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

Aug 3, 2026cs.LG

RamanPFN: learning from Raman spectral structure with a tabular foundation model

Raman spectroscopy enables label-free molecular characterization across materials science, analytical chemistry, biomedicine, and industrial process monitoring. However, machine learning for high-dimensional spectroscopy remains constrained by limited labelled data and a mismatch between the physical organization of spectra and feature-agnostic models. Channel coverage alone does not ensure that related bands share a common inference context. Here we present RamanPFN, a general-purpose spectral foundation framework that enables unified in-context inference through physics-guided spectral learning. It captures full-spectrum compositional covariation via Global Compositional Unmixing (GCU), which decomposes distributed, multi-band mixture signatures into shared non-negative latent bases. Simultaneously, it resolves local vibrational structure through Local Vibrational Subspace Encoding (LVSE), which preserves fine-grained peak morphology, intensity fluctuations, and peak shifts within contiguous spectral neighborhoods. Extensive evaluation across 74 diverse public Raman datasets covered 129 regression targets and was further extended to 21 classification tasks. RamanPFN achieved state-of-the-art performance across all reported aggregate metrics against 28 independently reproduced methods spanning chemometrics, spectral neural networks, deep tabular learners and tabular foundation models. RamanPFN establishes a physics-guided paradigm for scientific spectroscopy, enabling data-efficient predictive learning across diverse chemical systems.

Xingyu Pan, Huan Wang, Jinjia Guo +3

Beihang University · Cleer Science

Tabular Foundation Models Representation Learning Physics-Informed ML Raman Spectroscopy Spectral Methods

Aug 3, 2026physics.med-ph

Cardiovascular Digital Twins from Physics Based to Data Driven Approaches

Cardiovascular digital twins aim to create patient-specific computational models that evolve with clinical data to support diagnosis, prognosis, and therapy optimisation. Mechanistic models provide physiological interpretability but remain computationally demanding, whereas data-driven approaches improve scalability yet risk limited robustness. Emerging physics-informed, graph-based, and hybrid methods integrate physical constraints with relational learning across vascular networks. We review modelling paradigms, data assimilation frameworks, validation challenges, and translational pathways toward clinically deployable cardiovascular digital twins.

Emmanuel Lwele, Francis Chikweto

Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield, United Kingdom. · Medical Engineering and Cardiology Department, Institute of Development, Aging and Cancer (IDAC), Tohoku University, Sendai, Japan.

Data Assimilation Physics-Informed ML Digital Twins

Aug 3, 2026cs.AI

Physics-Informed Neural Networks for Complex Eigenfrequency Identification and Mode Structure Reconstruction of the Ground-State ITG Branch

Physics-informed neural networks (PINNs) combine sparse observations with physical equations, providing an important approach for modeling complex plasma processes and inferring unknown physical quantities. The steep-gradient pedestal of high-confinement-mode tokamaks is closely linked to plasma confinement and edge transport. Analyzing ion-temperature-gradient (ITG) drift waves in this region requires jointly identifying complex eigenfrequencies and reconstructing two-dimensional complex-valued mode fields. Localized high-frequency oscillations, strong real-imaginary coupling, and nonlinear coupling between the mode field and eigenfrequency challenge PINN representation and joint optimization. To address these challenges, we propose a physics-informed neural framework combining Fourier feature encoding, complex-valued feature propagation, and three-stage training. Under sparse observations and physical constraints, it jointly solves for the complex eigenfrequency and mode field of a representative ground-state ITG branch. Experiments show that the framework accurately recovers the target complex eigenfrequency and two-dimensional complex-valued mode field and outperforms representative PINN baselines. It also provides a basis for analyzing higher-order and multiple-branch drift-wave modes.

Dengdi Sun, Bingbing Zhang, Xiao Wang +5

School of Artificial Intelligence, Anhui University, Hefei, China · School of Computer Science and Technology, Anhui University, Hefei, China · School of Physics and Electronic Information, Anhui Normal University, Wuhu, China +1

Neural PDE Solvers Physics-Informed ML

Aug 1, 2026cs.LG

Adaptive Quantum Physics-Informed Neural Networks for Differential Equations with Applications to Fluid Dynamics

Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems. Here, we present a hybrid quantum-classical framework that enhances Quantum PINNs (QPINNs) through adaptive collocation point sampling and loss-aware attention mechanisms. By dynamically prioritizing points in regions with large PDE residuals or steep solution gradients, our method mitigates the spectral bias inherent in conventional PINNs. Current Quantum Physics-Informed Neural Networks are commonly assumed to be limited by the expressive power of quantum circuits. In our work, we observed that, across diverse differential equations, optimization - not only expressivity - can be an important bottleneck. Furthermore, a trainable loss-weighting scheme balances contributions from physics residuals, boundary conditions, and data fidelity during training. Integrating these strategies with quantum computing techniques (including variational quantum circuits and quantum gradient estimation) can yield at least a 60% improvement in solution accuracy under specific regimes for benchmark fluid flows and reaction-diffusion systems. Finally, we argue that merely increasing model expressivity is insufficient for resolving complex PDEs via QPINNs, as they remain constrained by the structural optimization limitations of classical PINNs. This framework provides a scalable pathway for quantum-enhanced scientific machine learning, bridging physics-based modeling with emerging quantum computational capabilities.

