-Constrained Neural Solver with Stochastic Physics-Informed Regularization

Standard physics-informed neural networks (PINNs) struggle to simulate highly oscillatory Helmholtz solutions in heterogeneous media because pointwise minimization of second-order PDE residuals is computationally expensive, biased toward smooth solutions, and requires artificial absorbing boundary layers to restrict the solution. To overcome these challenges, we introduce a Green-Integral (GI) neural solver for the acoustic Helmholtz equation. It departs from the PDE-residual-based formulation by enforcing wave physics through an integral representation that imposes a nonlocal constraint. Oscillatory behavior and outgoing radiation are encoded directly through the integral kernel, eliminating second-order spatial derivatives and enforcing physical solutions without additional boundary layers. Theoretically, optimizing this GI loss via a neural network acts as a spectrally tuned preconditioned iteration, enabling convergence in heterogeneous media where the classical Born series diverges. By exploiting FFT-based convolution to accelerate the GI loss evaluation, our approach substantially reduces GPU memory usage and training time. However, this efficiency relies on a fixed regular grid, which can limit local resolution. To improve local accuracy in strong scattering regions, we also propose a hybrid GI+PDE loss, enforcing a lightweight Helmholtz residual at a small number of nonuniformly sampled collocation points. We evaluate our method on seismic benchmark models characterized by structural contrasts and subwavelength heterogeneity at frequencies up to 20Hz. GI-based training consistently outperforms PDE-based PINNs, reducing computational cost by over a factor of ten. In models with localized scattering, the hybrid loss yields the most accurate reconstructions, providing a stable, efficient, and physically grounded alternative.

Mohammad Mahdi Abedi, David Pardo, Tariq Alkhalifah

University of the Basque Country (UPV/EHU), Department of Mathematics, Spain · Basque Center for Applied Mathematics (BCAM), Bilbao, Spain · Ikerbasque, Basque Foundation for Science, Bilbao, Spain +1

Neural PDE Solvers PDE Solving Physics-Informed ML

Apr 22, 2026math.NA

CO $_2$ sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)

This paper presents the hybrid solver for a

CO_2

sequestration problem. The solver uses the IGA-ADS (IsoGeometric Analysis Alternating Directions solver) to compute the saturation scalar field update using the explicit method, and CRVPINN (Collocation-based Robust Variational Physics Informed Neural Networks solver) to compute the pressure scalar field. The study focuses on simulating the physical behavior of

CO_2

in porous structures, excluding chemical reactions. The mathematical model is based on Darcy's Law. The CRVPINN is pretrained on the initial pressure configuration, and the time step pressure updates require only 100 iterations of the Adam method per time step. We compare our hybrid IGA-ADS solver, coupled with the CRVPINN method, with a baseline of the IGA-ADS solver coupled with the MUMPS direct solver. Our hybrid solver is over 3 times faster on a single computational node from the ARES cluster of ACK CYFRONET. Future work includes extensive testing, inverse problem solving, and potential application to

H_2

storage problems.

Askold Vilkha, Tomasz Służalec, Marcin Łoś +1

AGH University of Krakow, Faculty of Computer Science, Al. Mickiewicza 2026 30, Kraków, 30-059, Poland

Neural PDE Solvers PDE Solving Physics-Informed ML Computational Fluid Dynamics

Apr 22, 2026cs.CV

Physics-Informed Conditional Diffusion for Motion-Robust Retinal Temporal Laser Speckle Contrast Imaging

