Physics-Informed ML

ML: Machine Learning

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Physics-informed machine learning studies how to combine observations with governing equations, conservation laws, symmetries, and other scientific knowledge. Common approaches include physics-informed neural networks (PINNs) that penalize equation residuals, weak or variational formulations, neural operators for families of PDE solutions, and hybrid models that learn corrections to mechanistic simulators. These methods are used for forward simulation, inverse problems, parameter estimation, forecasting, and fast surrogates when measurements or computational resources are limited. A central challenge is that physical constraints can improve data efficiency and consistency but can also hinder training or harm predictions when the equations, discretization, or assumed structure do not match the system.

Latest papers

843 papers75 papers in the last four weeks, down 13% on the four weeks before. 0.4% of all new papers.

Feb 27, 2026

A Stability-Aware Frozen Euler Autoencoder for Physics-Informed Tracking in Continuum Mechanics (SAFE-PIT-CM)

Material parameters such as thermal diffusivity govern how microstructural fields evolve during processing, but difficult to measure directly. The Stability-Aware Frozen Euler Physics-Informed Tracking for Continuum Mechanics (SAFE-PIT-CM), is an autoencoder that embeds a frozen convolutional layer as a differentiable PDE solver in its latent-space transition to jointly recover diffusion coefficients and the underlying physical field from temporal observations. When temporal snapshots are saved at intervals coarser than the simulation time step, a single forward Euler step violates the von Neumann stability condition, forcing the learned coefficient to collapse to an unphysical value. Sub-stepping with SAFE restores stability at negligible cost each sub-step is a single frozen convolution, far cheaper than processing more frames with recovery error converging monotonically with substep count. Validated on thermal diffusion in metals, the method recovers both the diffusion coefficient and the physical field with near-perfect accuracy, both with and yet without pre-training. Backpropagation through the frozen operator supervises an attention-based parameter estimator without labelled data. The architecture generalises to any PDE with a convolutional finite-difference discretisation.

Emil Hovad

Section for Statistics and Data Analysis, DTU Compute, Technical University of Denmark, Kgs. Lyngby, Denmark

Physics-Informed ML PDE Inverse Problems Neural PDE Solvers Materials Property Prediction

Feb 26, 2026

Physics-informed neural particle flow for the Bayesian update step

The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff differential equations. Conversely, existing deep learning approximations typically treat the update as a black-box task or rely on asymptotic relaxation, neglecting the exact geometric structure of the finite-horizon probability transport. In this work, we propose a physics-informed neural particle flow, which is an amortized inference framework. To construct the flow, we couple the log-homotopy trajectory of the prior to posterior density function with the continuity equation describing the density evolution. This derivation yields a governing partial differential equation (PDE), referred to as the master PDE. By embedding this PDE as a physical constraint into the loss function, we train a neural network to approximate the transport velocity field. This approach enables purely unsupervised training, eliminating the need for ground-truth posterior samples. We demonstrate that the neural parameterization acts as an implicit regularizer, mitigating the numerical stiffness inherent to analytic flows and reducing online computational complexity. Experimental validation on multimodal benchmarks and a challenging nonlinear scenario confirms better mode coverage and robustness compared to state-of-the-art baselines.

Domonkos Csuzdi, Tamás Bécsi, Olivér Törő

Particle Filtering Bayesian Filtering Physics-Informed ML

Feb 25, 2026

Physics-Informed Machine Learning for Vessel Shaft Power and Fuel Consumption Prediction: Interpretable KAN-based Approach

Accurate prediction of shaft rotational speed, shaft power, and fuel consumption is crucial for enhancing operational efficiency and sustainability in maritime transportation. Conventional physics-based models provide interpretability but struggle with real-world variability, while purely data-driven approaches achieve accuracy at the expense of physical plausibility. This paper introduces a Physics-Informed Kolmogorov-Arnold Network (PI-KAN), a hybrid method that integrates interpretable univariate feature transformations with a physics-informed loss function and a leakage-free chained prediction pipeline. Using operational and environmental data from five cargo vessels, PI-KAN consistently outperforms the traditional polynomial method and neural network baselines. The model achieves the lowest mean absolute error (MAE) and root mean squared error (RMSE), and the highest coefficient of determination (R^2) for shaft power and fuel consumption across all vessels, while maintaining physically consistent behavior. Interpretability analysis reveals rediscovery of domain-consistent dependencies, such as cubic-like speed-power relationships and cosine-like wave and wind effects. These results demonstrate that PI-KAN achieves both predictive accuracy and interpretability, offering a robust tool for vessel performance monitoring and decision support in operational settings.

Hamza Haruna Mohammed, Dusica Marijan, Arnbjørn Maressa

Simula Research Laboratory, Oslo, Norway · Navtor AS, Egersund, Norway

Maritime Transportation Physics-Informed ML Kolmogorov-Arnold Networks Neural Network Interpretability

Feb 25, 2026

Solving stiff dark matter equations via Jacobian Normalization with Physics-Informed Neural Networks

Stiff differential equations pose a major challenge for Physics-Informed Neural Networks (PINNs), often causing poor convergence. We propose a simple, hyperparameter-free method to address stiffness by normalizing loss residuals with the Jacobian. We provide theoretical indications that Jacobian-based normalization can improve gradient descent and validate it on benchmark stiff ordinary differential equations. We then apply it to a realistic system: the stiff Boltzmann equations (BEs) governing weakly interacting massive particle (WIMP) dark matter (DM). Our approach achieves higher accuracy than attention mechanisms previously proposed for handling stiffness, recovering the full solution where prior methods fail. This is further demonstrated in an inverse problem with a single experimental data point - the observed DM relic density - where our inverse PINNs correctly infer the cross section that solves the BEs in both Standard and alternative cosmologies.