Fabio Pereira dos Santos, Renato Portugal, Júlio de Castro Vargas Fernandes +1

Coordination of Mathematical and Computational Methods National Laboratory of Scientific Computing Av. Getúlio Vargas, 333 - Quitandinha, Petrópolis - RJ, 25651-075 · Center for Computation and Technology - Louisiana State University, 888 S. Stadium Dr., Baton Rouge, LA 70808, USA

PDE Solving Hybrid Quantum-Classical ML Adaptive Sampling Physics-Informed ML

Aug 1, 2026cs.LG

An Embedded RISC-V Evaluation of Kolmogorov--Arnold Networks in Hard-Constrained Recurrent Physics-Informed Models

Hard-constrained recurrent physics-informed networks (HRPINNs) embed known dynamics inside a recurrent numerical integrator and restrict a neural branch to learning only the residual dynamics that the first-principles model does not capture. Kolmogorov--Arnold Networks (KANs) have been proposed as parameter-efficient replacements for multilayer perceptrons (MLPs) in such residual branches, but their learnable B-spline activations follow a markedly different execution profile. Building on prior work that characterized when a vanilla B-spline KAN matches or underperforms an MLP as an HRPINN residual branch in discovery accuracy, this paper asks whether that parameter efficiency survives deployment. Using identical trained weights, we measured execution latency, energy per integration step, and dependability under post-training quantization in the closed recurrent loop on a RISC-V RV64GC platform without vector extensions (StarFive VisionFive~2, SiFive U74). For the two accuracy-comparable pairs, the KAN residual branch executed

13.5\times

and

8.0\times

slower and consumed

11.3\times

and

5.6\times

more energy per integration step (3.7,

μ

J against 0.33,

μ

J for the smallest pair); across all four parameter-matched size tiers the ranges are

4.7\times

--

14.5\times

and

4.7\times

--

18.7\times

. Under INT8 quantization, KAN trajectories diverged up to

43\times

earlier than matched MLPs; the damage traces to weight quantization, not to input-side knot-interval misassignment. These results indicate that the parameter efficiency reported for KANs does not transfer to deployment cost on scalar embedded cores, and that an MLP residual branch is the more dependable default for embedded HRPINN deployment unless specific quantization co-design is used.

Enzo Nicolas Spotorno, Josafat Leal Filho

Department of Informatics and Statistics - Graduate Program in Computer Science (PPGCC)

Efficient Neural Network Inference Kolmogorov-Arnold Networks Physics-Informed ML On-Device Inference

Jul 31, 2026cs.LG

A Physics-Chemistry-Informed Neural Network (PCINN) for Real-Time Spatial-ALD Coverage Prediction and Reliable Kinetics Inversion

Spatial atomic layer deposition (SALD) is a leading atmospheric-pressure, high-throughput route to industrial ALD, but design and control are limited by the cost of predicting surface coverage: high-fidelity CFD is far too slow for operating-window scans, while analytic models miss transport modulation such as the gas curtain. We present a physics-chemistry-informed neural network (PCINN), a hybrid surrogate with CFD-level accuracy at real-time speed: a query returns coverage in about 7 ms, roughly 5x10^4 times faster than a CFD solve, reaching a test R^2_log = 0.998 (leave-one-out R^2_raw = 0.974) from only 30 training cases spanning four orders of magnitude in coverage. The architecture is not a black box: a small network learns only the operating-condition to near-wall concentration closure, while the known surface kinetics is a hard-coded, trainable chemistry layer integrated along the substrate trajectory. This single-scalar bottleneck keeps it accurate under sparse data, interpretable and invertible. We add a full identifiability analysis (Fisher information, profile likelihood). The adsorption energy E_ads and desorption rate k_des are robustly identifiable; k_ads is not separately identifiable at a single temperature (only k_ads*c_wall is). Across four temperatures the prefactor nu and E_ads bind along a weakly identifiable degeneracy valley of slope 0.065 eV/decade, derived analytically as k_B T_eff ln(10) and turned into a reliability diagnostic: a seven-chemistry mismatch matrix shows it is invariant under any single-Arrhenius mismatch and shifts only when a second thermally activated process appears, so a slope departure flags unmodelled site heterogeneity. Data come from simulation with known ground truth inverted by the same kinetic form, so the study verifies pipeline self-consistency and the identifiability boundary, not real parameters.

Ning Hu, Chang Liu, Yunlei Jiang +1

School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou, China · Information Engineering School, Hangzhou Dianzi University, Hangzhou, China

Neural Surrogate Modeling Parameter Identifiability Semiconductor Manufacturing Model Calibration Physics-Informed ML

Jul 31, 2026cs.LG

PiDDM: Physics-Informed Differentiable Degradation Modeling for Lithium-Ion Battery State-of-Health Prediction

Accurate prediction of lithium-ion battery state of health (SOH) is essential for reliable energy storage operation. However, purely data-driven models may generalize poorly across cycling protocols and produce physically implausible behavior during long-term extrapolation. We developed a physics-informed differentiable degradation modeling framework (PiDDM) for battery SOH prediction. PiDDM incorporates empirical Arrhenius degradation kinetics associated with solid electrolyte interphase growth and loss of lithium inventory into the training objective, encouraging physically consistent capacity fade under diverse operating conditions. The framework was evaluated using a public dataset of 55 batteries cycled under six operating protocols. PiDDM achieved the lowest average prediction error among the evaluated models and substantially reduced mean squared error relative to a multilayer perceptron and a baseline physics-informed neural network. For extrapolation, the models were trained on the first 90% of each battery's cycle life and evaluated on the unseen final 10%. PiDDM captured accelerated end-of-life degradation while avoiding the nonphysical capacity regeneration produced by the baseline models. These results show that incorporating degradation physics into neural network training improves predictive accuracy and physical consistency, providing a promising approach for practical battery health monitoring.