Retinal laser speckle contrast imaging (LSCI) is a noninvasive optical modality for monitoring retinal blood flow dynamics. However, conventional temporal LSCI (tLSCI) reconstruction relies on sufficiently long speckle sequences to obtain stable temporal statistics, which makes it vulnerable to acquisition disturbances and limits effective temporal resolution. A physically informed reconstruction framework, termed RetinaDiff (Retinal Diffusion Model), is proposed for retinal tLSCI that is robust to motion and requires only a few frames. In RetinaDiff, registration based on phase correlation is first applied to stabilize the raw speckle sequence before contrast computation, reducing interframe misalignment so that fluctuations at each pixel primarily reflect true flow dynamics. From the long registered sequence this step yields a high-quality multiframe tLSCI map that serves only as the reconstruction target, while a motion-corrected contrast prior is computed independently from the few input frames. Next, guided by this prior, a conditional diffusion model performs inverse reconstruction by jointly conditioning on the registered few-frame sequence and the prior. On stable sequences acquired with an in-house retinal LSCI system, RetinaDiff improved SSIM from 0.159 to 0.533, PSNR from 14.83 to 18.06 dB, and FID from 211.50 to 111.55 compared with direct five-frame reconstruction, showing improved structural continuity and statistical stability over representative baselines. The framework also remains effective in a small number of extremely challenging cases, where both the direct five-frame input and the conventional multiframe reconstruction are severely degraded. Overall, this work provides a practical and physically grounded route for reliable retinal tLSCI reconstruction from extremely limited frames. The source code and model weights will be released upon acceptance.

Qian Chen, Yuehao Chen, Qiang Wang +3

Department of Biomedical Engineering, Peking University, Beijing, China · Institute of Medical Technology, Peking University, Beijing, China · Institute of Biomedical Engineering, Peking University Shenzhen Graduate School, Shenzhen, China +2

Image Reconstruction Physics-Informed ML

Apr 22, 2026cs.LG

Physics-Enhanced Deep Learning for Proactive Thermal Runaway Forecasting in Li-Ion Batteries

Accurate prediction of thermal runaway in lithium-ion batteries is essential for ensuring the safety, efficiency, and reliability of modern energy storage systems. Conventional data-driven approaches, such as Long Short-Term Memory (LSTM) networks, can capture complex temporal dependencies but often violate thermodynamic principles, resulting in physically inconsistent predictions. Conversely, physics-based thermal models provide interpretability but are computationally expensive and difficult to parameterize for real-time applications. To bridge this gap, this study proposes a Physics-Informed Long Short-Term Memory (PI-LSTM) framework that integrates governing heat transfer equations directly into the deep learning architecture through a physics-based regularization term in the loss function. The model leverages multi-feature input sequences, including state of charge, voltage, current, mechanical stress, and surface temperature, to forecast battery temperature evolution while enforcing thermal diffusion constraints. Extensive experiments conducted on thirteen lithium-ion battery datasets demonstrate that the proposed PI-LSTM achieves an 81.9% reduction in root mean square error (RMSE) and an 81.3% reduction in mean absolute error (MAE) compared to the standard LSTM baseline, while also outperforming CNN-LSTM and multilayer perceptron (MLP) models by wide margins. The inclusion of physical constraints enhances the model's generalization across diverse operating conditions and eliminates non-physical temperature oscillations. These results confirm that physics-informed deep learning offers a viable pathway toward interpretable, accurate, and real-time thermal management in next-generation battery systems.

Salman Khan, Syed Sajid Ullah, Muhammad Zunair Zamir +3

Recurrent Neural Networks Physics-Informed ML Lithium-Ion Batteries

Apr 21, 2026eess.SP

A Hybrid Windkessel-Neural Approach for Improved Noninvasive Blood Pressure Monitoring

Owing to the recent advancements in wearable devices for health care, the importance of BP estimation without cuffs increases. Cuff technologies are inappropriate for continuous BP measurement due to their inconvenient usage, invasive character, necessity of calibration, large size, and inability to perform long-term monitoring. Normally, the algorithm used for cuffless BP prediction employs machine learning models that operate according to the data-driven approach. However, although they show high numerical accuracy, ML models do not provide any interpretability, resulting in poor physiological validity and clinical applicability. We propose a combination of Windkessel and ML models that incorporates the physical aspects into the latter one. It is performed by reformulating Windkessel into a form that will allow employing ML models. The result is a system of ODEs which can be used in the neural network. Thus, the inclusion of physical constraints improves the data-driven approach by making models consistent with physics, understandable, and robust. For illustration, we apply the described technique using a publicly available MIMIC-II database that we obtain from the UCI Machine Learning Repository.