M. P. Bento, H. B. Câmara, J. R. Rocha +1

Departamento de Física and CFTP, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal · Institute of Experimental and Applied Physics, Czech Technical University in Prague, Prague 160 00, Czech Republic

Physics-Informed ML Dynamical Systems High-Energy Physics

Feb 25, 2026

Dual-Regime Hybrid Aerodynamic Modeling of Winged Blimps With Neural Mixing

Winged blimps operate across distinct aerodynamic regimes that cannot be adequately captured by a single model. At high speeds and small angles of attack, their dynamics exhibit strong coupling between lift and attitude, resembling fixed-wing aircraft behavior. At low speeds or large angles of attack, viscous effects and flow separation dominate, leading to drag-driven and damping-dominated dynamics. Accurately representing transitions between these regimes remains a fundamental challenge. This paper presents a hybrid aerodynamic modeling framework that integrates a fixed-wing Aerodynamic Coupling Model (ACM) and a Generalized Drag Model (GDM) using a learned neural network mixer with explicit physics-based regularization. The mixer enables smooth transitions between regimes while retaining explicit, physics-based aerodynamic representation. Model parameters are identified through a structured three-phase pipeline tailored for hybrid aerodynamic modeling. The proposed approach is validated on the RGBlimp platform through a large-scale experimental campaign comprising 1,320 real-world flight trajectories across 330 thruster and moving mass configurations, spanning a wide range of speeds and angles of attack. Experimental results demonstrate that the proposed hybrid model consistently outperforms single-model and predefined-mixer baselines, establishing a practical and robust aerodynamic modeling solution for winged blimps.

Xiaorui Wang, Hongwu Wang, Yue Fan +2

The authors are with the Robotics and Control Laboratory, School of Advanced Manufacturing and Robotics, and the State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing, 100871, China

Vehicle Dynamics System Identification Physics-Informed ML

Feb 24, 2026

Physics-constrained symbolic regression for discovering closed-form equations of multimodal water retention curves from experimental data

Modeling the unsaturated behavior of porous materials with multimodal pore size distributions presents significant challenges, as standard hydraulic models often fail to capture their complex, multi-scale characteristics. A common workaround involves superposing unimodal retention functions, each tailored to a specific pore size range; however, this approach requires separate parameter identification for each mode, which limits interpretability and generalizability, especially in data-sparse scenarios. In this work, we introduce a fundamentally different approach: a physics-constrained machine learning framework designed for meta-modeling, enabling the automatic discovery of closed-form mathematical expressions for multimodal water retention curves directly from experimental data. Mathematical expressions are represented as binary trees and evolved via genetic programming, while physical constraints are embedded into the loss function to guide the symbolic regressor toward solutions that are physically consistent and mathematically robust. Our results demonstrate that the proposed framework can discover closed-form equations that effectively represent the water retention characteristics of porous materials with varying pore structures. To support third-party validation, application, and extension, we make the full implementation publicly available in an open-source repository.

Yejin Kim, Hyoung Suk Suh

Department of Civil and Environmental Engineering, Case Western Reserve University, United States

Porous Media Flow Symbolic Regression Scientific Discovery Physics-Informed ML

Feb 23, 2026

Unlearning Noise in PINNs: A Selective Pruning Framework for PDE Inverse Problems

Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization objective. However, the ill-posed nature of PDE inverse problems makes them highly sensitive to noise. Even a small fraction of corrupted observations can distort internal neural representations, severely impairing accuracy and destabilizing training. Motivated by recent advances in machine unlearning and structured network pruning, we propose P-PINN, a selective pruning framework designed to unlearn the influence of corrupted data in a pretrained PINN. Specifically, starting from a PINN trained on the full dataset, P-PINN evaluates a joint residual--data fidelity indicator, a weighted combination of data misfit and PDE residuals, to partition the training set into reliable and corrupted subsets. Next, we introduce a bias-based neuron importance measure that quantifies directional activation discrepancies between the two subsets, identifying neurons whose representations are predominantly driven by corrupted samples. Building on this, an iterative pruning strategy then removes noise-sensitive neurons layer by layer. The resulting pruned network is fine-tuned on the reliable data subject to the original PDE constraints, acting as a lightweight post-processing stage rather than a complete retraining. Numerical experiments on extensive PDE inverse-problem benchmarks demonstrate that P-PINN substantially improves robustness, accuracy, and training stability under noisy conditions, achieving up to a 96.6% reduction in relative error compared with baseline PINNs. These results indicate that activation-level post hoc pruning is a promising mechanism for enhancing the reliability of physics-informed learning in noise-contaminated settings.

Yongsheng Chen, Yong Chen, Wei Guo +1

School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China. · Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, PA 19104, USA. · Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 70409, USA.

Physics-Informed ML PDE Inverse Problems Neural Network Pruning Learning with Noisy Labels Machine Unlearning

Feb 23, 2026

Scale-PINN: Learning Efficient Physics-Informed Neural Networks Through Sequential Correction

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern numerical solvers. We introduce the Sequential Correction Algorithm for Learning Efficient PINN (Scale-PINN), a learning strategy that bridges modern physics-informed learning with numerical algorithms. Scale-PINN incorporates the iterative residual-correction principle, a cornerstone of numerical solvers, directly into the loss formulation, marking a paradigm shift in how PINN losses can be conceived and constructed. This integration enables Scale-PINN to achieve unprecedented convergence speed across PDE problems from different physics domain, including reducing training time on a challenging fluid-dynamics problem for state-of-the-art PINN from hours to sub-2 minutes while maintaining superior accuracy, and enabling application to representative problems in aerodynamics and urban science. By uniting the rigor of numerical methods with the flexibility of deep learning, Scale-PINN marks a significant leap toward the practical adoption of PINNs in science and engineering through scalable, physics-informed learning. Codes are available at https://github.com/chiuph/SCALE-PINN.

