Papers
Machine learning for physics, as it is published.
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
Papers
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
4,567 papers in Physics-informed · newest first
q-bio.OT
Pediatric high-grade glioma is a dynamically heterogeneous disease in which therapeutic selection pressures, microenvironmental selection and developmental plasticity can reorganize cellular-state structure over time. Here we investigated these adaptive behaviors in glioma dynamics from single-cell ecologies by merging physics-driven artificial intelligence and complex systems theory. Specifically, this study explores canonical residual-based physics-informed neural networks (PINNs), dynamical systems modelling comparators, explainable artificial intelligence (XAI), and Block Decomposition Method (BDM) perturbation analysis to understand glioma cell fate decisions. The primary analyses distinguished longitudinal initial from recurrent H3K27M cells and, within the recurrent specimen set, stem/progenitor-like from differentiated/glial-like annotation-derived states. Across five-fold cross-validation, RD achieved AUC and macro-F1 for initial–recurrence discrimination, and AUC and macro-F1 for recurrent-state subtype discrimination. FP achieved AUC and , respectively. Cross-model XAI repeatedly prioritized PTGDS, CHI3L1, IGFBP7, SPARCL1 and NRXN3 in longitudinal progression. BDM perturbation rankings emphasized heat-shock/stress-response and immune-associated network signatures. These findings are candidate computational network biomarkers rather than experimentally established causal signatures. The study provides a reproducible bridge between physics-constrained latent dynamics, interpretable gene attribution, and data-driven algorithmic perturbation landscapes for in silico pattern generation about glioma cell fate plasticity and early recurrence detection.
gr-qc
We investigate the application of physics-informed neural networks (PINNs) to solve the vacuum Einstein equations in spherical symmetry. Our neural network architecture is designed to solve the 1+1D moving-puncture evolution, by minimizing a loss that combines a data term, the Ricci tensor of the reconstructed spacetime, and the moving-puncture gauge conditions. It represents the lapse, the shift and the Z4c conformal variables and , which remain regular at the puncture. We consider the evolution of a single, non-spinning black-hole in the puncture gauge and show that PINNs can interpolate numerical relativity (NR) data, predict its evolution, and reconstruct spacetime in regions where no data is provided. As an interpolant, the network provides a compact, differentiable representation of the NR data. Given only early-time and outer-boundary data, it evolves the puncture forward in time and reproduces the main features of the NR solution. Given only exterior data and no gauge condition, an ill-posed inverse problem, it recovers the interior of a Schwarzschild spacetime in coordinates of its own choosing, which we verify by learning the coordinate transformation to the Kerr–Schild form. Finally, we assess the strengths and limitations of PINNs for NR and outline their prospects for future applications.
math.OC
We develop a posteriori primal-dual bounds for numerical approximations of European option prices in the Uncertain Volatility Model. Given a smooth candidate approximation of the value function, a feedback control induced by its Hessian yields a primal lower bound. On the dual side, we derive a representation based on a matrix-valued Gamma field, which provides an upper bound through a nonnegative Hamiltonian penalty. We further show that, when the dual field is generated by the candidate itself, this upper bound admits an equivalent representation in terms of the residual of the associated Black-Scholes-Barenblatt equation. We then study discrete-time approximations of these primal and dual quantities and quantify the corresponding discretization errors. Finally, we investigate their numerical evaluation for candidates obtained by stochastic policy-gradient and physics-informed neural-network methods, and compare the resulting estimates with a martingale dual approach from the stochastic-control literature. The numerical experiments highlight the importance of derivative accuracy, and in particular of second-order information, for obtaining tight a posteriori bounds.
math.NA
Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accurate and typically trained by non-convex optimization without error control. We propose IGA-KAN, which uses local Kolmogorov-Arnold networks, fitted in closed form, to improve the IGA solution instead of replacing it. An IGA Galerkin solve produces u_h; on every knot-vertex patch a Kolmogorov-Arnold ridge model is fitted to the strong form of the equation, the exact boundary data and u_h, and the models are blended by IGA hat functions. With fixed inner functions the fit is one batched linear least-squares problem, without optimizer, learning rate or initialization. An a posteriori safeguard, motivated by a maximum-principle bound, decides where local models are used, keeping the IGA solution elsewhere. On eight benchmarks with exact solutions, five from the literature and one also posed on a domain fitted to a brain slice from MRI, the method reduces the error of IGA, at an unchanged number of Galerkin unknowns, by factors of 4.2 to 90 in L^2 and 4.1 to 220 in H^1 on the reference meshes, and its L^2 error is 6 to 6x10^4 times smaller than that of the best Kolmogorov-Arnold network trained from scratch on the same equations with a fixed budget. In an inverse problem it recovers an unknown constant source from one noise-free observation 167 times more accurately than IGA. The gain is attributed to the superconvergence of local averages of the Galerkin solution.