Vaibhav Gollapalli, Aniruth Ananthanarayanan

Department of Physics University of North Texas Denton, United States of America

Physics-Informed ML Wearable Health Monitoring Cuffless Blood Pressure Estimation

Apr 20, 2026cs.LG

Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential operator structure (e.g., reaction-diffusion) while learning constitutive terms via trainable neural subnetworks, enforced through soft residual penalties. Existing BINN studies are limited to

1\mathrm{D}{+}t

reaction-diffusion systems and focus on forward prediction, using the governing partial differential equation as a regulariser rather than an explicit identification target. Here, we extend BINNs to

2\mathrm{D}{+}t

systems within a PINN framework that combines data preprocessing, BINN-based equation learning, and symbolic regression post-processing for closed-form equation discovery. We demonstrate the framework's real-world applicability by learning the governing equations of lung cancer cell population dynamics from time-lapse microscopy data, recovering

2\mathrm{D}{+}t

reaction-diffusion models from experimental observations. The proposed framework is readily applicable to other spatio-temporal systems, providing a practical and interpretable tool for fast analytic equation discovery from data.

William Lavery, Jodie A. Cochrane, Christian Olesen +3

Dept. of Information Technology Uppsala University Uppsala, Sweden · Dept. of Medical Genetics Oslo University Hospital Oslo, Norway · Dept. of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, USA +1

Dynamical Systems PDE Discovery Physics-Informed ML

Apr 20, 2026math.NA

Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle

This paper is a step-by-step, self-contained guide to the complete training cycle of a Physics-Informed Neural Network (PINN) -- a topic that existing tutorials and guides typically delegate to automatic differentiation libraries without exposing the underlying algebra. Using a first-order initial value problem with a known analytical solution as a running example, we walk through every stage of the process: forward propagation of both the network output and its temporal derivative, evaluation of a composite loss function built from the ODE residual and the initial condition, backpropagation of gradients -- with particular attention to the product rule that arises in hidden layers -- and a gradient descent parameter update. Every calculation is presented with explicit, verifiable numerical values using a 1-3-3-1 multilayer perceptron with two hidden layers and 22 trainable parameters. From these concrete examples, we derive general recursive formulas -- expressed as sensitivity propagation relations -- that extend the gradient computation to networks of arbitrary depth, and we connect these formulas to the automatic differentiation engines used in practice. The trained network is then validated against the exact solution, achieving a relative

L^2

error of

4.290 \times 10^{-4}

using only the physics-informed loss, without any data from the true solution. A companion Jupyter/PyTorch notebook reproduces every manual calculation and the full training pipeline, providing mutual validation between hand-derived and machine-computed gradients.

Abdeladhim Tahimi

Campus de Engenharias e Ciências Agrárias (CECA), Universidade Federal de Alagoas (UFAL), Rio Largo, Alagoas, 57100-000, Brazil

Backpropagation Physics-Informed ML

Apr 20, 2026cs.LG

Scalable Physics-Informed Neural Differential Equations and Data-Driven Algorithms for HVAC Systems

We present a scalable, data-driven simulation framework for large-scale heating, ventilation, and air conditioning (HVAC) systems that couples physics-informed neural ordinary differential equations (PINODEs) with differential-algebraic equation (DAE) solvers. At the component level, we learn heat-exchanger dynamics using an implicit PINODE formulation that predicts conserved quantities (refrigerant mass

M_r

and internal energy

E_\text{hx}

) as outputs, enabling physics-informed training via automatic differentiation of mass/energy balances. Stable long-horizon prediction is achieved through gradient-stabilized latent evolution with gated architectures and layer normalization. At the system level, we integrate learned components with DAE solvers (IDA and DASSL) that explicitly enforce junction constraints (pressure equilibrium and mass-flow consistency), and we use Bayesian optimization to tune solver parameters for accuracy--efficiency trade-offs. To reduce residual system-level bias, we introduce a lightweight corrector network trained on short trajectory segments. Across dual-compressor and scaled network studies, the proposed approach attains multi-fold speedups over high-fidelity simulation while keeping errors low (MAPE below a few percent) and scales to systems with up to 16 compressor-condenser pairs.