Pao-Hsiung Chiu, Jian Cheng Wong, Chin Chun Ooi +3

Institute of High Performance Computing, A*STAR, Singapore. · Centre for Frontier AI Research, A*STAR, Singapore. · School of Mechanical Engineering, Tianjin University, China. +1

Neural PDE Solvers Physics-Informed ML Neural Network Optimization

Feb 23, 2026

PIS: A Physics-Informed System for Accurate State Partitioning of $Aβ_{42}$ Protein Trajectories

Understanding the conformational evolution of

β

-amyloid (

Aβ

), particularly the

Aβ_{42}

isoform, is fundamental to elucidating the pathogenic mechanisms underlying Alzheimer's disease. However, existing end-to-end deep learning models often struggle to capture subtle state transitions in protein trajectories due to a lack of explicit physical constraints. In this work, we introduce PIS, a Physics-Informed System designed for robust metastable state partitioning. By integrating pre-computed physical priors, such as the radius of gyration and solvent-accessible surface area, into the extraction of topological features, our model achieves superior performance on the

Aβ_{42}

dataset. Furthermore, PIS provides an interactive platform that features dynamic monitoring of physical characteristics and multi-dimensional result validation. This system offers biological researchers a powerful set of analytical tools with physically grounded interpretability. A demonstration video of PIS is available on https://youtu.be/AJHGzUtRCg0.

Qianfeng Yu, Ningkang Peng, Yanhui Gu

School of Computer and Electronic Information, Nanjing Normal University

Physics-Informed ML

Feb 22, 2026

Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit spectral bias, whereby low-frequency components of the solution are learned significantly faster than high-frequency modes. While spectral bias is often treated as an intrinsic representational limitation of neural architectures, its interaction with optimization dynamics and physics-based loss formulations remains poorly understood. In this work, we provide a systematic investigation of spectral bias in physics-informed and operator learning frameworks, with emphasis on the coupled roles of network architecture, activation functions, loss design, and optimization strategy. We quantify spectral bias through frequency-resolved error metrics, Barron-norm diagnostics, and higher-order statistical moments, enabling a unified analysis across elliptic, hyperbolic, and dispersive PDEs. Through diverse benchmark problems, including the Korteweg-de Vries, wave and steady-state diffusion-reaction equations, turbulent flow reconstruction, and earthquake dynamics, we demonstrate that spectral bias is not simply representational but fundamentally dynamical. In particular, second-order optimization methods substantially alter the spectral learning order, enabling earlier and more accurate recovery of high-frequency modes for all PDE types. For neural operators, we further show that spectral bias is dependent on the neural operator architecture and can also be effectively mitigated through spectral-aware loss formulations without increasing the inference cost.

Siavash Khodakarami, Vivek Oommen, Nazanin Ahmadi Daryakenari +2

Division of Applied Mathematics, Brown University, Providence, RI 02912, USA · School of Engineering, Brown University, Providence, RI 02912, USA

Spectral Bias Physics-Informed ML PDE Operator Learning

Feb 20, 2026

Scientific Knowledge-Guided Machine Learning for Vessel Power Prediction: A Comparative Study

Accurate prediction of main engine power is essential for vessel performance optimization, fuel efficiency, and compliance with emission regulations. Conventional machine learning approaches, such as Support Vector Machines, variants of Artificial Neural Networks (ANNs), and tree-based methods like Random Forests, Extra Tree Regressors, and XGBoost, can capture nonlinearities but often struggle to respect the fundamental propeller law relationship between power and speed, resulting in poor extrapolation outside the training envelope. This study introduces a hybrid modeling framework that integrates physics-based knowledge from sea trials with data-driven residual learning. The baseline component, derived from calm-water power curves of the form

P = cV^n

, captures the dominant power-speed dependence, while another, nonlinear, regressor is then trained to predict the residual power, representing deviations caused by environmental and operational conditions. By constraining the machine learning task to residual corrections, the hybrid model simplifies learning, improves generalization, and ensures consistency with the underlying physics. In this study, an XGBoost, a simple Neural Network, and a Physics-Informed Neural Network (PINN) coupled with the baseline component were compared to identical models without the baseline component. Validation on in-service data demonstrates that the hybrid model consistently outperformed a pure data-driven baseline in sparse data regions while maintaining similar performance in populated ones. The proposed framework provides a practical and computationally efficient tool for vessel performance monitoring, with applications in weather routing, trim optimization, and energy efficiency planning.

Orfeas Bourchas, George Papalambrou

Laboratory of Marine Engineering N.T.U.A.

Physics-Informed ML Residual Learning

Feb 20, 2026

Clapeyron Neural Networks for Single-Species Vapor-Liquid Equilibria

Machine learning (ML) approaches have shown promising results for predicting molecular properties relevant for chemical process design. However, they are often limited by scarce experimental property data and lack thermodynamic consistency. As such, thermodynamics-informed ML, i.e., incorporating thermodynamic relations into the loss function as regularization term for training, has been proposed. We herein transfer the concept of thermodynamics-informed graph neural networks (GNNs) from the Gibbs-Duhem to the Clapeyron equation, predicting several pure component properties in a multi-task manner, namely: vapor pressure, liquid molar volume, vapor molar volume and enthalpy of vaporization. We find improved prediction accuracy of the Clapeyron-GNN compared to the single-task learning setting, and improved approximation of the Clapeyron equation compared to the purely data-driven multi-task learning setting. In fact, we observe the largest improvement in prediction accuracy for the properties with the lowest availability of data, making our model promising for practical application in data scarce scenarios of chemical engineering practice.