cs.RO
Human demonstrations offer rich examples of precise dexterous manipulation and a promising source of robot training data. However, high-fidelity reproduction of demonstrated motions and hand-object interactions across robot embodiments remains challenging under physical constraints. We present DexForge, a differentiable physics-grounded framework for converting human video demonstrations into high-fidelity robot trajectories. We reconstruct spherical-Gaussian object models and hand-object motion from visual observations, then build a differentiable simulator combining efficient Gaussian collision detection with existing differentiable dynamics. Based on this simulator, DexForge combines contact-aware kinematic retargeting with force-aware dynamics retargeting: robot-adapted stable contacts guide kinematic reference construction and subsequent gradient-based control refinement for precise physical motion reproduction. Experiments on 130 DexYCB and HOT3D demonstrations across seven dexterous hands show success-rate gains of approximately 35-53 percentage points over the baseline, with object position and orientation tracking errors on successful trajectories reduced by approximately 34-67% and 71-78%, respectively. Further experiments demonstrate open-loop transfer to MuJoCo and real-robot execution. Our project page is available at https://wmz1226.github.io/DexForge/
math.AP
Physics-informed machine learning as recently emerged as a new paradigm for the resolution of partial differential equations, including functionalities for parametric modeling and inverse design, using neural networks to represent the solution fields. However, several difficulties have been reported concerning the training of such networks, resulting in slow convergence, low accurate solutions and sensitivity to the choice of hyper-parameters. In order to better understand the mechanisms underlying these difficulties, the present work proposes a rigourous comparison of neural networks and B-Splines representations within the same physics-informed learning framework. Four problems with closed-form solutions are numerically studied to establish a rigorous analysis of the accuracy and efficiency of the two representations, in terms of asymptotic convergence rates, sampling requirements, loss function minimization and arithmetic precision needed.
cs.LG
A multi-domain eXtended Physics-Informed Neural Network (XPINN) framework is developed for nonsmooth Delay Differential Equations (DDEs). This is the first implementation to demonstrate the efficacy of partitioning the temporal domain into subdomains of integer multiples of the characteristic time delay and progressively training the associated subnetworks while freezing previously learned parameters. The efficacy of the proposed framework is demonstrated using a machining dynamics model that incorporates both regenerative and nonsmooth frictional effects. Results demonstrate that the proposed multi-domain XPINN framework leads to better solution reconstruction in DDEs and improved parameter estimation compared to a generic PINN (SPINN) formulation. The proposed method works particularly well for extended temporal domains and non-constant history functions. The robustness of inverse XPINN (I-XPINN) is also assessed using reference data contaminated with Gaussian measurement noise. Results indicate that I-XPINN remains resilient to measurement noise and the physics-informed constraints guide the network toward accurately recovering the underlying dynamics. This demonstrates, for the first time, the potential of the proposed framework for reliable parameter identification in DDEs characterised by nonsmoothness and large time delays.
cs.LG
Recent neural power-flow solvers, including emerging foundation models, achieve accurate voltage predictions, yet such accuracy does not necessarily imply physically consistent solutions. Even small complex voltage errors can yield large AC power-balance residuals. We study this accuracy-consistency gap across PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA on realistic 2224-bus Great Britain network (GBnetwork) scenarios, with cross-grid evaluation of GridSFM over 31 systems. Using a singular value decomposition (SVD) basis fitted to training AC power-flow solutions, we find that neural prediction errors contain substantial components outside the dominant solution subspace. To address this mismatch, calibrated solution-subspace projection (CSP) suppresses off-subspace prediction components after train-only bias calibration, reducing Mean PB by 67.0%, 37.8%, 40.5%, and 68.9% for PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA, respectively, relative to calibrated predictions, while improving voltage-magnitude accuracy in all four models. These results identify output-error geometry as an important factor in physics-consistent neural AC power flow. Code: https://github.com/Kimchangheon/neural-acpf-error-geometry
eess.SY
The advanced operation of heat exchangers plays a critical role in the development of efficient and sustainable multivector energy systems. This paper proposes a hybrid physics-informed and data-driven framework for the analysis, identification, and regulation of transient heat transfer in counter-flow heat exchangers. A parameterized physical model combines classical heat-transfer relations with transport equations to capture convective propagation, transport-induced delays, and nonlinear effects associated with flow-rate variations. The heat-transfer coefficient is identified from experimental data, enabling the characterization of flow-dependent heat-transfer dynamics over a broad operating range. The identified model is then used to develop a hierarchical real-time control strategy. An inner loop regulates the volumetric flow rate using a high-order data-driven linear model, while an outer loop regulates the exchanged heat power using a machine-learning controller initially trained on the physical model and subsequently refined with experimental data. Experimental results demonstrate accurate reproduction of transient heat-transfer dynamics and effective heat-flow-rate regulation under varying thermal boundary conditions (identification fit above 94% in normalized root-mean-square error and total variation of the flow rate reduced by half compared to a proportional-integral controller). The proposed framework combines physical interpretability with data-driven adaptation for the analysis and real-time operation of dynamic heat-transfer systems.