Zeping Chen, Ruda Jian, Sachin Sigdel +3

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN, USA · Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, USA · Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA +1

RUL Estimation Physics-Informed ML Lithium-Ion Batteries

Jul 30, 2026math.DG

A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem

This proceedings contribution elaborates on the findings of arXiv:2605.26234v2: a joint work with Marco Usula, where we introduced a machine learning framework based on physics-informed neural networks (PINNs), aimed at constructing near-minimal discs in hyperbolic space asymptotic to a prescribed knot at infinity. We used this method to provide numerical evidence for a conjecture of Joel Fine relating minimal surfaces in

H^{4}

to the coefficients of the HOMFLY polynomial. This is a methodological companion to that paper, based on a presentation given at the 2026 edition of the workshop "DANGER: Data, Numbers, and Geometry". Rather than reviewing the results, which are presented extensively in the preprint above, we discuss the two aspects of the framework which, in our experience, determined whether the method worked at all. First, the geometry of the problem must be encoded in the architecture of the model, so that the boundary condition and asymptotics at infinity hold exactly for every value of the learnable parameters - leaving us with a single-component loss function; second, the evaluation of the PDE residual must be engineered with care to ensure that complete trainings can be performed in a reasonable time. On the latter point, we describe two implementation techniques which are not spelled out in detail in the original paper: replacing nested reverse-mode automatic differentiation with the forward propagation of second-order jets, and compiling the computational graph of the residual once instead of rebuilding it at every optimisation step. Together, on identical hardware, these two changes reduce the cost of a training step by a factor of roughly forty to fifty. We hope these methodological discussions can be useful for researchers in differential geometry and geometric analysis who wish to deploy PINNs on problems of their own.

Tancredi Schettini Gherardini

University of Bonn and Max Planck Institute for Mathematics, Bonn, Germany.

Physics-Informed ML

Jul 30, 2026cs.LG

Chem World: A Large-Scale Benchmark and Physics-Informed Framework for Trustworthy Chemical Property Prediction

Chemical property prediction plays a critical role in accelerating scientific discovery in chemistry, materials science, and drug development. However, existing benchmarks often suffer from limited task diversity, fragmented datasets, and inconsistent evaluation protocols, making it challenging to systematically assess the reliability and generalization of AI models. In this work, we introduce Chem World, a comprehensive benchmark for chemical property prediction that integrates 17 diverse chemical datasets with over 800,000 molecular samples, covering various properties including density, electrical conductivity, solubility, and other molecular characteristics. Chem World provides a unified platform for evaluating AI models across multiple property prediction tasks. Furthermore, we propose Mixture-PINN, a physics-informed neural network based prediction framework that incorporates chemical prior knowledge into data-driven learning, improving the accuracy, robustness, and reliability of chemical property prediction. Extensive experiments on Chem World demonstrate the effectiveness of our approach compared with existing methods. By combining large-scale standardized evaluation with physics-informed learning, Chem World establishes a foundation for developing trustworthy AI systems for computational chemistry and advancing AI-driven scientific discovery.

Tianyou Bai, Huan Wang, Mingchen Gao +4

1Cleer Science · Institute of Automation, Chinese Academy of Sciences · Department of Chemistry, Imperial College London +1

Physics-Informed ML Molecular Property Prediction

Jul 30, 2026math.AP

Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation

We study fractional parabolic initial-value problems with lower-order drift and potential terms in anisotropic spectral Barron spaces, defined by weighted space--time Fourier

L^1

norms adapted to parabolic scaling. We prove existence, uniqueness, and maximal regularity with a gain of one derivative in time and

γ

derivatives in space, where

γ>0

is the order of the fractional Laplacian. The evolution is defined only for

t\geq0

, whereas the finite-time norm requires a global extension with sufficient temporal Fourier decay. We construct a finite reflected semigroup extension using a Vandermonde system to match derivatives at

t=0

, obtaining temporal Fourier estimates uniform in the semigroup parameter. Combined with Fourier multiplier estimates for the damped principal operator, it yields maximal regularity. Dimension-independent multiplication estimates support a finite regularity bootstrap, while interpolation and sufficient damping absorb the lower-order terms in the base estimate. The a priori estimate and the method of continuity yield maximal regularity without smallness assumptions on the lower-order coefficients. A frequency-localized counterexample shows that a uniform-in-time spatial Barron bound on the forcing does not imply the corresponding two-derivative solution bound, even for the one-dimensional heat equation. Using this regularity, Fourier sampling yields

n^{-1/2}

approximation rates for the solution in mixed space--time Sobolev norms using shallow networks with suitable activations. Sampling in a product Hilbert space yields a population-level PINN consistency estimate for shallow cosine networks on a bounded cylinder. There exists a single width-

n

network for which the sum of the squared mixed-Sobolev solution error, the squared

L^2

-norm of the residual for the whole-space fractional equation, and the squared initial-data error is

O(n^{-1})

.

Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2

Neural PDE Solvers PDE Solving Neural Network Approximation Theory Physics-Informed ML

Jul 30, 2026cs.LG

Event-Structured Physics-Informed Neural Networks for Differentiable Critical Clearing Boundaries

Transient-stability assessment determines whether a power system can recover after a disturbance and is therefore essential to preventing generator trips and cascading outages. A key metric is the critical clearing time (CCT), which specifies the maximum time available to clear a fault before synchronism is lost. Reliable CCT estimation is challenging because complicated fault-clearing dynamics require repeated simulations over many fault severities and clearing times. We propose an event-structured physics-informed neural network (ES-PINN) that aligns its representation with the pre-fault, fault-on, and post-clearing swing dynamics and enforces exact state chaining across event interfaces. A smooth trajectory-induced stability margin defines a differentiable approximation of the CCT boundary, enabling accurate boundary extraction, local sensitivity analysis, and optional direct CCT prediction through a distilled readout. We further prove a local residual-to-trajectory-to-CCT error estimate, in which exact event chaining eliminates separate state-interface defect terms. Experiments on IEEE 9-, 14-, and 30-bus systems show that ES-PINN consistently improves held-out trajectory and stability-boundary accuracy over matched neural-surrogate baselines across mechanical and electrical contingencies with multiple clearing configurations. Additional full-network DAE validation, multi-fault experiments, and runtime analyses further demonstrate the effectiveness and computational efficiency of the proposed framework.

