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

Jul 16, 2026cs.CV

Physics-Informed Diffusion for Biomechanically Plausible 3D Sign Language Generation

Sign language production, which generates continuous 3D skeletal motion from spoken language input, must simultaneously satisfy two constraints: semantic fidelity, so that a deaf viewer can recognize the intended sequence of glosses, and biomechanical plausibility, so that the generated skeleton respects anatomical constraints. Existing approaches optimize semantic reconstruction through coordinate-based objectives that treat the skeleton as an unstructured vector, thus allowing for bone length drift, joint angle violations, and temporarily locked fingers. We introduce PIDiffSign, a physics-informed diffusion model for gloss-to-pose translation that incorporates anatomical constraints into both the architecture and training objective. The model uses a Transformer encoder-decoder, where the decoder is conditioned on the diffusion time step through adaptive zero-initialized layer normalization and cross-attends to gloss representations. A differentiable geometry module enforces bone length consistency and biologically valid joint angles throughout generation. Training combines anthropomorphic, kinematic, angular, and finger-joint constraints with a contrastive gloss-pose alignment loss and classifier-free guidance for semantically conditioned sampling. Experiments on the PHOENIX14T and CSL-Daily benchmarks show consistent improvements over a strong diffusion baseline in pose accuracy, joint-angle correctness, distributional realism, and back-translation quality. These results demonstrate that physics-informed diffusion improves both motion realism and semantic fidelity for sign language generation.

Emanuele Colonna, Moises Diaz, Gennaro Vessio +2

Department of Computer Science, University of Bari Aldo Moro, Bari, Italy · Institute for Technological Development and Innovation in Communications, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

Physics-Informed Diffusion Models Human Motion Generation Physics-Informed ML Conditional Diffusion Models Sign Language Generation

Jul 16, 2026cs.LG

Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data

Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitting errors are amplified through inverse estimation. Existing inverse methods often rely on high-fidelity observations and manually prespecified loss weights, limiting their adaptability and making them sensitive to noise and resolution degradation. We propose a Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework for robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data. PIE-PINN models displacement observation, strain-discrepancy, and equilibrium residuals using Laplace distributions within a unified probabilistic model. To improve robustness, the framework combines a B-spline-guided displacement network with a hierarchical half-Cauchy model for displacement residual scales. The B-spline provides a smooth global representation of the displacement field, while the neural network correction captures local variations. The hierarchical scale model adaptively downweights severe displacement fitting errors, enabling more robust recovery of the latent mean displacement field. An alternating maximum-likelihood training strategy updates the mean through weighted residual minimization and updates the scales to adjust the loss weights. Systematic case studies across varying noise levels and observation resolutions demonstrate the robustness of PIE-PINN.

Tatthapong Srikitrungruang, Jaesung Lee

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

Structural Mechanics Materials Property Prediction Adaptive Loss Weighting Physics-Informed ML PDE Inverse Problems Inverse Problems

Jul 15, 2026cs.LG

LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE). However, PINNs have been shown to perform poorly, sometimes even converging to trivial solutions, in challenging PDE domains, or when generalizing to unseen but related PDE domains. Previously proposed solutions detail hyperparameter tuning to reduce loss imbalance between data-driven and physics guided losses, curriculum learning based training strategies, or dynamic re-sampling of hard collocation points. These methods face certain pitfalls: hyperparameter tuning is expensive, designing a training curriculum is ambiguous in multi-parameter PDE settings, and dynamic resampling still fails in complex PDE settings. Complementary to this line of thinking, we believe the initial PINN network weights also play a crucial role in the emergence of catastrophic failures during training, yet the effect of PINN weight initialization has been surprisingly under-investigated. To this end, we propose a framework for Learned Initialization via Gated Layerwise Optimization (LIGO-PINN) to overcome PINN convergence failures. Through rigorous evaluation on 1D and 2D PDE domains, including a challenging 2D fluid dynamics setting, we demonstrate that our methodology outperforms state-of-the-art methods designed to alleviate PINN failures, achieving a 91.5% average performance improvement across six baselines and 81% over the strongest baseline. We also verify that LIGO-PINN generalizes to 3D unstructured domains. Finally, we analyze training dynamics across all three PDE domains to explain both LIGO-PINN's improvement and the convergence failure of traditional PINNs. Code: https://github.com/scailab/ligo-pinn Keywords: Machine Learning, Physics-Informed Neural Networks, Deep Learning, PDE Modeling

Nilay Anurag, Shital Adhikari, Taniya Kapoor +1

Department of Computer Science, Stevens Institute of Technology · Artificial Intelligence Group, Wageningen University & Research

Neural PDE Solvers Neural Network Optimization Physics-Informed ML

Jul 15, 2026stat.ML

Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography

The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber

κ^2

complex. Inferring such fields from sparse, noisy data calls for solvers that also quantify their own uncertainty. Physics-informed Gaussian-process (GP) regression supplies this by returning a posterior over the solution, yet operator-conditioned formulations have been developed almost exclusively for real-valued fields. We extend operator-informed GP regression to complex-valued Helmholtz problems by realifying the complex operator into an equivalent coupled real block, which enables inference with standard real-valued GP conditioning. The construction admits a family of priors, from a proper diagonal prior to coregionalized and multiscale variants, and conditions on PDE residuals and boundary traces. On benchmark problems in one to three dimensions, the solver is competitive with finite-difference and neural-network baselines at a far smaller interior-constraint budget. Unlike those deterministic baselines, it returns a posterior over the complex wavefield rather than a point estimate. Applied to \textit{in vivo} brain magnetic resonance elastography, a proper multiscale prior reconstructs the shear curl field to a correlation of

0.77

with measurement, above a

0.75

target. The gain arises from the multiscale kernel rather than from real--imaginary coupling. We further identify a low-frequency accuracy ceiling set by model mismatch and a posterior uncertainty that is not yet calibrated. Calibrated uncertainty therefore emerges as the central next step for probabilistic wavefield inference in dissipative media.