Hanfeng Zhai, Hongtao Qiao, Hassan Mansour +1

Department of Mechanical Engineering, Stanford University, Stanford, CA · Mitsubishi Electric Research Laboratories, Cambridge, MA

Neural Surrogate Modeling Physics-Informed ML Neural ODEs

Apr 20, 2026cs.LG

Dissipative Latent Residual Physics-Informed Neural Networks for Modeling and Identification of Electromechanical Systems

Accurate dynamical modeling is essential for simulation and control of embodied systems, yet first-principles models of electromechanical systems often fail to capture complex dissipative effects such as joint friction, stray losses, and structural damping. While residual-learning physics-informed neural networks (PINNs) can effectively augment imperfect first-principles models with data-driven components, the residual terms are typically implemented as unconstrained multilayer perceptrons (MLPs), which may inadvertently inject artificial energy into the system. To more faithfully model the dissipative dynamics, we propose DiLaR-PINN, a dissipative latent residual PINN designed to learn unmodeled dissipative effects in a physically consistent manner. Structurally, the residual network operates only on unmeasurable (latent) state components and is parameterized in a skew-dissipative form that guarantees non-increasing energy for any choice of network parameters. To enable stable and data-efficient training under partial measurability of the state, we further develop a recurrent rollout scheme with a curriculum-based sequence length extension strategy. We validate DiLaR-PINN on a real-world helicopter system and compare it against four baselines: a pure physical model (without a residual network), an unstructured residual MLP, a DiLaR variant with a soft dissipativity constraint, and a black-box LSTM. The results demonstrate that DiLaR-PINN more accurately captures dissipative effects and achieves superior long-horizon extrapolation performance.

Youyuan Long, Gokhan Solak, Arash Ajoudani

Human-Robot Interfaces and Interaction Lab, Istituto Italiano di Tecnologia, 16163 Genoa, Italy

Dynamical Systems Residual Learning Nonlinear System Identification Physics-Informed ML

Apr 19, 2026cs.LG

Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data

Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. In this work, we address the problem of learning symbolic representations of nonlinear Hamiltonian dynamical systems under extreme data scarcity by explicitly incorporating physical structure into the learning architecture. We introduce Adaptable Symplectic Recurrent Neural Networks (ASRNNs), a parameter-cognizant, structure-preserving model that combines Hamiltonian learning with symplectic recurrent integration, avoiding time derivative estimation, and enabling stable learning under noise. We demonstrate that ASRNNs can accurately predict long-term dynamics even when each training trajectory consists of only two irregularly spaced time points, possibly corrupted by correlated noise. Leveraging ASRNNs as structure-preserving data generators, we further enable symbolic discovery using independent regression methods (SINDy and PySR), recovering exact symbolic equations for polynomial systems and consistent polynomial approximations for non-polynomial Hamiltonians. Our results show that such architectures can provide a robust pathway to interpretable discovery of Hamiltonian dynamics from sparse and noisy data.

Vedanta Thapar, Abhinav Gupta

The Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom · Center for Theoretical Physics, St. Stephen’s College, University of Delhi, Delhi 110007, India

Nonlinear System Identification Recurrent Neural Networks Hamiltonian Neural Networks System Identification Physics-Informed ML Hamiltonian Dynamics+1

Apr 19, 2026cs.LG

What Physics do Data-Driven MoCap-to-Radar Models Learn?

Data-driven MoCap-to-radar models generate plausible micro-Doppler spectrograms, but do they actually learn the underlying physics? We introduce a physics-based interpretability framework to answer this question via two proposed complementary metrics: one measures alignment between model predictions and the physics-derived Doppler frequency, while the other tests whether predictions preserve the velocity-frequency relationship under velocity intervention. Both metrics require only MoCap input and model predictions, without access to measured radar data. Experiments across several model architectures reveal that low reconstruction error does not guarantee physical consistency: some, but not all, models achieve low error yet perform poorly on the two physics-based metrics. Further analysis shows that temporal attention is critical for transformer-based models to learn the underlying physics.