Baoli Hao, Chenxi Hu, Ming Zhong +1

Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA · Department of Computer Science, The Hang Seng University of Hong Kong, Sha Tin, Hong Kong · Department of Mathematics, University of Houston, Houston TX 77204, USA +1

Neural Surrogate Modeling Physics-Informed ML Power Systems

Jul 29, 2026math.NA

Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem

We develop two parametric data-driven reduced models: a physics-informed neural network (PINN) and a non-intrusive tensorial reduced-order model (TROM), and apply both approaches to the parametrized one-dimensional shallow-water dam-break problem. Neither reduced model requires time integration: both learn a direct parameter-to-solution map from space, time, and dam-break parameters to the physical state, with the PINN providing predictions at arbitrary times and the TROM reconstructing solutions at the stored snapshot times. In addition, we demonstrate that it is essential to introduce shock-aware collocation to improve the robustness of the PINN model.

Anton Myshak, Md Rezwan Bin Mizan, Ilya Timofeyev

Dept. of Mathematics, University of Houston, Houston, TX 77204

PDE Surrogate Modeling Reduced-Order Modeling Physics-Informed ML Computational Fluid Dynamics

Jul 29, 2026stat.ML

PIKS: Universal Physics-Informed Kernel Methods

Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models. While physics-informed neural networks (PINNs) dominate empirical applications, the complexity of neural network architectures and optimization landscapes hinders the development of a corresponding learning theory. In turn, kernel methods offer an appealing alternative with closed-form solutions and analytical tractability, yet existing guarantees primarily cover the well-specified setting where the target belongs to the native Reproducing Kernel Hilbert Space (RKHS). This imposes unrealistic regularity assumptions that physical targets often fail to satisfy. In this paper, we introduce and analyze Physics-Informed Kernel methodS (PIKS). We establish the universal consistency of PIKS for linear differential constraints, proving that for universal kernels (such as Gaussian or Matérn), the estimator asymptotically learns the target while satisfying physical constraints. We further derive finite-sample bounds under suitable source conditions. Our analysis is based on extending classical operator-theoretic analysis of kernel methods to physics-informed machine learning. Numerical experiments demonstrate that PIKS can be competitive with PINNs and traditional finite element methods.

Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria +1

MaLGa Center, DIBRIS, Università degli Studi di Genova, Genoa, Italy · MaLGa Center, DIMA, Università degli Studi di Genova, Genoa, Italy · Istituto Italiano di Tecnologia, Genoa, Italy

Kernel Methods Physics-Informed ML Statistical Learning Theory

Jul 29, 2026cs.AI

EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics. While Large Language Models (LLMs) offer a promising avenue for automated design, unconstrained code generation often yields mathematically invalid or numerically unstable solutions under strict scientific computing constraints. To bridge this gap, we propose \textbf{EvoPINN}, an agentic framework that reformulates PINN development from labor-intensive manual design into a rigorous, execution-grounded algorithm discovery problem. EvoPINN navigates a modular search space by decoupling neural representations from training programs, utilizing an LLM agent to iteratively propose memory-conditioned programmatic modifications. To ensure scientific validity, all candidates undergo strict structural verification and budget-matched PDE evaluation. Extensive experiments across diverse PDE regimes (oscillatory, elliptic, dissipative, and nonlinear transport) demonstrate that EvoPINN discovers PDE-specialized learning algorithms that significantly reduce relative

L_{2}

error compared to baselines. Crucially, EvoPINN autonomously invented SLRC-PINN, a novel architecture whose performance gains persist under rigorous parameter-matched comparisons, establishing the viability of execution-grounded agents for discovering genuinely new scientific computing mechanisms.

Peng Yin, Kai Li, Yifan Zhang +1

School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China · Institute of Automation, Chinese Academy of Sciences, Beijing, China

Automated Algorithm Discovery LLM-Based Program Synthesis Physics-Informed ML Large Language Model-Guided Scientific Discovery

Jul 28, 2026cs.CV

Where Physics Meets Privacy: Federated PINNs for Privacy-Preserving Brain Tumor Biomechanical Modeling

Brain tumors such as glioma, meningioma, and pituitary adenoma alter the mechanical behavior of soft brain tissue, yet common diagnostic methods rely on static imaging that cannot capture tumor growth, tissue displacement, or changes in stiffness over time. Deep learning models for this task typically require pooling patient data at one site, which conflicts with privacy rules such as GDPR and HIPAA and limits generalization across institutions, a challenge that is pronounced in neuro oncology given patient diversity. This study presents a federated physics informed neural network combining federated learning with a physics informed loss built on the equations of linear elasticity. Three simulated clinical sites each train a local network on patient specific MRI data using a physics informed loss, and only model weights are shared with a central server through the FedAvg protocol over one hundred rounds, keeping raw data at its site of origin. The federated model reached an overall accuracy of 91.4%, against 90.0% for a non federated baseline trained on pooled data, an average AUC of 0.985 across tumor classes, and a rise in pituitary tumor accuracy from 85.6 to 94.5%. Training produced smooth, divergence free displacement fields consistent with expected tissue deformation, showing that federated training can be paired with physics based constraints without a meaningful loss in performance.

Mahmuda Akter Sristy, Md Al-Mahfuz Chowdhury, Momota Ahsana Meem +2

Dept. of Computer Science and Engineering, United International University Dhaka, Bangladesh

Privacy-Preserving ML Oncology Physics-Informed ML Federated Learning

Jul 28, 2026cs.LG

Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks. However, their reliance on computationally expensive gradient-based optimization and deep architectures often results in slow training, high computational cost, and limited scalability. In this work, we propose a novel physics-informed broad learning system (PI-BLS), the first physics-informed learning framework based on broad RdNNs. The proposed formulation embeds the governing differential operator and the associated initial and boundary constraints directly into a linear output-layer optimization problem, thereby replacing nonlinear gradient-based training with a deterministic least-squares solution obtained via the pseudoinverse. Consequently, the entire learning process is reduced to a single linear optimization stage while preserving the underlying physical constraints. As a result, PI-BLS offers an efficient learning paradigm for a physics-informed learning framework for solving PDEs that eliminates iterative backpropagation while preserving the underlying physical constraints. Experimental results on representative forward PDE benchmarks demonstrate that PI-BLS achieves competitive and often superior performance with reduced training time and model parameters compared with conventional PINNs.