cs.LG
Physics-informed neural network (PINN) training minimizes a weighted combination of partial differential equation (PDE), boundary-condition, and initial-condition losses. Because adaptive methods modify these weights during training, their weighted total losses are not always directly comparable. We compare fixed-weight PINN, gradient-normalized PINN (GNPINN), and a rule-based adaptive controller (AgenticPINN) under matched settings on a heat-equation benchmark and a simplified Czochralski-oriented thermal-fluid problem. In the crystal-growth MLP experiment, adaptive control reduced the PDE residual from the order of to , while the boundary-condition loss increased from the order of to . On the heat-equation benchmark, GNPINN achieved the lowest relative field error (0.054), whereas AgenticPINN obtained the smallest PDE residual but a relative error of 1.368. Gaussian-process surrogates were additionally evaluated using case-wise holdout tests on corrected Czochralski CFD parameter sweeps. The temperature-field error for the temperature sweep was approximately 6%, whereas the axial-velocity error for the crystal-rotation sweep was approximately 42%. These findings show that adaptive control can improve equation satisfaction while weakening other physical constraints. PINN training should therefore be evaluated using separate PDE, boundary-condition, and solution-error metrics rather than weighted total loss alone.
physics.comp-ph
The quasi-static Biot system, which governs coupled fluid-solid interactions in poroelastic media, poses significant computational challenges due to its strong coupling and multiscale nature. To address these, we propose a hybrid fixed-stress transferable neural network (HFS-TransNet) method. In HFS-TransNet, a data-driven TransNet module first approximates observed data on an initialization domain to supply a high-quality starting point for the subsequent physics-informed stage, which then drives fixed-stress splitting iterations via TransNet and admits an error bound. After each iteration, a greedy update strategy on a validation domain prevents model degradation and a relative tolerance criterion governs convergence termination. HFS-TransNet thereby inherits the robustness of the fixed-stress splitting scheme, the flexibility of data-driven modeling, and the transferability of TransNet, effectively overcoming the strong coupling and locking instability inherent in the Biot system. Ablation studies and comparisons with FS-FEM and FS-PINN confirm HFS-TransNet's superior performance in capturing multiscale coupled physics across varying physical parameters and boundary conditions. By bridging classical decoupled iterative schemes with hybrid scientific machine learning, HFS-TransNet offers a novel perspective for complex poroelastic simulations, as demonstrated by its successful application to brain edema simulations.
cs.NI
Many existing wireless digital twins (DTs) rely heavily on ray-tracing (RT)-based channel simulators to achieve scalability in large-scale environments. However, the geometric-optics (GO) approximations underlying RT become inaccurate in propagation regimes dominated by diffraction and refraction, which are prevalent at sub-6 GHz carrier frequencies. This paper presents a hybrid RT and physics-embedded physics-informed neural network (PE-PINN) framework that enhances site-specific wireless DTs with physics-consistent full-wave accuracy. Building on prior PE-PINN work, we introduce targeted architectural extensions, including a finite-length edge diffraction kernel and a lossy dielectric formulation based on complex wavenumbers, to accurately model electromagnetic wave interactions with realistic objects and materials. To balance accuracy and efficiency, we further propose a localized tunnel strategy that deploys PE-PINN models only along dominant propagation paths, selectively replacing or augmenting RT predictions in regions where GO assumptions break down. Comprehensive evaluations against full-wave COMSOL simulations demonstrate that the proposed framework closely matches reference solutions and significantly outperforms RT-only approaches in diffraction- and refraction-dominated scenarios. We further demonstrate seamless integration of the proposed approach into a realistic indoor wireless DT, highlighting its practicality and scalability for next-generation wireless network design.