Kevin Chen, Kenneth W. Parker, Anish Arora

Computer Science & Engineering The Ohio State University Columbus, Ohio · Unaffiliated Waterford, Virginia

Physics-Informed ML

Apr 18, 2026cs.LG

Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles

Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconstruction of turbulent flow fields from sparse data. However, most existing PINN formulations are deterministic and do not provide reliable quantification of epistemic uncertainty, which is critical for ill-posed problems such as data-driven Reynolds-averaged Navier-Stokes (RANS) modeling. In this work, we develop and systematically evaluate a set of probabilistic extensions of PINNs for uncertainty quantification in turbulence modeling. The proposed framework combines (i) Bayesian PINNs with Hamiltonian Monte Carlo sampling and a tempered multi-component likelihood, (ii) Monte Carlo dropout, and (iii) repulsive deep ensembles that enforce diversity in function space. Particular emphasis is placed on the role of ensemble diversity and likelihood tempering in improving uncertainty calibration for PDE-constrained inverse problems. The methods are assessed on a hierarchy of test cases, including the Van der Pol oscillator and turbulent flow past a circular cylinder at Reynolds numbers Re=3,900 (direct numerical simulation data) and Re = 10,000 (experimental particle image velocimetry data). The results demonstrate that Bayesian PINNs provide the most consistent uncertainty estimates across all inferred quantities, while function-space repulsive ensembles offer a computationally efficient approximation with competitive accuracy for primary flow variables. These findings provide quantitative insight into the trade-offs between accuracy, computational cost, and uncertainty calibration in physics-informed learning, and offer practical guidance for uncertainty quantification in data-driven turbulence modeling.

Khemraj Shukla, Zongren Zou, Theo Kaeufer +2

Division of Applied Mathematics, Brown University, Providence, RI, USA · Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA · Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

Uncertainty Quantification Deep Ensembles Physics-Informed ML Uncertainty Calibration PDE Inverse Problems Computational Fluid Dynamics

Apr 18, 2026cs.CV

Physics-Informed Tracking (PIT)

We propose Physics-Informed Tracking (PIT), a video-based framework for tracking a single particle from video, where a neural network autoencoder localizes a particle as a heatmap peak (landmark) and a differentiable physics module embedded in the autoencoder constrains several landmarks over time (a trajectory) to satisfy known dynamics. The novel Physics-Informed Landmark Loss (PILL) compares this predicted trajectory back against the landmarks, enforcing physical consistency without labels. Its supervised variant (PILLS) instead compares the prediction against ground-truth position, velocity, and bounce from simulation, enabling end-to-end backpropagation. To support supervised and unsupervised learning, we use an autoencoder with a split bottleneck that separates A) tracking-related structure via landmark heatmaps from B) background noise and subsequent image reconstruction. We evaluate a replicated 26 factorial design (n = 4 replicates, 64 configurations), showing that PILLS consistently achieves sub-pixel tracking accuracy for the bilinear and physics-refined decoder outputs under both clean and noisy conditions.

Emil Hovad, Allan Peter Engsig-Karup

Department of Applied Mathematics and Computer Science (DTU Compute) Technical University of Denmark

Point Tracking Visual Object Tracking Physics-Informed ML

Apr 18, 2026math.NA

Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches

This thesis develops numerical and theoretical approaches for understanding and analyzing singularity formation in Partial Differential Equations (PDEs). The singularity formation in the Navier-Stokes Equation (NSE) is famously challenging as one of the seven Clay Prize problems. Unlike simpler equations such as the Nonlinear Heat (NLH) or Keller-Segel (KS) equations, where formal asymptotics near blowup are better understood, the intrinsic complexity of NSE makes quantitative analytical treatment difficult, if not impossible, without numerical guidance. Building on numerical insights, we introduce a robust analytical framework to simplify and systematize pen-and-paper proofs for simpler singular PDEs. We present a novel approach based on enforcing vanishing modulation conditions for perturbations around approximate blowup profiles, complemented by singularly weighted energy estimates. We demonstrate the efficacy of our method on PDEs with complicated asymptotics, such as NLH and the Complex Ginzburg-Landau (CGL) equation, and address the open problem of singularity formation in the 3D KS equation with logistic damping. We develop and refine numerical approaches that facilitate deeper insights into singularity formation. We demonstrate that machine learning methods significantly enhance our capability to identify and characterize potential blowup solutions with high precision. We improve on existing Physics-Informed Neural Network (PINN) and Neural Operator (NO) frameworks. Moreover, we present a novel machine learning paradigm, the Kolmogorov-Arnold Network (KAN) architecture, whose interpretability and excellent scaling properties are achieved through learnable nonlinearities.