Pinki Khatun, M. Sajid, Abhinav Jha +1

Department of Industrial Engineering, Università degli Studi di Firenze, Viale Morgagni 40/44, 50134 Firenze, Italy · Department of Mathematics, Indian Institute of Technology Indore, Indore 453552, India · Department of Mathematics, Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar, 382055, Gujarat, India

Neural PDE Solvers PDE Solving Physics-Informed ML

Jul 28, 2026cs.LG

GeoID-PINN: Identifiability-Aware Regional Epidemic Inference with Geographic Coupling

Regional surveillance data reflect local transmission, reporting, seeding, and external infection pressure, which are difficult to identify separately. We introduce GeoID-PINN, a physics-informed neural network (PINN) for susceptible-infectious-recovered-deceased (SIRD) dynamics. The model represents spatial dependence with a row-stochastic source-composition matrix whose rows assign nonnegative source weights that sum to one. We regularize this matrix toward a spatial prior constructed from distance, adjacency, commuting, or lead-lag information. In a four-region simulation with known truth, a compatible distance prior gives source-composition error 0.099. The error rises to 0.159 without regularization and 0.577 under a strongly misspecified prior, while trajectory fit and transmission-scale estimates remain similar. Accurate trajectories therefore do not guarantee recovery of the regional dependence structure. We also evaluate GeoID-PINN retrospectively using COVID-19 data from 64 Louisiana counties. Relative to an autoregressive negative-binomial baseline, Forecast-Trained Geo-PINN reduces mean squared error (MSE) from 32,957 to 11,468 and mean absolute error (MAE) from 70.60 to 57.73. The baseline has lower negative log likelihood (NLL), 5.158 versus 5.346, indicating better distributional fit but worse point accuracy. In a controlled 15-county comparison, county adjacency reduces MSE by 6.85 percent and MAE by 3.1 percent. Similar performance across plausible priors supports structured regularization but not unique edge recovery. These results require prior-sensitivity and observation-model checks before interpretation.

Weixiong Hua, Fan Bu

Department of Biostatistics · University of Michigan · Ann Arbor, Michigan, USA

Epidemic Forecasting Parameter Identifiability Physics-Informed ML

Jul 27, 2026cs.NE

Fourier Feature Physics-Informed Neural Networks for Elasto-Plastic Analysis of Geomaterials with a Non-Associative Mohr-Coulomb Model

Elasto-plastic boundary value problems in geotechnical engineering are conventionally solved by the Finite Element Method (FEM), which incurs high computational cost from incremental-iterative procedures. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative but suffer from spectral bias, failing to resolve the sharp gradients arising at elastic-plastic boundaries and within localized plastic zones. This limitation is particularly consequential for the non-associative Mohr-Coulomb model, whose pressure-dependent yield surface and dilatant flow rule generate narrower plastic zones and steeper stress gradients than pressure-independent criteria. This study proposes a Fourier Feature Physics-Informed Neural Network (FF-PINN) for two-dimensional elasto-plastic problems governed by this model. Random Fourier feature mapping is embedded into the input layer to mitigate spectral bias, supported by a multi-objective loss function enforcing equilibrium, constitutive relations, and Karush-Kuhn-Tucker conditions against high-fidelity FEM data, together with a strain-adaptive sampling strategy. Benchmarked across three test cases, FF-PINN achieves superior accuracy across most predicted fields, with error reductions up to approximately 66 percent in displacement and 27 percent in stress components, and reproduces the plastic failure zone geometry with markedly closer fidelity to FEM. Sensitivity analysis confirms robustness across training data size, collocation density, loss weighting, and noise levels up to 2.0 percent. FF-PINN converges in half the training epochs required by the conventional PINN, halving wall-clock training time while achieving greater predictive accuracy. The framework therefore offers a computationally efficient and physics-consistent alternative to FEM for elasto-plastic geotechnical analysis.

Apisit Robjanghvad, Sompote Youwai

AI research group, Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Thailand

Materials Science Physics-Informed ML

Jul 27, 2026cs.LG

Physics-Informed CNN-LSTM for Street-Scale Urban Flood Prediction: Reconciling Aggregate Accuracy and Street-Level Plausibility

Deep learning surrogate models trained with mean-squared-error loss produce statistically accurate but physically unconstrained flood predictions: water may flow uphill, appear spontaneously, or smooth over street-level corridors. We develop a physics-informed training framework for CNN-LSTM models that predict urban flood depths at 15 min intervals over a 128x128 spatial grid. Three differentiable penalty terms are embedded into the loss: (i) a gravity loss penalizing depth increases against the water-surface-elevation gradient, (ii) a continuity loss enforcing local mass conservation with rainfall-adaptive thresholds, and (iii) a topography-aware false-alarm penalty modulated by the topographic wetness index (TWI). We evaluate on the Norfolk, Virginia flood dataset spanning two storm events (August 2017 and September 2022, 300 samples), with all variants trained on identical splits and robustness assessed over repeated random splits and leave-one-storm-out tests. A road-proximal evaluation restricted to a TWI-derived street mask quantifies street-level skill. The physics-constrained model achieves near-zero gravity violations (order 1e-6) and the highest street-channel recall (0.77 +/- 0.09 vs 0.44 +/- 0.10 for the unconstrained baseline), the capability most relevant to traffic routing, and its advantage more than doubles on a held-out storm; a uniform false-alarm variant attains 16% lower mean absolute error but suppresses street recall to 0.25. The TWI-modulated penalty reconciles this trade-off: it improves on the uniform variant on every metric, recovering 60% higher street recall at the lowest MAE among constrained variants and the best street-level F1. These results expose a fundamental tension between aggregate pixel-level error and application-specific physical plausibility, and show that terrain-aware loss modulation offers a principled resolution.