Jan Pavšek, Alexander Mitsos, Elvis J. Sim +1

Process Systems Engineering (AVT.SVT), RWTH Aachen University · JARA Center for Simulation and Data Science (CSD) · Institute of Climate and Energy Systems ICE-1: Energy Systems Engineering, Forschungszentrum Jülich GmbH

Molecular Property Prediction Materials Property Prediction Physics-Informed ML Physics-Informed GNNs

Feb 20, 2026

Deepmechanics

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across diverse physical phenomena remains limited, particularly in conservative and dissipative systems. In addition, benchmarking that has been done thus far does not integrate out full trajectories to check stability. In this work, we benchmark three prominent physics-informed architectures such as Hamiltonian Neural Networks (HNN), Lagrangian Neural Networks (LNN), and Symplectic Recurrent Neural Networks (SRNN) using the DeepChem framework, an open-source scientific machine learning library. We evaluate these models on six dynamical systems spanning classical conservative mechanics (mass-spring system, simple pendulum, double pendulum, and three-body problem, spring-pendulum) and non-conservative systems with contact (bouncing ball). We evaluate models by computing error on predicted trajectories and evaluate error both quantitatively and qualitatively. We find that all benchmarked models struggle to maintain stability for chaotic or nonconservative systems. Our results suggest that more research is needed for physics-informed deep learning models to learn robust models of classical mechanical systems.

Abhay Shinde, Aryan Amit Barsainyan, Jose Siguenza +3

Deep Forest Sciences, Mumbai, Maharashtra, India · Deep Forest Sciences, Bengaluru, Karnataka, India · Deep Forest Sciences, Palo alto, California, USA +1

Symplectic RNNs Lagrangian Neural Networks Physics-Informed ML Dynamical Systems Hamiltonian Neural Networks Recurrent Neural Networks

Feb 20, 2026

PINEAPPLE: Physics-Informed Neuro-Evolution Algorithm for Prognostic Parameter Inference in Lithium-Ion Battery Electrodes

Accurate, real-time, yet non-destructive estimation of internal states in lithium-ion batteries is critical for predicting degradation, optimizing usage strategies, and extending operational lifespan. Here, we introduce PINEAPPLE (Physics-Informed Neuro-Evolution Algorithm for Prognostic Parameter inference in Lithium-ion battery Electrodes), a novel framework that integrates physics-informed neural networks (PINNs) with an evolutionary search algorithm to enable rapid, scalable, and interpretable parameter inference with potential for application to next-generation batteries. The meta-learned PINN utilizes fundamental physics principles to achieve accurate zero-shot prediction of electrode behavior with test errors below 0.1

\%

while maintaining an order-of-magnitude speed-up over conventional solvers. PINEAPPLE demonstrates robust parameter inference solely from voltage-time discharge curves across multiple batteries from the open-source CALCE repository, recovering the evolution of key internal state parameters such as Li-ion diffusion coefficients across usage cycles. Notably, the inferred cycle-dependent evolution of these parameters exhibit consistent trends across different batteries without any customized degradation physics-embedded heuristic, highlighting the effective regularizing effect and robustness that can be conferred through incorporation of fundamental physics in PINEAPPLE. By enabling computationally efficient, real-time parameter estimation, PINEAPPLE offers a promising route towards the non-destructive, physics-based characterization of inter-cell and intra-cell variability of battery modules and battery packs, thereby unlocking new opportunities for downstream on-the-fly needs in next-generation battery management systems such as individual cell-scale state-of-health diagnostics.

Karkulali Pugalenthi, Jian Cheng Wong, Qizheng Yang +4

Singapore Institute of Manufacturing Technology, Agency for Science, Technology and Research, 5 Cleantech Loop, Singapore, 636732, Singapore · Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, Singapore, 138632, Singapore · Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR, China +3

Parameter Estimation Lithium-Ion Batteries Physics-Informed ML Neural Surrogate Modeling

Feb 19, 2026

Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priors

Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in handling complex physics. These limitations become more pronounced in multi-material, multi-physics problems whose objective or constraint functions are not self-adjoint. To address these challenges, we propose a framework based on physics-informed Gaussian processes (PIGPs). In our approach, the primary, adjoint, and design variables are represented by independent GP priors whose mean functions are parametrized via neural networks whose architectures are particularly beneficial for surrogate modeling of PDE solutions. We estimate all parameters of our model simultaneously by minimizing a loss that is based on the objective function, multi-physics potential energy functionals, and design-constraints. We demonstrate the capability of the proposed framework on benchmark TO problems such as compliance minimization, heat conduction optimization, and compliant mechanism design under single- and multi-material settings. Additionally, we leverage thermo-mechanical TO with single- and multi-material options as a representative multi-physics problem. We also introduce differentiation and integration schemes that dramatically accelerate the training process. Our results demonstrate that the proposed PIGP framework can effectively solve coupled multi-physics and design problems simultaneously -- generating super-resolution topologies with sharp interfaces and physically interpretable material distributions. We validate these results using open-source codes and the commercial software package COMSOL.