Boyuan Deng, Kshitiz Upadhyay, Michael Shields

Department of Civil and Systems Engineering, Johns Hopkins University · Department of Aerospace Engineering and Mechanics, University of Minnesota

PDE Solving Physics-Informed ML PDE Inverse Problems

Jul 15, 2026math.NA

Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

For low-dimensional problems (

d\leq3

), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems (

4 \leq d \lesssim 10

), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems (

d\gg 10

), spectral methods suffer frome the curse of dimensionality. Physics-informed neural networks (PINNs) have emerged as a promising approach to overcome this challenge, offering scalability to high dimensions, but often suffer from limited accuracy and efficiency. Recently proposed spectral-informed neural networks (SINNs) combine spectral methods with PINNs, operating directly in the spectral domain to avoid spatial derivative computations and to reduce memory consumption. In this work, we introduce Modified SINNs, which integrate coefficient decay scaling and basis embeddings motivated by harmonic analysis to enhance accuracy in high-dimensional problems and enable accurate approximation of unknown spectral coefficients. Numerical experiments on steady and time-dependent partial differential equations demonstrate that Modified SINNs outperform sparse grid spectral methods on middle-dimensional problems with incomplete spectral information and achieve superior accuracy compared to PINNs on high-dimensional problems.

Tianchi Yu, Ivan Oseledets

1AXXX · 2Applied AI Institute · 3INM

PDE Solving Physics-Informed ML Spectral Methods

Jul 14, 2026q-bio.NC

Real-time fall detection based on vision for low-power edge platforms

Falling detection is vital for elderly care and intelligent surveillance; however, prevailing vision-based approaches predominantly frame it as static pose classification or discrete temporal pattern matching, fundamentally overlooking the instability dynamics of the human support system. This paper proposes a physics-informed falling detection framework that recasts falling as a stability-loss event in a coupled dynamical system. We introduce a novel dual-LTC architecture comprising a Center-of-Mass (CoM) subsystem and a Base-of-Support (BoS) subsystem, both instantiated as Liquid Time-Constant (LTC) neural networks to continuously model inertial trajectory evolution and ground-contact adjustment through adaptive time constants, Physical interpretability of falling motion. A learnable coupling module emulates physical interaction between the two subsystems, while a Stability Manifold classifier operates in the joint latent space to detect boundary crossing via Lyapunov-inspired stability metrics. Complementary counterfactual trajectory projection and Time-to-Collision (TTC) estimation further enable irreversibility assessment and early warning. The architecture is designed to support a three-state prediction paradigm (Normal, Falling, Fallen); in this preliminary study, we validate the core stability discrimination capability on a two-class dataset (Normal vs. Falling), leaving the full three-state temporal transition to future work. Unlike conventional CNN--RNN pipelines, the proposed formulation encodes continuous-time mechanical inertia, yielding a sub-50K-parameter network capable of real-time inference on resource-constrained edge devices. Extensive experiments demonstrate competitive accuracy with superior physical interpretability, validating its efficacy for low-compute visual fall detection.

Wenjun Xia, Zhicheng Peng, Haopeng Li +1

Jiangsu University, Zhenjiang, China

Fall Detection Physics-Informed ML

Jul 14, 2026cs.LG

Energy-Based Physics-Informed Form Finding for Clustered Tensegrity Structures

Tensegrity form-finding and physical property prediction are fundamental inverse problems in structural mechanics, which aim to determine equilibrium configurations and internal force distributions. These problems are challenging due to strong nonlinearity arising from the coupling between geometry and forces, the need to ensure structural stability, and the enforcement of constraints such as boundary conditions and symmetry. Moreover, traditional methods often lack robustness to noise and outliers. This paper proposes an energy-based learning framework for clustered tensegrity form finding and physical property prediction. The proposed approach incorporates total potential energy minimization and constitutive relations into the training objective, enabling the simultaneous prediction of equilibrium nodal configurations and associated physical quantities, including member forces and force densities. By incorporating energy-based physical losses directly into the learning process, the framework improves physical consistency, robustness, and data efficiency. Numerical experiments on tensegrity structures, including prism and lander systems, show the great potential of the proposed approach and demonstrate its capability for scalable form finding and accurate prediction of structural properties.

Jing Qin, Muhao Chen

Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA · Department of Mechanical and Aerospace Engineering, University of Houston, Houston, TX 77204, USA

Structural Mechanics Energy-Based Models Physics-Informed ML

Jul 14, 2026cs.LG

A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground

Accurate and efficient prediction of subsurface temperature fields is essential for the design and operation of borehole heat exchanger (BHE) systems. Here we develop a parametric hybrid analytical and physics-informed neural network (PINN) framework for long-term multi-BHE simulations in heterogeneous underground. The method analytically extracts the singular line source response and enables the effective training of neural correction associated with subsurface heterogeneity. An explicit parametrization of the thermal conductivity allows physics-informed learning of a single feedforward neural network to generalize across different subsurface conditions. By formulating the correction in borehole-centered relative coordinates, the learned correction can be reused as a universal corrector through spatial and temporal superposition principles. Numerical experiments based on the infinite line source (ILS), finite line source (FLS) and moving finite line source (MFLS) models show that the hybrid method outperforms analytical approximations with stable accuracy over long simulation horizons and achieves orders-of-magnitude speedups over traditional solvers. The proposed framework therefore combines the efficiency of analytical models with the ability of numerical methods to capture heterogeneous subsurface physics, providing a fast and accurate approach for repeated long-term simulation of multi-BHE systems.