cs.CE
This paper proposes a label-free physics-informed neural network (PINN) for non-associated Mohr-Coulomb plasticity with incremental strength reduction for the reliability of spatially variable - slopes. The PINN is trained with a virtual-work loss on the finite-element mesh and solves many random fields at once on a graphics processing unit. With a solver budget fixed on the homogeneous slopes, it reproduces the Abaqus factor of safety within 2 to 3% root-mean-square on 52 random fields and locates the failure mechanism in the same weak zones, with the plastic strain in the band under-resolved. A neural operator trained only on the PINN solutions predicts the factor of safety, displacement path and failure mode of a million fields in seconds. No finite-element solution enters the pipeline: Monte Carlo fields, importance samples and operator training data come from the PINN, and Abaqus serves only to verify the result. Monte Carlo simulation, the first-order reliability method, importance sampling and the operator give consistent failure probabilities down to for the slope studied, but a 3% scatter in the factor of safety inflates a probability of by up to a factor of two, and the absolute values refer to one mesh. A heterogeneous Bishop analysis gives failure probabilities 2.6 and 8.3 times lower although its critical circles follow the PINN mechanism, because a small difference in the factor of safety is amplified in the tail. The operator also yields the failure mechanism and displacement response conditional on failure.
cs.LG
Despite the growing popularity of physics-informed neural networks (PINNs), their applicability in the long-time integration of partial differential equations (PDEs) remains constrained. We argue that this problem stems from the lack of consideration of temporal causality in the original PINN formulation, resulting in a bias towards satisfying governing equations at later times before learning the initial condition and hence leading to erroneous solutions. To this end, we propose a novel method that seamlessly integrates temporal causality into the training process. Drawing inspiration from classical numerical methods where the temporal causality is reflected, we divide the time domain into nonoverlapping subintervals, assign a unique neural network to each subinterval, and construct a loss function founded on the integral form of PDEs within these subintervals. The proposed networks undergo sequential training, beginning with the initial time step. Our method demonstrates significant improvement in accuracy for long-time simulations of various PDE problems where the original PINN method fails while it requires less computational cost and memory compared to the PINN method. A parallelization algorithm is provided to further enhance the computational efficiency, showing a significant speedup for solving time-dependent PDEs.
cs.LG
We give checkable positive-definiteness criteria for the limiting neural tangent kernel (NTK) and high-probability finite-width gradient-descent guarantees for scalar- or vector-valued physics-informed neural networks (PINNs) with linear constraints. The constraints may be strong-form differential rows of any fixed finite order, including coupled systems, with any linear initial or boundary conditions; weak-form residual and boundary functionals; or finite-measure nonlocal observations such as integral, nonlocal-diffusion, and Dirac-data rows, all in any dimension. For each class, positive definiteness of the limiting NTK is equivalent to a rank condition on a finite coefficient, functional, or moment matrix of the fixed design: a certificate computed before training that detects structural zero modes. The model hypotheses are those of an ordinary two-layer PINN, a smooth nonpolynomial activation with bounded symmetric initialization, and are met by standard choices such as with uniform initialization. Given a certificate, explicit width and step-size conditions ensure, with high probability, that the empirical NTK retains at least half the limiting gap and that full-batch gradient descent decreases the training loss geometrically at every iteration. Controlled experiments check the certificates and the finite-width mechanism.
cs.CE
Additive friction stir deposition (AFSD) involves coupled thermal and material-flow fields governed by frictional heating, plastic deformation, and tool-imposed boundary conditions. High-fidelity finite-volume methods (FVMs) can resolve these fields but are computationally expensive, while constant-property approximations can distort the predicted thermo-mechanical response. This work develops a steady-state multi-task coupled physics-informed neural network (MCoPINN) to predict three-dimensional temperature and material-flow fields while reconstructing temperature-dependent thermal conductivity, density, and specific heat from sparse property measurements. A theoretical analysis decomposes prediction error into property reconstruction and neural field-solver contributions and characterizes the discrepancy associated with constant-property models. A controlled one-dimensional nonlinear-conduction study evaluates property reconstruction under sparse measurements. The framework is then evaluated for AFSD against a temperature-dependent FVM benchmark and experimental thermocouple measurements. MCoPINN reproduces the reference thermal and material-flow fields and reduces average temperature root-mean-square error from 50.13 K for the constant-property CoPINN to 30.28 K across four traverse speeds. MCoPINN requires approximately 8.5 hours of training per condition, compared with 52 hours for the FVM benchmark. These results demonstrate computationally efficient, physics-coupled prediction with temperature-dependent material properties.