Xiangyu Sun, Shirin Hosseinmardi, Amin Yousefpour +1

Department of Mechanical and Aerospace Engineering, University of California, Irvine · Department of Civil and Environmental Engineering, University of California, Irvine

Topology Optimization Physics-Informed ML PDE Surrogate Modeling

Feb 19, 2026

Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method

Physics-governed models are increasingly paired with machine learning for accelerated predictions, yet most "physics--informed" formulations treat the governing equations as a penalty loss whose scale and meaning are set by heuristic balancing. This blurs operator structure, thereby confounding solution approximation error with governing-equation enforcement error and making the solving and learning progress hard to interpret and control. Here we introduce the Neural Basis Method, a projection-based formulation that couples a predefined, physics-conforming neural basis space with an operator-induced residual metric to obtain a well-conditioned deterministic minimization. Stability and reliability then hinge on this metric: the residual is not merely an optimization objective but a computable certificate tied to approximation and enforcement, remaining stable under basis enrichment and yielding reduced coordinates that are learnable across parametric instances. We use advective multiscale Darcian dynamics as a concrete demonstration of this broader point. Our method produce accurate and robust solutions in single solves and enable fast and effective parametric inference with operator learning.

Yuhe Wang, Min Wang

Institute for Scientific Computation, Texas A&M University, College Station, TX 77843, USA · Department of Mathematics, University of Houston, Houston, TX 77204, USA

Neural PDE Solvers Physics-Informed ML PDE Operator Learning Neural Surrogate Modeling Computational Fluid Dynamics

Feb 19, 2026

QuPAINT: Physics-Aware Instruction Tuning Approach to Quantum Material Discovery

Characterizing two-dimensional quantum materials from optical microscopy images is challenging due to the subtle layer-dependent contrast, limited labeled data, and significant variation across laboratories and imaging setups. Existing vision models struggle in this domain since they lack physical priors and cannot generalize to new materials or hardware conditions. This work presents a new physics-aware multimodal framework that addresses these limitations from both the data and model perspectives. We first present Synthia, a physics-based synthetic data generator that simulates realistic optical responses of quantum material flakes under thin-film interference. Synthia produces diverse and high-quality samples, helping reduce the dependence on expert manual annotation. We introduce QMat-Instruct, the first large-scale instruction dataset for quantum materials, comprising multimodal, physics-informed question-answer pairs designed to teach Multimodal Large Language Models (MLLMs) to understand the appearance and thickness of flakes. Then, we propose Physics-Aware Instruction Tuning (QuPAINT), a multimodal architecture that incorporates a Physics-Informed Attention module to fuse visual embeddings with optical priors, enabling more robust and discriminative flake representations. Finally, we establish QF-Bench, a comprehensive benchmark spanning multiple materials, substrates, and imaging settings, offering standardized protocols for fair and reproducible evaluation.

Xuan-Bac Nguyen, Hoang-Quan Nguyen, Sankalp Pandey +4

CVIU Lab, University of Arkansas, USA · University of Utah, USA · Department of Physics, University of Arkansas, USA

Microscopy Image Analysis Multimodal Instruction Tuning Materials Science Physics-Informed ML Synthetic Data Augmentation

Feb 18, 2026

TopoFlow: Topography-aware Pollutant Flow Learning for High-Resolution Air Quality Prediction

We propose TopoFlow (Topography-aware pollutant Flow learning), a physics-guided neural network for efficient, high-resolution air quality prediction. To explicitly embed physical processes into the learning framework, we identify two critical factors governing pollutant dynamics: topography and wind direction. Complex terrain can channel, block, and trap pollutants, while wind acts as a primary driver of their transport and dispersion. Building on these insights, TopoFlow leverages a vision transformer architecture with two novel mechanisms: topography-aware attention, which explicitly models terrain-induced flow patterns, and wind-guided patch reordering, which aligns spatial representations with prevailing wind directions. Trained on six years of high-resolution reanalysis data assimilating observations from over 1,400 surface monitoring stations across China, TopoFlow achieves a PM2.5 RMSE of 9.71 ug/m3, representing a 71-80% improvement over operational forecasting systems and a 13% improvement over state-of-the-art AI baselines. Forecast errors remain well below China's 24-hour air quality threshold of 75 ug/m3 (GB 3095-2012), enabling reliable discrimination between clean and polluted conditions. These performance gains are consistent across all four major pollutants and forecast lead times from 12 to 96 hours, demonstrating that principled integration of physical knowledge into neural networks can fundamentally advance air quality prediction.

Ammar Kheder, Helmi Toropainen, Wenqing Peng +4

Department of Computational Engineering, Lappeenranta–Lahti University of Technology LUT, Finland · Atmospheric Modelling Centre Lahti, Lahti University Campus, Finland · Institute for Atmospheric and Earth System Research, University of Helsinki, P.O. Box 64, Helsinki 00014, Finland +2

Air Quality Prediction Spatiotemporal Forecasting Physics-Informed ML

Feb 18, 2026

RSS map-assisted MIMO channel estimation in the upper mid-band under pilot constraints

Accurate wireless channel estimation is critical for next-generation wireless systems, enabling precise precoding for effective user separation, reduced interference across cells, and high-resolution sensing, among other benefits. Traditional model-based channel estimation methods suffer, however, from performance degradation in complex environments with a limited number of pilots, while purely data-driven approaches lack physical interpretability, require extensive data collection, and are usually site-specific. This paper presents a novel physics-informed neural network (PINN) framework that synergistically combines model-based channel estimation with a deep network to exploit prior information about environmental propagation characteristics and achieve superior performance under pilot-constrained scenarios. The proposed approach employs an enhanced U-Net architecture with transformer modules and cross-attention mechanisms to fuse initial channel estimates with RSS maps to provide refined channel estimates. Comprehensive evaluation using realistic ray-tracing data from urban environments demonstrates significant performance improvements, achieving over 5 dB gain in NMSE compared to state-of-the-art methods, with particularly strong performance in pilot-limited scenarios and robustness across different frequencies and environments with only minimal fine-tuning. We further extend the decoder for multi-step temporal prediction, enabling accurate forecasting of several future channel snapshots from a single estimate, useful for proactive beamforming and scheduling in mobile scenarios. The proposed framework maintains practical computational complexity, making it viable for massive MIMO systems in upper-mid band frequencies. Unlike black-box neural approaches, the physics-informed design provides a more interpretable channel estimation method.