Moke Rao, Thomas Hamacher, Smajil Halilovic

Technical University of Munich, Chair of Renewable and Sustainable Energy Systems, Germany

Neural Surrogate Modeling PDE Surrogate Modeling Physics-Informed ML

Jul 13, 2026eess.SY

Generating Physically Plausible Parachute Dynamics with Deep Generative Modeling

Accurately modeling the dynamics of planetary parachute and entry vehicle systems is critical for Entry, Descent, and Landing events such as vehicle separation and sensor activation. These dynamics are difficult to capture with traditional system-identification methods as parachute motion is highly nonlinear, the governing equations are not fully known, and relevant test data are scarce and expensive to acquire. In this work, we sidestep these challenges by leveraging a physics-aware generative modeling approach that learns parachute dynamics directly from data. The proposed method, Symplectic Parachute Generative Adversarial Network (SPar-GAN), adapts a Hamiltonian generative architecture to the parachute setting by conditioning on canopy design and freestream velocity, while enforcing conservation of energy through symplectic integration. We apply SPar-GAN to subscale parachute tests conducted at the National Full-Scale Aerodynamics Complex and show that it reproduces qualitatively accurate pitch-yaw dynamics of different parachute configurations while recovering a compact two-degree-of-freedom phase-space consistent with canopy axisymmetry. These results suggest that physics-constrained generative models can characterize parachute dynamics across operating conditions and may help reduce the volume of physical testing required to assess performance.

Yulong Yang, Clara O'Farrell, Christine Allen-Blanchette

Mechanical and Aerospace Engineering, Engineering Quadrangle, Princeton, NJ 08544 · Group Supervisor, Dynamics, Modeling, Flight Mechanics & UQ, 4800 Oak Grove Dr, M/S 198-326, Pasadena, CA 91011, AIAA Member · Center for Statistics and Machine Learning, Engineering Quadrangle, Princeton, NJ 08544

Physics-Informed Generative Modeling Physics-Informed ML Conditional Generative Modeling Physics-Based Simulation Generative Adversarial Networks

Jul 13, 2026cs.LG

SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations

Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions. We show these failures are multi-causal, arising from the concurrent interplay of (i) spectral bias against sharp features, (ii) imbalanced multi-term optimization and loss-weight collapse, (iii) violation of temporal causality, and (iv) under-resolved collocation. We present SPARC-Net, a unified architecture and training framework that jointly addresses all four pathologies. SPARC-Net leverages an adaptive multi-scale spectral encoder with a learnable spectral gate, a gated residual backbone, adaptive activations, and a hard-constraint output ansatz that exactly enforces initial and boundary conditions, structurally eliminating loss-weight collapse. Training employs stabilized gradient-norm loss balancing, floored causality-respecting residual weighting, and residual-based adaptive collocation (RAD). Validated against exact analytic and high-order spectral reference solutions across four canonical benchmarks -- viscous Burgers', Allen-Cahn, convection (beta=30), and reaction -- SPARC-Net yields substantial improvements over vanilla PINNs: relative L2 error drops from 1.47e-1 to 1.14e-1 on Burgers' (22% reduction), 9.93e-1 to 5.78e-2 on Allen-Cahn (94% reduction), and 9.82e-1 to 3.54e-3 on reaction (100% reduction). A characteristic-coordinate encoder for hyperbolic transport further reduces convection error from 5.14e-1 to 9.88e-5 (100% reduction). We report five-seed mean +/- standard deviation errors, Wilcoxon significance tests, full ablation studies, hyperparameter sensitivities, an extension to the 2D heat equation, and comparisons against parameter-matched baselines.

Divyavardhan Singh, Dimple Sonone, Hammad Mohammad +1

Dept. of Electronics Engg. SVNIT Surat, India

PDE Solving Spectral Bias Physics-Informed ML

Jul 13, 2026cs.CV

FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction

Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.

Zheng Zhang, Hao Tang, Yingying Hu +2

Centre for Smart Health, The Hong Kong Polytechnic University, Hong Kong, China · Department of Nuclear Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China · Research Center for Medical AI, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

Flow Matching Image Reconstruction PET/CT Imaging Physics-Informed ML

Jul 13, 2026cs.LG

Multi-dimensional training-priority weighting based on physical information propagation paths: a unified residual-weighting framework for physics-informed neural networks

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy. Existing causal training methods focus mainly on the temporal dimension, lacking a unified characterization of spatial and boundary dimensions. To address this, we define a unified class of training priorities according to the physical information propagation path: premise regions should be learned before dependent regions; temporal, spatial, and boundary priorities are instances of this principle. Using neural tangent kernel (NTK) dynamics, we theoretically analyze why standard PINNs do not obey this priority: their residual convergence order is governed by the NTK spectrum and is independent of the propagation path. Accordingly, we propose a unified multi-dimensional priority-constraint framework that partitions the domain along the propagation path and constructs negative-exponential residual weights, converting the physical propagation order into a training priority. For cases with coexisting priorities, we introduce a directional compatibility coefficient to clarify that "orthogonal directions can be coupled multiplicatively in synergy, whereas coaxial opposite directions cannot." Benchmark cases show that this method consistently improves the convergence behavior and prediction accuracy of PINNs on problems with clear propagation paths or constraint-dominated structures, without modifying the network architecture and with controllable additional computational cost.