math.NA
We study a physics-informed neural network (PINN) approximation of a coupled PDE system that models the interaction between fluid and elastic dynamics. The canonical heat-wave model considered here couples a parabolic and a hyperbolic equation through transmission conditions on a fixed boundary interface, and serves as a prototype for the Stokes-elastic systems that arises in real world applications. This coupling makes the error analysis more delicate than that for a single PDE. We bound the error between the exact and PINN solutions by the associated PINN residuals, and we moreover prove that the generalization error is controlled by the training error, the number of quadrature points, and the size of the network. {To the best of our knowledge}, these are the first error estimates for a PINN approximation of a coupled fluid-structure interaction PDE system. We also show that numerical experiments with respect to a given test problem.
cs.LG
Physics-Informed Neural Networks (PINNs) typically exhibit spectral bias, where some frequencies of the target function converge more slowly than others. In this work, we analyze the training dynamics of Fourier Feature PINNs in the Neural Tangent Kernel regime to address this limitation. We derive an explicit evolution equation to estimate the residual error in the frequency domain, demonstrating that the convergence rate of specific frequencies is primarily governed by the product of the differential operator's symbol and the spectral density of the initialization weights. Leveraging this theoretical insight, we propose an informative initialization strategy that tailors the initial weight distribution to the specific PDE being solved. With this method, we can diminish the operator-induced spectral bias, balancing the convergence rates across the frequency spectrum and achieving better prediction accuracy. Numerical experiments on linear and nonlinear partial differential equations confirm that this initialization strategy improves learning dynamics and approximation accuracy across frequencies compared to standard initialization methods, with no additional training cost.
cs.LG
Uncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for this class of problems face the curse of dimensionality, and existing neural solvers often ignore the stochastic structure that makes moments and calibration tractable. We introduce a stochastic separable physics-informed neural network, dubbed S-PINN, that represents the solution of a random PDE with a learnable Gaussian spatial dictionary, Fourier temporal features, and a generalized polynomial chaos (gPC) stochastic basis, coupled by a low-rank Canonical Polyadic (CP) tensor decomposition core. The method is trained with a hybrid strong-form and gPC-projected residual loss. Our theoretical analysis establishes that the separable class is dense in under mild conditions, and the projected residual corresponds exactly to a stochastic Galerkin constraint. Furthermore, we show that mini-batch projection coefficients are logarithmically dependent on the number of gPC modes, and that the orthogonality penalty controls the conditioning of the learned spatial dictionary. Using four manufactured random PDE benchmarks, we show that S-PINN outperforms nine baselines in terms of mean and variance accuracy, as well as calibration, while using significantly fewer parameters. Further evaluations on non-manufactured Poisson and Darcy problems, a stochastic Navier–Stokes problem, a diffusion scaling study of higher random dimensions, and two stochastic inverse problems reveal the generalization capabilities of the proposed structure. Together, these results support stochastic separability as an effective design principle for physics-informed neural UQ. The code for the experiments can be found in https://github.com/DMax1314/s2pinn
cs.LG
Biologically-informed neural networks (BINNs) have emerged as a flexible subclass of physics-informed neural networks (PINNs) for learning terms in partial differential equations from data. BINNs are particularly suited for biological systems, where the governing equations are highly nonlinear and only partially known a priori, and where data observations are often sparse, noisy, and incomplete. However, applying BINNs effectively in practice depends critically on hyperparameter selection, which remains a central challenge in equation-learning frameworks. Hyperparameters are often chosen heuristically and only cursorily documented, which limits the reproducibility of results and the transferability of methods. We present a diagnostic workflow for hyperparameter selection that can be used when the ground-truth equations are not known. The workflow is guided by three main questions: (1) Are the benefits of greater network capacity worth the cost? (2) Do more training epochs keep reducing the validation loss? (3) Do the learned terms stop changing as network capacity and training increase? We apply our workflow to synthetic systems of varying complexity with known ground truth, spanning diffusion and growth right-hand side terms and data ranging from 1D+t to 2D+t. We demonstrate that the validation loss generally follows the true error in the learned terms and distil practical rules of thumb for selecting hyperparameters in the BINN architecture. By providing a structured workflow, practical guidelines, and suggested starting values for hyperparameter selection, this work lowers the barrier to BINN-based equation learning.