Alireza Javid, Nuria González-Prelcic

Department of Electrical and Computer Engineering, University of California San Diego, USA

Channel Estimation Wireless Communications Physics-Informed ML

Feb 18, 2026

AI-Driven Structure Refinement of X-ray Diffraction

Artificial intelligence can rapidly propose candidate phases and structures from X-ray diffraction (XRD), but these hypotheses often fail in downstream refinement because peak intensities cannot be stably assigned under severe overlap and diffraction consistency is enforced only weakly. Here we introduce the whole-pattern expectation--maximization (WPEM) algorithm, a physics-constrained whole-pattern decomposition and refinement workflow that turns Bragg's law into an explicit constraint within a batch expectation--maximization framework. WPEM models the full profile as a probabilistic mixture density and iteratively infers component-resolved intensities while keeping peak centres Bragg-consistent, producing a continuous, physically admissible intensity representation that remains stable in heavily overlapped regions and in the presence of mixed radiation or multiple phases. We benchmark WPEM on standard reference patterns (PbSO

_4

and Tb

_2

BaCoO

_5

), where it yields lower

R_p/R_{wp}

than widely used packages (FullProf and TOPAS) under matched refinement conditions. We further demonstrate generality across realistic experimental scenarios, including phase-resolved decomposition in multiphase materials, quantitative recovery of mixture compositions, separation of crystalline peaks from amorphous backgrounds in semicrystalline systems, high-throughput operando lattice tracking, automated refinement of compositionally disordered solid solutions, and quantitative phase-resolved analysis of complex archaeological samples from synchrotron powder XRD. By providing Bragg-consistent, uncertainty-aware intensity partitioning as a refinement-ready interface, WPEM closes the gap between AI-generated hypotheses and diffraction-admissible structure refinement on challenging XRD data.

Bin Cao, Qian Zhang, Zhenjie Feng +4

Guangzhou Municipal Key Laboratory of Materials Informatics, Advanced Materials Thrust, Sustainable Energy and Environment Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511453, China · Materials Genome Institute, Shanghai University, Shanghai 200444, China · Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China +1

Materials Science Physics-Informed ML

Feb 18, 2026

Optical Inversion and Spectral Unmixing of Spectroscopic Photoacoustic Images with Physics-Informed Neural Networks

Accurate estimation of the relative concentrations of chromophores in a spectroscopic photoacoustic (sPA) image can reveal immense structural, functional, and molecular information about physiological processes. However, due to nonlinearities and ill-posedness inherent to sPA imaging, concentration estimation is intractable. The Spectroscopic Photoacoustic Optical Inversion Autoencoder (SPOI-AE) aims to address the sPA optical inversion and spectral unmixing problems without assuming linearity. Herein, SPOI-AE was trained and tested on in vivo mouse lymph node sPA images with unknown ground truth chromophore concentrations. SPOI-AE better reconstructs input sPA pixels than conventional algorithms while providing biologically coherent estimates for optical parameters, chromophore concentrations, and the percent oxygen saturation of tissue. SPOI-AE's unmixing accuracy was validated using a simulated mouse lymph node phantom ground truth.

Sarkis Ter Martirosyan, Xinyue Huang, David Qin +2

School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States · Institute of Biological and Medical Imaging, Helmholtz Zentrum Munich, 85764 Neuherberg, Germany · Chair of Biological Imaging, Technische Universität München, 80333 München, Germany +1

Spectral Unmixing Photoacoustic Tomography Medical Imaging Image Inverse Problems Autoencoders Physics-Informed ML

Feb 18, 2026

Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappings

Several complex physical systems are governed by multi-scale partial differential equations (PDEs) that exhibit both smooth low-frequency components and localized high-frequency structures. Existing physics-informed neural network (PINN) methods typically train with fixed coordinate system inputs, where geometric misalignment with these structures induces gradient stiffness and ill-conditioning that hinder convergence. To address this issue, we introduce a mapping paradigm that reshapes the input coordinates through differentiable geometric compactification mappings and couples the geometric structure of PDEs with the spectral properties of residual operators. Based on this paradigm, we propose Geometric Compactification (GC)-PINN, a framework that introduces three mapping strategies for periodic boundaries, far-field scale expansion, and localized singular structures in the input domain without modifying the underlying PINN architecture. Extensive empirical evaluation demonstrates that this approach yields more uniform residual distributions and higher solution accuracy on representative 1D and 2D PDEs, while improving training stability and convergence speed.

Zhenzhen Huang, Haoyu Bian, Jiaquan Zhang +6

School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China · Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China · Institute of Software Chinese Academy of Sciences, Beijing, China +1

Neural PDE Solvers Physics-Informed ML

Feb 18, 2026

Muon with Spectral Guidance: Efficient Optimization for Scientific Machine Learning

Physics-informed neural networks and neural operators often suffer from severe optimization difficulties caused by ill-conditioned gradients, multi-scale spectral behavior, and stiffness induced by physical constraints. Recently, the Muon optimizer has shown promise by performing orthogonalized updates in the singular-vector basis of the gradient, thereby improving geometric conditioning. However, its unit-singular-value updates may lead to overly aggressive steps and lack explicit stability guarantees when applied to physics-informed learning. In this work, we propose SpecMuon, a spectral-aware optimizer that integrates Muon's orthogonalized geometry with a mode-wise relaxed scalar auxiliary variable (RSAV) mechanism. By decomposing matrix-valued gradients into singular modes and applying RSAV updates individually along dominant spectral directions, SpecMuon adaptively regulates step sizes according to the global loss energy while preserving Muon's scale-balancing properties. This formulation interprets optimization as a multi-mode gradient flow and enables principled control of stiff spectral components. We establish rigorous theoretical properties of SpecMuon, including a modified energy dissipation law, positivity and boundedness of auxiliary variables, and global convergence with a linear rate under the Polyak-Lojasiewicz condition. Numerical experiments on physics-informed neural networks, DeepONets, and fractional PINN-DeepONets demonstrate that SpecMuon achieves faster convergence and improved stability compared with Adam, AdamW, and the original Muon optimizer on benchmark problems such as the one-dimensional Burgers equation and fractional partial differential equations.