Zhangyi Lian, Xinda Dong, Wenxuan Huo +3

College of Mechanical and Vehicle Engineering Chongqing University Chongqing 400030, China · State Key Laboratory of Tribology in Advanced Equipment Department of Mechanical Engineering Tsinghua University Beijing 100084, China

Neural PDE Solvers Adaptive Loss Weighting Physics-Informed ML

Jul 13, 2026cs.LG

Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen. However, before any operator is applied, the grid has already determined how modeling capacity is allocated across space, resolution, and spectral bandwidth. We argue that this hidden design choice should itself be learnable, leading to a question different from standard operator learning: can a surrogate learn where resolution should exist before predicting field evolution? We formulate adaptive discretization as a physics-constrained conditional generation problem over valid mesh displacements. The success of diffusion models in PDE field prediction suggests their potential for learning adaptive discretizations under similar structured constraints. This leads to a two-stage diffusion framework: Stage 1 learns an r-adaptive displacement mesh conditioned on the observed dynamics, while Stage 2 predicts the solution evolution from the mesh-informed representation. The mesh generator is regularized by physics-aware proxy channels, geometric validity constraints, and local spectral concentration so that adaptation remains physically interpretable and numerically legal. Across five PDE regimes, the results show that diffusion-based learned discretization is competitive with adaptive-mesh and reduced-order baselines, with particularly strong gains in regimes where fixed or handcrafted allocation is insufficient. The main conclusion is not that there exists a universal optimal mesh rule, but that discretization should be learned in a regime-dependent manner: different spatial and spectral structures favor different allocation behaviors. This reframes adaptive meshing for neural PDE solvers from a solver-specific heuristic into a generative representation-learning problem.

Zixuan Shen, Bingchuan Wang, Zhi Wang +1

Central South University · Central South University, Changsha, Hunan 410083, China · Nanjing University +1

Neural PDE Solvers PDE Surrogate Modeling Physics-Informed ML Adaptive Mesh Refinement Diffusion Models

Jul 12, 2026cs.AI

Incremental Transformer for Surrogate-Based Inverse Design of Geopolymer Mixtures

Small-data inverse design is challenging in engineering informatics when observations are heterogeneous, mixed-type, and constrained by physical relations among design variables. This work proposes a topology-aware surrogate framework guided by an Incremental Transformer (INCRT) for physics-constrained inverse design, applied to geopolymer mixture design. The method integrates intrinsic-dimensionality analysis, mixed-variable design-space representation, tabular surrogate prediction, INCRT-based manifold rationalisation, and constrained inverse optimisation. Using a public benchmark of fly-ash and slag-based geopolymer concrete mixtures with compressive-strength and carbon-emission targets, the high-dimensional design space proves strongly redundant, organising around fewer effective mixture regimes. Compressive strength requires nonlinear tabular surrogates, while carbon emission is largely determined by composition and well recovered by regularised linear models. INCRT thus acts not as a replacement for tabular predictors but as a rationalisation layer providing prototype regimes and a manifold-support score for inverse design. Three strategies are compared: unconstrained surrogate optimisation, physics-constrained optimisation, and topology-aware physics-constrained optimisation. Unconstrained optimisation can match target strength but may yield physically invalid or off-manifold candidates; physics-only constraints do not always ensure data support. The topology-aware strategy yields candidates balancing target compliance, carbon reduction, physical admissibility, and proximity to the learned feasible manifold. The framework aims not to replace experimental validation but to support screening of credible candidate mixtures from small, mixed, physically constrained engineering datasets.

Giansalvo Cirrincione, Filippo Grassia

Laboratory of Innovative Technologies (LTI, EA 3899) University of Picardie Jules Verne, Amiens, 80025, Hauts-de-France, France

Surrogate Modeling Materials Property Prediction Materials Science Constrained Optimization Physics-Informed ML Inverse Design

Jul 11, 2026cs.AI

Co4ICF: Co-evolving Physics-Informed Surrogate and RL-based Pulse Optimizer for Inertial Confinement Fusion

Offline-trained surrogates for Inertial Confinement Fusion (ICF) suffer a well-known failure mode that iterative optimizers drive inputs into out-of-distribution (OOD) regions where predictions become unreliable. Here we present Co4ICF, a co-evolving framework that couples a physics-informed surrogate with a PPO-based pulse optimizer. The surrogate is iteratively fine-tuned on policy-induced trajectories, correcting extrapolation errors as the optimizer shifts the input distribution; the optimizer queries this evolving surrogate as a fast environment. In the 1D MULTI environment, Co4ICF achieves 146.1% normalized yield based on current laser design baseline; as a post-hoc cross-fidelity check, the optimized pulse further attains 246.9% normalized yield when directly evaluated in 2D-MULTI without any 2D training or fine-tuning. Budget-matched ablations support that the gains are not explained solely by additional simulation data and are consistent with the co-evolving mechanism playing a key role. We release a large-scale MULTI-IFE simulation dataset to support future benchmarking.