Luc DCosta, Yidi Wang, Jonathan L. Goodall +1

Chandra Robot Autonomy Lab, Department of Computer Science, University of Virginia, Charlottesville, VA 22904, USA · Link Lab, Multidisciplinary Research Center, University of Virginia, Charlottesville, VA 22904, USA · Hydroinformatics Research Group, Department of Civil and Environmental Engineering, University of Virginia, Charlottesville, VA 22904, USA

Convolutional RNNs Flood Inundation Mapping Physics-Informed ML Flood Forecasting

Jul 27, 2026cs.LG

Lantern: Conflict-Aware Gradient Blending for Physics-Guided Diffusion Models in Calorimeter Simulation

Monte Carlo simulation of calorimeter showers is a principal bottleneck for the High-Luminosity LHC, and diffusion models have emerged as fast, high-fidelity surrogates. Their denoising objective is purely statistical, however: a model can minimize it while placing the physics wrong. Existing physics-informed generative methods cannot close this gap, because they assume a closed-form law, a governing PDE residual or a hard per-sample constraint, that a shower does not supply: no per-sample PDE governs a stochastic cascade, and energy conservation fixes only one scalar per shower. Standard metrics ignore the correlation structure across calorimeter layers and voxels, comparing showers only in a physics feature space. We address both gaps. We introduce the Correlation Frobenius Distance (CFD), a single normalized score for correlation fidelity at layer-wise and voxel-wise scales. We then encode the soft per-sample structure available in a shower as two physics-aware auxiliary losses: a variance-stabilized voxel residual loss grounded in counting statistics, and a graph Laplacian loss over the detector geometry. We combine both with denoising through GradBlend, which anchors the step magnitude to the denoising gradient while letting the auxiliary steer its direction, yielding Lantern, a physics-guided diffusion surrogate. On CaloChallenge Dataset 2, injecting the physics losses through task-symmetric rules such as PCGrad, GradNorm, IMTL-G, and ConFIG inflates FPD by 2-100x relative to denoising alone, whereas GradBlend admits the same signal without regression and, with the Laplacian loss, Lantern improves both FPD and CFD. Our ablation on the auxiliary loss scheduler shows that the voxel residual loss, whose gradient conflicts with denoising, requires a terminal denoising-only phase to preserve shower fidelity, whereas the non-conflicting Laplacian loss is insensitive to the schedule.

Farzana Yasmin Ahmad, Vanamala Venkataswamy, Geoffrey Fox

Computer Science Department, University of Virginia USA · Visiting Scholar, University of Virginia USA · Computer Science Department, Biocomplexity Institute, University of Virginia USA

Physics-Informed Generative Modeling Gradient Interference Physics-Informed ML Physics-Based Simulation Diffusion Models

Jul 27, 2026cs.LG

Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs

The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing field of scientific machine learning. In these methods, a neural network is trained to approximate the PDE solution by using (stochastic) gradient descent to minimize the PDE residual of the neural network. Due to the non-convexity of the PDE residual objective function, the trained neural network may, in principle, only converge to a local minimizer of the objective function (which would not be a solution of the PDE). Therefore, there is a longstanding question regarding the mathematical foundations of these algorithms, and it is highly valuable to establish that the trained neural network will converge to the PDE solution. In this paper, we consider a class of semilinear PDEs with nonlinearities in the solution and its first derivative. For this class of PDEs, we prove that neural networks trained with gradient descent to minimize the PDE residual objective function will converge to the PDE solution as the network width and training time

\rightarrow \infty

.

Justin Sirignano, Konstantinos Spiliopoulos, Samuel Cohen

Mathematical Institute, University of Oxford · Department of Mathematics and Statistics, Boston University

Neural PDE Solvers Optimization Convergence Analysis PDE Solving Physics-Informed ML

Jul 27, 2026cs.CV

ELECTRIC: Evidential Learning-Enhanced CT Reconstruction via Iterative Correction

Here we introduce ELECTRIC (Evidential Learning-Enhanced CT Reconstruction via Iterative Correction), a physics-guided Bayesian formulation. An evidential neural network provides an image proposal and an error-predictive epistemic-uncertainty surrogate. The latter is converted into an adaptive precision field and inserted into a Poisson-weighted MAP update. The resulting image-evidence-precision-reconstruction loop treats prior confidence as a learned state variable of iterative reconstruction. In addition to the formulation and theoretical analysis, we report two simulation studies on image slices from the AAPM Mayo Clinic Low-Dose CT dataset: a mechanism-validation pilot using transparent surrogate estimators, and a feasibility study in which a trained Normal-Inverse-Gamma evidential network drives the full closed loop. On held-out patients, the learned prior mean reduces reconstruction error by roughly 70 percent relative to filtered back-projection, the learned epistemic uncertainty is error-predictive and supports selective trust, and the physics-guided update restores measurement consistency while the adaptive-precision reconstruction matches or exceeds a validation-tuned fixed prior and remains markedly more robust to prior-strength misspecification. Together these results demonstrate the complete ELECTRIC closed-loop pipeline, while identifying formal uncertainty calibration and joint training as the principal directions for future work.

Ge Wang

Department of Biomedical Engineering Department of Electrical, Computer and Systems Engineering Department of Computer Science Rensselaer Polytechnic Institute, Troy, New York, USA

Evidential Deep Learning Bayesian Inverse Problems Physics-Informed ML Computed Tomography Epistemic Uncertainty

Jul 27, 2026cs.LG

Variational Boosting for Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution. However, monolithic PINNs often suffer from ill-conditioning, spectral bias, and optimization instability. We introduce a variational boosting framework in which solutions are constructed additively in function space. Each stage trains a weak learner whose converged correction satisfies a local orthogonality condition, equivalent to a projected functional gradient descent step onto the tangent space of the network's function manifold. Because each correction network is deliberately small, the restricted minimization admits full Newton or conjugate gradient updates, which are typically infeasible in large PINNs. The resulting method separates global nonlinear refinement into a sequence of well-conditioned subproblems while preserving the full variational structure of the operator. This framework provides a geometric interpretation of multi-stage PINNs as projected functional gradient descent and enables stable second-order optimization for nonlinear differential equations.