Binghang Lu, Jiahao Zhang, Guang Lin

Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA · Department of Mathematics & School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA

Muon Optimizer Physics-Informed ML Physics-Informed Neural Operators

Feb 17, 2026

Imaging-Derived Coronary Fractional Flow Reserve: Advances in Physics-Based, Machine Learning, and Physics-Informed Methods

Purpose of Review Imaging derived fractional flow reserve (FFR) is rapidly evolving beyond conventional computational fluid dynamics (CFD) based pipelines toward machine learning (ML), deep learning (DL), and physics informed approaches that enable fast, wire free, and scalable functional assessment of coronary artery stenosis. This review synthesizes recent advances in computed tomography (CT)- and angiography-based FFR measurement, with particular emphasis on emerging physics-informed neural networks and neural operators (PINNs and PINOs), as well as key considerations for their clinical translation. Recent Findings ML/DL approaches have markedly improved automation and computational speed, enabling prediction of pressure and FFR from anatomical descriptors or angiographic contrast dynamics. However, their real-world performance and generalizability can remain variable and sensitive to domain shift, due to multi-center heterogeneity, interpretability challenges, and differences in acquisition protocols and image quality. Physics informed learning introduces conservation structure and boundary condition consistency into model training, improving generalizability and reducing dependence on dense supervision while maintaining rapid inference. Recent evaluation trends increasingly highlight deployment oriented metrics, including calibration, uncertainty quantification, and quality control gatekeeping, as essential for safe clinical use. Summary The field is converging toward imaging derived FFR methods that are faster, more automated, and more reliable. While ML/DL offers substantial efficiency gains, physics informed frameworks such as PINNs and PINOs may provide a more robust balance between speed and physical consistency. Prospective multi center validation and standardized evaluation will be critical to support broad and safe clinical adoption.

Tanxin Zhu, Emran Hossen, Chen Zhao +4

Department of Applied Computing, Michigan Technological University, Houghton, MI, USA · Department of Computer Science, Kennesaw State University, Marietta GA, USA · Department of Biomedical Engineering, Michigan Technological University, Houghton, MI, USA +3

Medical Image Analysis Physics-Informed ML Physics-Informed Neural Operators Computational Fluid Dynamics

Feb 17, 2026

Hybrid Model Predictive Control with Physics-Informed Neural Network for Satellite Attitude Control

Reliable spacecraft attitude control depends on accurate prediction of attitude dynamics, particularly when model-based strategies such as Model Predictive Control (MPC) are employed, where performance is limited by the quality of the internal system model. For spacecraft with complex dynamics, obtaining accurate physics-based models can be difficult, time-consuming, or computationally heavy. Learning-based system identification presents a compelling alternative; however, models trained exclusively on data frequently exhibit fragile stability properties and limited extrapolation capability. This work explores Physics-Informed Neural Networks (PINNs) for modeling spacecraft attitude dynamics and contrasts it with a conventional data-driven approach. A comprehensive dataset is generated using high-fidelity numerical simulations, and two learning methodologies are investigated: a purely data-driven pipeline and a physics-regularized approach that incorporates prior knowledge into the optimization process. The results indicate that embedding physical constraints during training leads to substantial improvements in predictive reliability, achieving a 68.17% decrease in mean relative error relative. When deployed within an MPC architecture, the physics-informed models yield superior closed-loop tracking performance and improved robustness to uncertainty. Furthermore, a hybrid control formulation that merges the learned nonlinear dynamics with a nominal linear model enables consistent steady-state convergence and significantly faster response, reducing settling times by 61.52%-76.42% under measurement noise and reaction wheel friction.

Carlo Cena, Mauro Martini, Marcello Chiaberge

Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy

Spacecraft Attitude Determination Model Predictive Control Feedback Control Nonlinear System Identification Physics-Informed ML

Feb 16, 2026

Parameter-Minimal Neural DE Solvers via Horner Polynomials

We propose a parameter-minimal neural architecture for solving differential equations by restricting the hypothesis class to Horner-factorized polynomials, yielding an implicit, differentiable trial solution with only a small set of learnable coefficients. Initial conditions are enforced exactly by construction by fixing the low-order polynomial degrees of freedom, so training focuses solely on matching the differential-equation residual at collocation points. To reduce approximation error without abandoning the low-parameter regime, we introduce a piecewise ("spline-like") extension that trains multiple small Horner models on subintervals while enforcing continuity (and first-derivative continuity) at segment boundaries. On illustrative ODE benchmarks and a heat-equation example, Horner networks with tens (or fewer) parameters accurately match the solution and its derivatives and outperform small MLP and sinusoidal-representation baselines under the same training settings, demonstrating a practical accuracy-parameter trade-off for resource-efficient scientific modeling.