Jiatong Zhao, Tengyue Zhang, Yuhan Wang +2

School of Physics and Astronomy Zhiyuan College Shanghai Jiao Tong University Shanghai, China · School of Physics and Astronomy Shanghai Jiao Tong University Shanghai, China · School of Artificial Intelligence Shanghai Jiao Tong University Shanghai, China

Reinforcement Learning Surrogate-Assisted Optimization Physics-Informed ML

Jul 11, 2026cs.RO

PIER-Flow: Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation

Autonomous navigation in dense and highly dynamic environments requires both physically feasible control and low-latency replanning. Optimization-based methods such as Model Predictive Control (MPC) explicitly handle robot kinematics and safety constraints, but repeated nonlinear optimization can limit real-time responsiveness. Deterministic behavior-cloning policies enable efficient inference but may fail to represent multimodal avoidance behaviors, whereas diffusion policies capture multimodality at the cost of time-consuming iterative denoising. We propose PIER-Flow (Physics-Informed Efficient Rectified Flow), a lightweight navigation policy for mobile robots. By distilling an MPC expert into a continuous-time Ordinary Differential Equation (ODE), PIER-Flow achieves single-step action generation through parallel latent sampling and lightweight feasibility selection. We introduce a physics-informed training objective to enforce kinematic consistency, paired with an asynchronous action chunking architecture for robust sim-to-real deployment. Extensive simulations demonstrate that PIER-Flow achieves a 98.85% success rate and zero collisions, with an average inference of

\sim

1.29 ms, which accelerates planning by 37.2

\times

compared to MPC and over 800

\times

against standard diffusion models. Crucially, real-world deployment on a resource-constrained edge computer further achieves an approximately stable inference latency of

\sim

5.3 ms, avoiding the latency spikes and freezing events observed with planning baselines.

Shibo Li, Zhongcheng Wang, Jiahe Cao +2

School of Automation, Northwestern Polytechnical University, Xi’an, China · Department of Robotics, Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi SE45 05, United Arab Emirates

Constrained Motion Planning Robot Policy Learning Rectified Flow Robot Navigation Physics-Informed ML

Jul 11, 2026cs.LG

The Differential Neural Tangent Kernel and Its Positivity

The Neural Tangent Kernel (NTK) is one powerful tool for analyzing the training dynamics of neural networks in the over-parameterized regime. Recently, the theoretical framework has been extended to physics-informed neural networks (PINNs) for solving linear PDEs, one highly popular class of neural PDE solvers. In the analysis, the positivity of the associated NTK plays a fundamental role. However, establishing the positivity of the NTK for PINNs is highly challenging, due to the presence of multiple differential operators. In this work, we propose a new theoretical framework, called Differential Neural Tangent Kernel (DNTK), for analyzing PINNs through the lens of the NTK, and establish the positivity of the infinite width DNTK for both shallow and deep neural networks for a wide class of activation functions, including RePU and smooth but non-polynomial activations, for all linear differential operators. These theoretical results lay the foundation for the analysis of gradient type algorithms for training PINNs.

Bangti Jin, Longjun Wu

Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China

Neural PDE Solvers Physics-Informed ML Neural Network Training Dynamics Neural Tangent Kernel

Jul 10, 2026physics.flu-dyn

Entropy-Constrained Machine Learning with Residual Data Augmentation for Modeling Chemical Kinetics

We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.

Okezzi Ukorigho, Opeoluwa Owoyele

Department of Mechanical and Industrial Engineering Louisiana State University, Baton Rouge, LA 70810, USA

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

Jul 10, 2026cs.RO

Residual Physics-Informed Neural Networks for High-Fidelity BLDC Motor Modeling

Accurate dynamics modeling of Brushless DC (BLDC) motors is fundamental to high-performance robotic joint control. This paper presents a Physics-Informed Neural Network (PINN) with a deep residual (ResNet) backbone that learns a continuous-time surrogate of the full six-state BLDC motor dynamics. Given simulation time, applied three-phase voltages, and excitation parameters as inputs, the network directly predicts all motor state variables -- rotor angle, angular velocity, three-phase currents, and winding temperature -- while simultaneously satisfying the governing electromechanical and thermal ODEs through a composite physics-data loss. A curriculum scheduling strategy gradually activates the physics penalty to prevent premature convergence. Training runs are completed in under two minutes on a standard CPU. Crucially, once trained, PINN inference achieves latencies of 0.1--22, mu s per query, up to 118x faster than conventional ODE solvers, making it suitable for real-time observer and control applications.

Haitham El-Hussieny

Department of Mechatronics and Robotics Engineering, Egypt-Japan University of Science and Technology (E-JUST), New Burg El-Arab City, Alexandria, Egypt

Neural Surrogate Modeling Physics-Informed ML

Jul 9, 2026cs.AI

PARA-PV: Physics-Aware Retrieval-Augmented PV Prediction Based on Frozen Foundation Model and Distribution Shift Correction

Accurate photovoltaic (PV) power forecasting is essential for reliable grid dispatch and renewable energy integration, yet it remains challenging because PV generation is jointly shaped by weather variability, day-night transitions, regime-dependent dynamics, and strict physical constraints. We propose PARA-PV, a Physics-Aware Retrieval-Augmented framework that embeds physical knowledge throughout the forecasting process. The framework first encodes multivariate PV observations into patch-level representations and, through a physics-aware retrieval-augmented learner, retrieves historical patches and analog trajectories that are consistent with the current window in temporal shape, power level, PV operating state, and intra-day period; this yields a physically grounded base forecast. To supplement local memory with broader temporal knowledge, the base forecast is then calibrated against a frozen Chronos time-series foundation-model prior through a lightweight residual adapter, so that general temporal regularities are adapted to PV-specific dynamics without overriding the physically grounded prediction. Because residual conditional distribution shifts persist when weather and diurnal regimes change, a physics-aware distribution shift correction module subsequently adjusts the preliminary forecast using power, weather, timestamp, and day/night conditions, applying gated mean-shift and scale corrections selectively. Finally, a physics-constrained loss function partitions the samples into peak, ramping, night-time, and regular regimes and adaptively reweights their error contributions, preventing the dominant regular regime from suppressing learning of operationally critical states. Our code is available at https://github.com/weican1103/PARA-PV.