Yixuan Wang

CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California · [math.NA]

PDE Solving Kolmogorov-Arnold Networks PDE Operator Learning Physics-Informed ML

Apr 17, 2026cs.LG

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

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

Huan Lin, Lianghui Ding

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

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

Apr 17, 2026cs.NE

Neuromorphic Parameter Estimation for Power Converter Health Monitoring Using Spiking Neural Networks

Always-on converter health monitoring demands sub-mW edge inference, a regime inaccessible to GPU-based physics-informed neural networks. This work separates spiking temporal processing from physics enforcement: a three-layer leaky integrate-and-fire SNN estimates passive component parameters while a differentiable ODE solver provides physics-consistent training by decoupling the ODE physics loss from the unrolled spiking loop. On an EMI-corrupted synchronous buck converter benchmark, the SNN reduces lumped resistance error from

25.8\%

to

10.2\%

versus a feedforward baseline, within the

\pm 10\%

manufacturing tolerance of passive components, at a projected

{\sim}270\times

energy reduction on neuromorphic hardware. Persistent membrane states further enable degradation tracking and event-driven fault detection via a

+5.5

percentage-point spike-rate jump at abrupt faults. With

93\%

spike sparsity, the architecture is suited for always-on deployment on Intel Loihi 2 or BrainChip Akida.

Hyeongmeen Baik, Hamed Poursiami, Maryam Parsa +1

University of Wisconsin–Madison Madison, Wisconsin, USA · George Mason University Fairfax, Virginia, USA

Parameter Estimation Predictive Maintenance Fault Detection Spiking Neural Networks Neuromorphic Computing Physics-Informed ML

Apr 17, 2026cs.LG

PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs

We present PINNACLE, an open-source computational framework for physics-informed neural networks (PINNs) that integrates modern training strategies, multi-GPU acceleration, and hybrid quantum-classical architectures within a unified modular workflow. The framework enables systematic evaluation of PINN performance across benchmark problems including 1D hyperbolic conservation laws, incompressible flows, and electromagnetic wave propagation. It supports a range of architectural and training enhancements, including Fourier feature embeddings, random weight factorization, strict boundary condition enforcement, adaptive loss balancing, curriculum training, and second-order optimization strategies, with extensibility to additional methods. We provide a comprehensive benchmark study quantifying the impact of these methods on convergence, accuracy, and computational cost, and analyze distributed data parallel scaling in terms of runtime and memory efficiency. In addition, we extend the framework to hybrid quantum-classical PINNs and derive a formal estimate for circuit-evaluation complexity under parameter-shift differentiation. Results highlight the sensitivity of PINNs to architectural and training choices, confirm their high computational cost relative to classical solvers, and identify regimes where hybrid quantum models offer improved parameter efficiency. PINNACLE provides a foundation for benchmarking physics-informed learning methods and guiding future developments through quantitative assessment of their trade-offs.

Shimon Pisnoy, Hemanth Chandravamsi, Ziv Chen +4

†Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, Israel. · ‡Corresponding author. · §The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering, Technion Israel Institute of Technology, Haifa, Israel. +2

Neural PDE Solvers PDE Surrogate Modeling Hybrid Quantum-Classical ML Distributed Training Physics-Informed ML

Apr 17, 2026cs.LG

Physics-Informed Neural Networks with Learnable Loss Balancing and Transfer Learning

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or heuristic weighting of physics residuals and data loss, our approach introduces a learnable blending neuron that dynamically adjusts the relative contribution of each term based on their uncertainties. This mechanism enables stable training and improved generalization without manual tuning. To further enhance efficiency, we integrate a transfer learning strategy that reuses representations from related domains and adapts them to new physical systems with limited data. We validate the framework for the prediction of heat transfer in liquid-metal miniature heat sinks using only 87 CFD datapoints, where the adaptive PINN achieves an error <8%, outperforming shallow neural networks, kernel methods, and physics-only baselines. Our framework provides a general recipe for embedding physics adaptively into neural networks, offering a robust and reproducible approach for data-scarce problems across various scientific domains, including fluid dynamics and material modeling.

Reza Pirayeshshirazinezhad

Texas A&M University College Station, TX, USA

Self-Supervised Learning Adaptive Loss Weighting Scientific ML Physics-Informed ML