Kaylee Vo, Pavlos Protopapas

Harvard University

Ensemble Learning PDE Solving Second-Order Optimization Physics-Informed ML

Jul 26, 2026cs.LG

Physics-Informed Neural Networks for Predicting Nitrous Oxide Flux

Nitrous oxide (N

_2

O) is the dominant ozone-depleting substance emitted in the 21st century, and the third largest contributor to anthropogenic greenhouse gases due to its high potency and long atmospheric lifetime, with more than 70% of N

_2

O emissions occurring as a result of agricultural processes. Current approaches to predicting N

_2

O flux emissions include process-based models such as DayCent and Cycles, as well as classical AI models, but the application of Physics-Informed Neural Networks (PINNs) to predicting N

_2

O flux emissions is largely underexplored. Our paper draws upon the mechanistic equations that underlie the DayCent family of process-based models to construct a rigorously derived, literature-traceable physics residual. We then build and train an MLP-based PINN on a multi-site agricultural dataset spanning four geographically distinct US agricultural sites. Across all tested values of the physics loss weighting hyperparameter

λ

, our PINN consistently and substantially outperformed uncalibrated Cycles simulation (R

^2=0.01

), with our MLP baseline achieving mean R

^2=0.411

across ten random seeds. Physics constraints consistently degrade model performance in holdout validation, with marginal degradation at low

λ

and significant degradation at high

λ

, but consistently improve model performance and reduce performance variability in leave-one-site-out validation. This suggests that physics constraints sacrifice in-distribution accuracy for out-of-distribution robustness, anchoring the model toward biogeochemically plausible behavior on unfamiliar soil conditions --- though cross-site generalization remains challenging, with negative R

^2

across all seeds and

λ

values on our geographically distinct held-out site.

Freddy Yu, Jashanjeet Kaur Dhaliwal, Subhadeep Chakraborty

Harvard University · Department of Biosystems Engineering and Soil Science University of Tennessee · Department of Mechanical and Aerospace Engineering University of Tennessee

Climate Science Physics-Informed ML

Jul 26, 2026cs.LG

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system. Constituting a cornerstone of scientific advancement, it has become during the past decade a major line of research in the rapidly evolving field of Physics-informed Machine Learning (PiML). Among the remaining open problems to address in this domain, the post-hoc evaluation of discovered PDEs raises the particular difficulty of being multifaceted. Indeed, it requires jointly considering predictive accuracy, physical consistency, interpretability, and out-of-distribution generalization capacity. Given that some of these properties are conflicting, it is worth noting that the wide range of existing evaluation metrics only partially address the overall problem, potentially leading to overly interpreted conclusions about the validity of a presumed new physical theory. From an abundant literature spanning machine learning, numerical analysis, information theory or symbolic regression, we propose, to our knowledge, the first taxonomy of PDE evaluation metrics, and discuss their advantages and limitations in depth. Based on the observation that evaluation is often achieved on a case-by-case basis and that a universally accepted methodology remains elusive, we further provide recommendations with the aim of promoting standardized and reliable practices, before sketching promising future lines of research in this field. We argue that this paper is intended both for ML experts who design new PDE discovery algorithms and for users of these methods aiming, in real applications, to discover and validate well-founded scientific laws.

Baptiste Mathevon, Farah Cherfaoui, Amaury Habrard +1

Université Jean Monnet Saint-Étienne, CNRS, Institut d’Optique Graduate School, Inria, Laboratoire Hubert Curien UMR 5516, F-42023, SAINT-ÉTIENNE, France · Institut Universitaire de France (IUF)

PDE Discovery Physics-Informed ML

Jul 26, 2026cs.LG

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem

Locating periodic solutions of chaotic dynamical systems normally requires an initial guess close enough to the target orbit for numerical continuation or gradient-based search to converge. We show that Physics-Informed Neural Networks (PINNs) trained on sparse, noisy observations \emph{without} initial conditions recover periodic orbits of the gravitational three-body problem, including orbit families absent from the training data. The method rests on a second-order ODE formulation, fixed-frequency Fourier features, percentile-based adaptive refinement, and a trainable scaling parameter, each validated on forward problems. Across two 100-seed ensembles,

23

--

25\%

of runs converge to families not present in the training data. We then ask what determines which family emerges. Two

χ^2

tests give a consistent answer: changing the training data source significantly shifts the distribution of recovered families (

p < 0.001

, Cramér's

V = 0.339

), whereas switching between the two initialization distributions tested does not (

p = 0.620

,

V = 0.094

). The random seed selects which family a given run recovers; the \emph{distribution} the weights are drawn from does not shift the aggregate frequencies, but the training data does. The evidence is empirical: we do not characterize the loss landscape analytically, and PINNs remain slower than conventional integrators on well-posed initial-value problems. What the experiments establish is that the recovered orbits are verifiable rather than merely plausible: the identified ones refine to genuine periodic solutions, a network trained on Lagrange data recovers the figure-eight choreography (Li--Liao class I.A.1, matched to seven significant digits in

T^*

), and one trained on figure-eight data recovers a Broucke--Hadjidemetriou--Hénon orbit closing to

δ_T < 10^{-9}

.

Nikolaos Kollias, Nikolaos Matzakos

School of Science and Technology, Hellenic Open University, Athens, Greece. · School of Pedagogical and Technological Education (ASPETE), Athens, Greece.