Hang Fan, Weican Liu, Ying Lu +3

School of Economics and Management, North China Electric Power University, 102206, Beijing, China · School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, 50 Nanyang Avenue, Singapore · Department of Electrical Engineering, Tsinghua University, 100084, Beijing, China

Time Series Forecasting Non-Stationary Time Series Forecasting Solar Power Forecasting Physics-Informed ML Retrieval-Augmented Time Series Forecasting

Jul 8, 2026cs.CV

Beyond Thermal Imaging: Inferring Thermophysical Properties from Time-Resolved Thermal Observations

Inferring latent physical properties from sensory observations is a fundamental challenge in machine perception. Among available sensing modalities, thermal imaging is particularly promising because temperature evolution is directly governed by heat-transfer physics and therefore encodes information about underlying thermophysical properties of a scene. Recovering spatially resolved thermophysical properties from thermal observations could transform applications ranging from digital twins and infrastructure monitoring to robotics and scientific imaging. However, existing thermal scene reconstruction methods can recover temperature fields in complex 3D environments without identifying the thermophyiscal properties that govern thermal evolution, whereas inverse methods provide physically interpretable parameter estimation but typically rely on simplified geometries and controlled experimental conditions. Here we introduce ThermoField, a framework that unifies thermal scene reconstruction and thermophysical parameter estimation through differentiable heat-transfer simulation. The proposed framework represents these quantities as spatially varying neural fields and constrains them through scene geometry, governing heat-transfer physics, and temporal thermal observations. We demonstrate that ThermoField jointly reconstructs geometry, estimates spatially varying thermal diffusivity, and predicts thermal evolution under previously unseen environmental conditions. By integrating neural scene representations with differentiable heat-transfer solver, the framework enables physically interpretable parameter inference in complex 3D scenes. Our results establish a bridge between thermal scene reconstruction and inverse heat-transfer analysis, providing a unified approach for geometry reconstruction, thermophysical property estimation, and predictive thermal simulation from thermal observations.

Chenghao Xu, Malcolm Mielle, Olga Fink

Intelligent Maintenance and Operations Systems, ´Ecole polytechnique f´ed´erale de Lausanne, Station 18, Lausanne, 1015, Vaud, Switzerland. · Schindler Lab EPFL, Schindler Holding AG, Station 18, Lausanne, 1015, Vaud, Switzerland.

Thermal Imaging 3D Reconstruction Materials Property Prediction Physics-Informed ML Inverse Problems

Jul 8, 2026cs.LG

Physics-Informed Machine Learning Under Small-Data Constraints: Lessons from Abrasive Waterjet Milling

In physically dominated machining processes, experimental datasets are small, expensive, and material-specific; in this regime, data curation, evaluation design, and the form of physics integration can matter as much as the learning algorithm. Using an abrasive waterjet milling dataset (

n{=}155

, Inconel,718), we make three methodological contributions. First, we separate physics-based data \emph{cleaning} from statistical \emph{curation} and treat the latter as competing modelling hypotheses rather than silent preprocessing. Second, we find that model rankings from a 15-point hold-out set can be unstable: the single-split winner drops from rank~~1 to rank~~7 under 10-fold cross-validation, while Gaussian Process (GP) variants occupy the top ranks. Third, we study a spectrum of physics integration levels and find that residual learning on a compact physics baseline is competitive for GP, yielding lower variance and an interpretable decomposition, but degrades tree-based models. Bayesian hyper parameter tuning improves parameter-sensitive baselines such as gradient boosting and SVR, yet harms multi-stage hybrid pipelines at this sample size. GP uncertainty intervals are approximately calibrated (

86\%

empirical coverage at nominal

90\%

). The resulting picture is methodological: for small, expensive process datasets, our results suggest that, in this setting, reliable model comparison benefits from explicit curation hypotheses, robust evaluation, and careful choices about how physics enters the model.

Sarah Grewe, Jörg Frochte

Bochum University of Applied Sciences Germany

Surrogate Modeling Residual Learning Physics-Informed ML Gaussian Process Regression Data-Efficient Learning

Jul 8, 2026cs.LG

HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization

Deep generative models offer a promising paradigm for topology optimization, enabling rapid design exploration. However, these approaches lack intrinsic physics guidance, often leading to poor generalizability across unseen boundary conditions and the formation of floating material artifacts. To address these limitations, we propose Hierarchical Physics-Guided Diffusion (HPG-Diff), a novel diffusion framework that enforces physics consistency through two synergistic mechanisms. First, we introduce a hierarchical physics-guided strategy that aligns different precomputed physics features with the denoising process, guiding material distribution toward optimal load paths to enhance generalizability. Second, we propose a floating material suppression loss as a differentiable connectivity constraint inspired by thermal conduction to improve topological connectivity. By simulating a virtual heat propagation process from load positions, this mechanism explicitly penalizes floating material during training. Quantitative evaluations demonstrate that HPG-Diff achieves average compliance errors of 0.87% (in-distribution) and 5.29% (out-of-distribution), while reducing floating material ratios to 2.90% and 2.44%, respectively. Furthermore, case studies on a 3:1 rectangular domain, including cantilever and bridge benchmarks, provide preliminary evidence that lightweight LoRA fine-tuning with a small dataset can support the adaptation of HPG-Diff to rectangular non-square domains.