T. Matulić, D. Seršić

Dept. of Electronic Systems and Information Processing, Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia

Neural PDE Solvers Polynomial Neural Networks Ordinary Differential Equations PDE Solving Physics-Informed ML

Feb 16, 2026

Pseudo-differential-enhanced physics-informed neural networks

We present pseudo-differential enhanced physics-informed neural networks (PINNs), an extension of gradient enhancement but in Fourier space. Gradient enhancement of PINNs dictates that the PDE residual is taken to a higher differential order than prescribed by the PDE, added to the objective as an augmented term in order to improve training and overall learning fidelity. We propose the same procedure after application via Fourier transforms, since differentiating in Fourier space is multiplication with the Fourier wavenumber under suitable decay. Our methods are fast and efficient. Our methods oftentimes achieve superior PINN versus numerical error in fewer training iterations, potentially pair well with few/fixed samples in collocation, and can achieve breakthrough rather than gradual effects on the error. Moreover, our methods are suitable for fractional derivatives. We establish that our methods, due to the dynamical effects, improve spectral eigenvalue decay of the neural tangent kernel (NTK), and so our methods contribute towards the learning of high frequencies in early training, mitigating the effects of frequency bias up to the polynomial order and possibly greater with smooth activations. In particular, our primary contribution can be characterized as gradient enhancement affects spectral bias, and we specialize to Fourier space, although our theory does not prove the ambient case exactly due to a result with the Plancherel theorem on the descent paths. Our methods accommodate advanced techniques in PINNs, such as Fourier feature embeddings. A pitfall of discrete Fourier transforms via the Fast Fourier Transform (FFT) is mesh subjugation, and so we demonstrate compatibility of our methods for greater mesh flexibility and invariance on alternative Euclidean and non-Euclidean domains via Monte Carlo methods and otherwise, although possessing trade-offs of their own.

Andrew Gracyk

Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

PDE Solving Spectral Bias Physics-Informed ML

Feb 14, 2026

A Unified Physics-Informed Neural Network for Modeling Coupled Electro- and Elastodynamic Wave Propagation Using Three-Stage Loss Optimization

Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the application of PINNs to solve a one dimensional coupled electro-elastodynamic system modeling linear piezoelectricity in stress-charge form, governed by elastodynamic and electrodynamic equations. Our simulation employs a feedforward architecture, mapping space-time coordinates to mechanical displacement and electric potential. Our PINN model achieved global relative L2 errors of 2.34 and 4.87 percent for displacement and electric potential respectively. The results validate PINNs as effective mesh free solvers for coupled time-dependent PDE systems, though challenges remain regarding error accumulation and stiffness in coupled eigenvalue systems.

Suhas Suresh Bharadwaj, Reuben Thomas Thovelil

Department of Electrical and Electronics Engineering, BITS Pilani, Dubai Campus, Dubai, United Arab Emirates

Neural PDE Solvers PDE Solving Physics-Informed ML Multiphysics Simulation

Feb 10, 2026

Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training

We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where PDE residuals can drive the model toward trivial or degenerate solutions, degrading the learned data distribution. To address this, we introduce a structure-preserving two-stage training strategy that decouples distribution learning from physics enforcement by freezing the coefficient decoder during physics-informed fine-tuning. We further propose a two-step residual objective that enforces physical consistency on refined, structurally valid generative trajectories rather than noisy single-step predictions. The resulting framework enables stable, high-fidelity inference for both unconditional generation and forward problems. We demonstrate that forward solutions can be obtained via a projection-based zero-shot inpainting procedure, achieving consistent accuracy of diffusion baselines with orders of magnitude reduction in computational cost.

Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin +2

Institute of Artificial Intelligence Innovation National Yang Ming Chiao Tung University Hsinchu, Taiwan · Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu, Taiwan · Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu, Taiwan National Center for Theoretical Sciences National Taiwan University Taipei, Taiwan

Physics-Informed Generative Modeling PDE Surrogate Modeling Few-Step Diffusion Sampling Physics-Informed ML Consistency Models

Feb 1, 2026

When Does Cheap Physics Help? Gated Multi-Fidelity Physics-Informed Networks with Provable Sample Savings and Conformal Guarantees

High-fidelity (HF) simulations of parametric partial differential equations are expensive, whereas low-fidelity (LF) models such as coarse grids or simplified physics are cheap but biased. Multi-fidelity physics-informed neural networks combine the two, yet it remains unclear when cheap physics actually reduces the number of HF solves, and existing methods silently fail when the LF model is misleading and offer no guaranteed uncertainty. We answer the first question with a sharp sample-complexity bound: learning the HF field through its discrepancy from the LF model reduces the number of HF samples needed for accuracy

\varepsilon

by the factor

κ^{2γ}

, where

κ

is the ratio of the complexity of the discrepancy to that of the HF field and

γ

is the effective-dimension exponent, and we confirm the predicted scaling with exact risk computations in a kernel model. Guided by the analysis, we propose GaMF-PINN, a gated multi-fidelity PINN that learns where to trust the LF model and falls back to physics-only learning where it does not, together with a function-level conformal procedure that returns uncertainty bands containing the entire HF solution with probability at least

1-α

in finite samples. We release MFPDE-Bench, an open benchmark of paired LF/HF solvers for four parametric PDEs with coarse-grid and simplified-physics LF models. Across MFPDE-Bench, GaMF-PINN reaches the accuracy of a standard HF-PINN with up to 8x fewer HF solves, remains robust when the LF model is deliberately corrupted, and attains the nominal coverage where Bayesian PINNs and deep ensembles under-cover.

Olaf Yunus Laitinen Imanov, Rana Irem Turhan, Isgandar Jafarli

Department of Mathematics and Statistics, University of Helsinki, Finland · School of Computer Science, University of Sheffield, United Kingdom · School of IT and Engineering, ADA University, Azerbaijan

Multifidelity Modeling Physics-Informed ML Sample Complexity