Dynamical Systems Chaotic Dynamical Systems Physics-Informed ML

Jul 26, 2026cs.LG

Generalization bounds and sample complexity for remaining useful life prediction from complete degradation trajectories

Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive. Practitioners currently lack principled guidance on how many failure examples suffice for a given model and accuracy target. This paper develops a sample complexity framework for RUL prediction comprising seven main results organised around three themes. First, we establish fundamental learning rates: a distribution-free generalization bound shows that the uniform deviation of the mean squared error decreases as

O(B^{2}\sqrt{p/n})

, where

p

is the model complexity and

n

the number of trajectories, and a minimax lower bound proves that the

Θ(p/n)

rate is unimprovable.} \rev{Second, we quantify how domain knowledge accelerates learning: incorporating degradation physics reduces data requirements by up to two orders of magnitude for deep networks, a Bernstein-type analysis achieves the minimax-optimal

O(p/n)

rate under high signal-to-noise conditions, and closed-form penalties reveal when an incorrectly assumed physics model hurts rather than helps. Third, we characterise the impact of data quality: fleet variability induces an irreducible bias

-

variance tradeoff, while right-censored observations suffer an efficiency loss that depends critically on the degradation class.} Closed-form expressions are provided for exponential, power-law, and stretched-exponential degradation. \rev{Cross-domain validation against published turbofan, battery, and bearing benchmarks confirms the theoretical predictions within a factor of 2

-

3 on average. The results yield practical guidelines for planning data collection, selecting model complexity, and evaluating physics model assumptions in prognostics applications.

Huy Hoang Le, Kim-Anh Nguyen

R&D Department, PowerMore Ltd., Da Nang 550000, Vietnam · Faculty of Electrical Engineering, University of Science and Technology, The University of Danang, Da Nang 550000, Vietnam

RUL Estimation Sample Complexity Physics-Informed ML Statistical Learning Theory

Jul 25, 2026eess.AS

PathRIR: Physics-Guided Acoustic Path Selection and Late-Tail Compensation for Fast Room Impulse Response Simulation

Image-source-method (ISM)-based room impulse response (RIR) simulation is a useful and physically interpretable tool for acoustic scene modeling, but full-order ISM becomes computationally expensive as the reflection order and room complexity increase. We propose a physics-guided framework for fast RIR simulation that preserves the geometric structure of ISM while learning to retain only acoustically important image-source paths during online traversal. To recover energy removed by pruning, the proposed PathRIR uses a lightweight compensation multilayer perceptron to predict the missing late-tail energy envelope and generate a compensation tail whose energy follows that envelope. Experiments on irregular 3D rooms show that PathRIR reduces image-source computation and improves runtime efficiency over a full-order ISM simulator, while achieving low waveform- and decay-related errors. Ablation results show that adding the compensation tail improves waveform fidelity and reduces energy-decay-curve error, reverberation-time error, and direct-to-reverberant-ratio error, with modest runtime overhead.

Shaoheng Xu, Chunyi Sun, Jihui Zhang +3

The Australian National University, Australia · The University of Queensland, Australia

Physics-Informed ML Spatial Audio Physics-Based Simulation Room Acoustics

Jul 24, 2026physics.flu-dyn

PRIMS: Physics-guided Representation for Fluid Identification in Multimodal Sensing

Accurate on-device fluid identification is essential for microfluidic applications, yet maintaining reliability under varying flow, pressure, and temperature remains a key challenge. Existing learning-based methods often treat sensor signals as domain-agnostic features, neglecting the underlying physical relationships that govern fluid behavior, thereby limiting generalization and interpretability. To address this, we propose PRIMS, a physics-aware multimodal Transformer that integrates physical knowledge into representation learning and attention mechanisms through three dedicated modules: (1) Physics-based Token Vectorization transforms raw Coriolis and pressure sensor signals into physically meaningful token embeddings; (2) Physical Component Synthesizer models viscosity-related dependencies among flow, pressure, and density; and (3) Physics-guided Fusion captures cross-physical correlations through attention-based integration. By embedding these physics-based relationships directly into the model architecture, PRIMS bridges analytical fluid mechanics and deep learning, enabling interpretable, data-efficient, and resilient fluid classification. Evaluations on a five-fluid benchmark under dynamic flow, pressure, and temperature conditions show that PRIMS achieves 98.92% average F1-score with only 0.46 million parameters, a 14 times reduction compared to state-of-the-art Transformer-based methods. PRIMS also consistently outperforms prior SOTA models under out-of-distribution shifts to unseen temperature ranges and unseen flow-rate ranges, indicating strong robustness to operating conditions not observed during training. These findings suggest that designing architectures that explicitly mirror governing physical relationships can make them learn transferable, environment-independent representations, improving real-world reliability for microfluidic sensing.

Hai-Long Nguyen, Trung Thanh Nguyen, Lars Holm +2

University of Twente, Netherlands · Nagoya University, Japan

OOD Generalization Physics-Informed ML Multimodal Sensor Fusion

Jul 24, 2026cs.LG

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data. Latent PDE mapping pulls back geometry-specific PDE residuals and boundary conditions to a predefined latent geometry via the deformation gradient, thereby enabling the automated calculation of geometry-consistent shape gradients that are missing in conventional physics-informed machine learning formulations. We demonstrate the utility of latent PDE mapping in solving the anisotropic Aliev-Panfilov PDE of cardiac electrophysiology using both physics-informed neural networks and physics-informed deep operator networks. The Aliev-Panfilov PDE serves as a challenging exemplar: a nonlinear, time-dependent PDE benchmark with sharp gradients that are expensive to capture using traditional numerical solvers. To represent the limited data regime, we train the networks using just fifteen geometric samples drawn from parameterized distributions in two and three spatial dimensions. While modest improvements appear for geometries parameterized by affine and shear deformations, latent PDE mapping demonstrates significant benefits on select geometric families, achieving a factor ~4-6 reduction in mean relative L2 error. Furthermore, our results show that the computational cost of applying latent PDE mapping was modest during network training, and negligible at inference. Taken together, our study highlights how latent PDE mapping facilitates the creation of generalizable physics-informed machine learning models from limited sets of training geometries.

Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban

Faculty of Health and Technology, Kristiania University of Applied Sciences, Oslo, Norway · Department of Computational Physiology, Simula Research Laboratory, Oslo, Norway

PDE Operator Learning Physics-Informed ML