Jinbo Yang, Mingyue Yuan, Boyuan Zhang +2

School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China · Computer Science and Engineering, University of New South Wales, Sydney, 2052, Australia · College of Intelligence and Computing, Tianjin University, Tianjin, 300072, China +1

Topology Optimization Physics-Informed Diffusion Models Diffusion Model Guidance Physics-Informed ML

Jul 8, 2026cs.LG

Physics-guided spatiotemporal neural models for fuel density prediction

This paper presents a physics-guided machine learning (PGML) framework for fuel density prediction, integrating physics constraints and domain knowledge into deep learning models to enhance model accuracy and stability. We explore three deep learning architectures -- ConvLSTM, Adaptive Fourier Neural Operator (AFNONet), and Video Vision Transformer (ViViT) -- to model the spatiotemporal evolution of fuel density. Our approach incorporates differentiable physics-informed terms in the loss function, including a mass-conserving fuel transport term and a rate-of-spread estimation. Experimental results, averaged across multiple independent trials, demonstrate that the proposed PGML framework outperforms purely data-driven baselines without physics constraints in both accuracy and stability. This framework enables computationally efficient, physically plausible fire forecasting to support adaptive prescribed burn management.

Tolga Caglar, Jaynil Jaiswal, Saqib Azim +3

San Diego Supercomputer Center University of California, San Diego

Wildfire Forecasting Physics-Informed ML Spatiotemporal Forecasting

Jul 7, 2026cs.RO

CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts

Physics-informed learning promises data-efficient and stable dynamics prediction, yet its strongest geometric guarantees have largely remained confined to closed conservative systems. This excludes robotic systems of interest, where actuation, dissipation, and constraints exchange energy and momentum with the environment. We introduce CaLiSym, a lightweight framework that extends symplectic learning to such systems by changing where the geometric prior is imposed. Rather than enforcing symplecticity on the measured state, CaLiSym embeds the state and its ports into a lifted phase space, where the dynamics evolve through a symplectic map. The lift is explicit and algebraic, requiring neither recurrent latent states, transformer decoders, implicit optimization, nor inference-time numerical integration. We instantiate the framework with SympNet predictors and introduce GRB-SympNet, a B-spline variant combining approximation with exact symplectic structure. Experiments on a controlled dissipative double pendulum, a real-world quadrotor, and a contact-constrained real-world quadruped demonstrate the lowest out-of-distribution autoregressive rollout error across systems, improving by up to 69.5% while using fewer parameters and up to 85x fewer floating-point operations per step than sequence-model baselines. The lifted dynamics preserve the symplectic form to numerical precision, extending symplectic learning beyond conservative mechanics toward real-world robotics.

Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares +2

Department of Engineering Science, University of Oxford, Oxford, UK · School of Mathematics and Physics, University of Sussex, Brighton, BN1 9RH, UK. National Centre for Quantum Computing, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire, OX11 0QX UK

Dynamical Systems Robotics Physics-Informed ML

Jul 7, 2026cs.AI

A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems

Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations while embedding the underlying physical laws directly into the learning process. This study presents a PINN-based framework for modeling transient elastodynamic wave propagation in bimaterial systems governed by the axisymmetric equations of linear elasticity. A steel-aluminum specimen representative of a Split Hopkinson Pressure Bar configuration is considered, and the governing elastodynamic equations, together with the corresponding initial, boundary, and interface conditions, are incorporated directly into the network through a physics-informed loss function. High-fidelity finite-element simulations performed using ANSYS Workbench Explicit Dynamics are used for validation and as supplementary data constraints during training. The proposed framework accurately predicts wave transmission and reflection across the bimaterial interface and reproduces axial and radial displacement histories, face-averaged responses, and the dominant stress and strain evolution with close agreement to the finite-element solutions. The trained network further demonstrates the ability to predict wave responses at previously unseen time instants and for modified material properties without requiring additional finite-element simulations, providing a continuous surrogate model for elastodynamic analysis. Mesh-sensitivity studies confirm numerical robustness, while additional material combinations demonstrate the generality of the proposed methodology. The results show that integrating physics-informed neural networks with explicit finite-element analysis provides an accurate and computationally efficient framework for elastodynamic wave propagation in heterogeneous solids, offering an effective surrogate modeling approach for high-rate solid mechanics and impact engineering applications.

Sonal Ankush Chibire, Jenn-Terng Gau, Bo Zhang

Department of Mechanical Engineering, Northern Illinois University, 1425 W Lincoln Hwy, DeKalb, 60115, IL, USA.

Structural Mechanics PDE Surrogate Modeling Physics-Informed ML

Jul 7, 2026cs.LG

Physics-Informed Neural Embeddings of PDE Solution Families

We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions. A head-orthogonalization penalty removes degeneracies in the latent representation and stabilizes the principal-component spectrum across training realizations. Because the initial condition is built into the network output by construction, these principal components measure the additional variability the network learns on top of the initial profile, not the full solution itself. We apply the method to the one-dimensional viscous Burgers equation, with the heat and wave equations as robustness checks. For a latent dimension

n_b=20

, the learned manifolds exhibit pronounced effective dimensional reduction: for Burgers dynamics, only

2

-

4

principal components capture about

95\%

of the latent-space variance, while

4

-

7

capture about

99\%

, depending on the initial-condition family; the same qualitative compression holds for the heat and wave equations. We also split the wavenumber axis into bands (``Fourier shells'') and measure how much each band contributes to every principal component. The resulting frequency profile is invariant under the change-of-basis freedom that the orthogonalization penalty leaves in the latent space, and is therefore reproducible across independent training runs. More broadly, this establishes the learned spectral profiles and principal components as robust observables of solution-manifold geometry.

Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas +3

Institute of Cosmos Sciences (ICC), University of Barcelona, Martí i Franquès 1, ES-08028, Barcelona, Spain. · Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092, Zürich, Switzerland. · Institute for Applied Computational Science, Harvard University, Cambridge, MA, USA. +1

Intrinsic Dimensionality PDE Solving Manifold Learning Physics-Informed ML

Jul 7, 2026cs.SD

Learning-based Physics-Constrained Neural Kernel for Sound Field Estimation With Source-Position-Dependent Directional Weighting

A learning-based physics-constrained neural kernel for sound field estimation is proposed. Sound field estimation aims to estimate the spatial distribution of an acoustic field from a discrete set of microphone measurements, which have a wide range of applications. Among existing sound field estimation methods, kernel-regression-based methods offer a flexible and principled framework for incorporating physical constraints and allow inference through linear operation. It is also possible to adapt the kernel function to the target acoustic environment by representing the directional weighting function as an implicit neural representation (INR) and optimizing hyperparameters using measurements. However, the kernel function is generally optimized for single snapshot measurements of the microphones, which can lead to strong overfitting and poor generalization. We propose a source-position-dependent INR for the directional weighting function, enabling the kernel function to capture common directional patterns and to generalize to unseen source positions in the target acoustic environment. Experimental results indicate that our proposed method outperforms the snapshot-based method by estimating a directional weighting function that matches the directivity of the target sound field.

Mattia Marella, Shoichi Koyama

National Institute of Informatics, Tokyo, Japan · University of Ferrara, Ferrara, Italy

Kernel Regression Implicit Neural Representations Kernel Methods Physics-Informed ML Spatial Audio

Jul 7, 2026cs.CV

PhyMRI-SR: Toward Physics-Aware MRI Image Super-Resolution

Magnetic resonance imaging (MRI) super-resolution is vital for improving diagnostic accessibility, yet most methods treat it as a deterministic mapping from a fixed low-resolution input to a high-resolution target. This overlooks a key property of MRI acquisition physics: spatial resolution and signal-to-noise ratio (SNR) are inherently coupled, making any given low-resolution scan merely one of many possible realizations under varying acquisition trade-offs. We rethink MRI super-resolution as a physics-aware reconstruction problem, in which the goal is to identify the optimal resolution-SNR configuration and then super-resolve it to obtain high-quality MRI results. A key implication of this formulation is that MRI resolution becomes dynamic rather than fixed. To handle such resolution-heterogeneous inputs, we adapt 2D Gaussian Splatting (2D GS) to MRI by formulating reconstruction as a coordinate-based, resolution-agnostic rendering problem. To further enhance fidelity, we introduce three innovations: (1) a prior-aware Gaussian representation that combines an Anatomical Structure Prior for tissue-specific kernel initialization with an Imaging System Prior that captures hardware characteristics via a covariance dictionary; (2) a physics-constrained signal modeling scheme that predicts intrinsic tissue parameters (proton density rho and effective relaxation rate R2) and synthesizes intensities through governing physical equations, ensuring biophysically plausible contrast; and (3) a meta-learning framework that alleviates paired-data scarcity by pretraining on simulated data and adapting to real-world conditions. Extensive experiments on dynamic-resolution datasets and standard benchmarks demonstrate that our method achieves state-of-the-art performance, highlighting its strong potential for clinical deployment.

Lihua Wei, Huatong Gao, Jia Gong +4

Medical Image Super-Resolution Magnetic Resonance Imaging Physics-Informed ML Gaussian Splatting

Jul 7, 2026cs.LG

Self-Supervised Implicit CEST Reconstruction via Physics-Informed Lorentz Encoding

Multi-Pool Chemical Exchange Saturation Transfer (CEST) MRI provides valuable metabolic information but is clinically limited by long acquisition times. Although sparse sampling reduces scanning time, reconstructing high-resolution Z-spectra from limited data remains an ill-posed inverse problem. Conventional interpolation and generic Implicit Neural Rep-resentations (INRs) often lack physical constraints, leading to spectral artifacts and physically invalid signals. To address this, we propose Lorentz Encoding (LE), a physics-informed framework that formulates CEST reconstruction as a self-supervised reconstruction task via implicit continuous coordinate learning. Unlike generic positional encodings, LE regularizes the continuous spectral mapping by projecting sparse coordinates into a physically constrained space governed by a combination of parametric Lorentzian profiles with learnable basis functions. This mechanism effectively reduces noise and enforces consistency with physical models. Experiments on in vivo human brain data demonstrate that LE significantly outperforms state-of-the-art methods. Specifically, under a 39-point sampling strategy, LE achieves a PSNR of 57.58 dB and an SSIM of 0.9994. Furthermore, the learned physics-informed encodings form a continuous, geometrically ordered trajectory in the latent space, ensuring accurate quantitative metabo-lite mapping (APT, NOE, MT).

Dexuan Li, Yupeng Wu, Chenglong Wang +4

Shanghai Key Laboratory of Magnetic Resonance, Institute of Magnetic Resonance and Molecular Imaging in Medicine, East China Normal University

Implicit Neural Representations Image Reconstruction Magnetic Resonance Imaging Physics-Informed ML