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
physics.optics
BARseq enables spatially resolved gene-expression profiling across intact tissue, but its sensitivity depends on accurate detection and decoding of dense fluorescent rolonies. Existing spot-calling approaches can be conservative where signals overlap, while supervised deep learning is limited by the lack of reliable manual ground truth in real tissue images. Here we present PhySeqNet, a physics-informed deep learning framework for annotation-free fluorescent foci detection in BARseq. PhySeqNet trains U-Net detectors entirely on semi-synthetic images generated from an instrument-matched optical model combined with real sample-free experimental noise, and is integrated into pyBARseq, a modular Python pipeline for BARseq analysis. PhySeqNet achieved high detection performance on held-out simulated data across wavelength bands. On real tissue images, where ground truth is unavailable, we evaluated detections by forward-model reconstruction: PhySeqNet with conservative barcode-aware non-maxima suppression (NMSB) achieved higher reconstruction fidelity (NCC and MS-SSIM) than the BarDensr single-shot estimator, tuned classical spot detectors, and a pretrained deep-learning detector. In the analyzed brain section, PhySeqNet with NMSB yielded a median of 51 counts per cell versus 47 for BarDensr, with a similar number of genes detected per cell. The recovered transcripts produced spatial expression patterns qualitatively consistent with Allen MERFISH reference data and preserved cell-type composition after scANVI label transfer. These results show that physics-informed simulation can train practical, annotation-free detectors that improve BARseq sensitivity without disrupting downstream biological interpretation.
hep-ph
A novel physics-informed neural networks (PINNs) based approach for solving functional renormalization group flow equations is presented. We investigate the finite temperature phase transition in models without relying on the large- approximation, which was used in earlier attempts with similar methods. We argue that these previous solutions cannot easily be generalized for more complex symmetries, and hence our approach can provide new insight. Our technique relies on a series of ansätze that combines the small- and large-field approximation schemes with a neural network, leading to a highly accurate approximation over the entire field range. We compare the PINNs approach with traditional grid-based Runge-Kutta results and show that the network can successfully learn the temperature, field, and scale dependencies of the effective potential in the local potential approximation.
cs.AI
Many machine learning approaches are two-level: an expert selects a class of methods, within this class the choice of key components is critical and usually manual. This paper addresses the automatic tuning of these components and proposes a framework transferable across models of different nature. The multi-agent large language model (LLM) framework has three roles—analyst, coder, and recorder~—with an experiment log and a sandboxed execution environment. Unlike systems that optimize the entire ML script or search architectures in a discrete space, the framework operates over an open but semantically narrow space: the agent generates code only for the specified components, leaving the overall network structure unchanged. The approach is validated in two directions: tuning a classification spiking neural network with correlation learning, and solving high-order differential equations with Physics-Informed Neural Networks (PINN). Across five tasks—spiking classification on MNIST and Digits, and boundary-value problems for the generalized nonlinear Schrödinger equation (GNLSE) and Kuramoto–Sivashinsky (KS) equations—the agent outperforms the baselines: classification accuracy is 13 percentage points (MNIST) and 6 percentage points (Digits) higher; the error against the analytical single-soliton solution is reduced approximately 2491-fold; the invariant-preservation error drops approximately 325-fold in the selected GNLSE run with a Gaussian perturbation and by more than 100-fold on average over repeated initializations; and the mass drift drops 14-fold for the KS problem with a Gaussian perturbation. The framework thus tunes key components on tasks of different nature without changing its internal structure.
cs.LG
Motivated by the success of large language models (LLMs) with broad generalizability and robustness to noisy or unreliable pre-training data, we explore in-context prediction of PDE solution fields using approximate pre-training data. In addition, inspired by the posterior predictive mean-based inference mechanism of the in-context learning in prior-data fitted networks (PFNs), we propose PDE-PFN, a prior-data fitted neural solver that approximates the posterior predictive mean of PDE solutions via in-context learning. PDE-PFN builds on a PFN architecture with self- and cross-attention mechanisms of Transformer and is pre-trained on noisy approximate solutions generated by physics-informed neural networks, serving as diverse but not necessarily exact priors. Through experiments on a range of two-dimensional PDEs, we demonstrate that PDE-PFN achieves empirical generalization across heterogeneous equations, robustness under noisy priors, and zero-gradient-update in-context inference capability. PDE-PFN achieves competitive or improved predictive accuracy relative to the evaluated baselines while supporting flexible context and query representations.
cs.LG
Physics-informed neural networks (PINNs) are trained to minimize the residual of a prescribed equation, so a low training loss does not indicate whether a coefficient in that equation was specified incorrectly. This study evaluates what can be inferred about the encoded parameter from the trained network alone. When the residual is linear in the parameter, written as , the least-squares estimate is obtained from a single evaluation of the frozen network, without retraining or reference data. Its accuracy depends on how closely the network satisfies its own equation, quantified by a normalized residual . Recovery error is associated with (log-log correlation 0.72 across 36 convection-diffusion networks), and empirical exponents of 0.63 to 1.20 across three equations decompose into one half plus a measurable angular term. For Burgers' equation, a single-model test based on a block-bootstrap standard error flagged 3 of 300 correctly specified networks (observed false-alarm rate 1%), all 2% misspecifications at a practical budget, and two thirds of 1% misspecifications after convergence. For the self-similar blowup rate of the Córdoba-Córdoba-Fontelos equation, where the rate also enters the architecture, the estimator recovers about half of the misspecification, whereas increases approximately quadratically and distinguishes a 0.2% error. When the incorrect rate enters both the equation and the architecture, errors of up to 2% were not detected at the precision reached. At practical budgets, the raw loss can be lower for the misspecified model, a scaling effect that does not share.
eess.IV
Accurate artery extraction from X-ray coronary angiography (XCA) is essential for coronary artery disease diagnosis and intervention. However, low vessel visibility, respiratory and cardiac motion, and limited annotations challenge existing methods. Moreover, most deep learning approaches produce binary vessel masks without preserving clinically relevant intra-arterial contrast information. We propose a Temporal Diffusion Bridge Model (TDBM) that formulates vessel extraction as image translation and learns from physics-informed synthetic data without manual vessel annotations. A physics-based XCA synthesis engine generates diverse, perfectly aligned pairs of contrast-enhanced and contrast-free images. Using these pairs, TDBM learns cross-domain mappings to recover high-fidelity vessel information. Temporal conditioning incorporates adjacent frames to improve consistency, while a vessel-aware contrastive loss exploits background-invariant synthetic pairs to enhance vascular discrimination. We evaluate TDBM on two XCA vessel segmentation datasets and conduct a reader study using two real-patient XCA sequence datasets. Zero-shot segmentation is further assessed on retinal imaging and fluorescence microscopy datasets. Results demonstrate that TDBM consistently outperforms existing methods and generalizes effectively across imaging modalities. Code and trained weights will be available at: https://github.com/Advanced-AI-in-Medicine-and-Physics-Lab/TDBM
cs.LG
High-dimensional sparse recipe formulation in process industries involves nonlinear association of various covariates, bounded by sparsity constraints and multi-criteria tolerances. Traditional physics-based classical methods (such as Kubelka-Munk) fail to generate sparse candidate recipes properly due to their simplified assumptions and industrial process variations. This study proposes a hybrid physics-informed uncertainty-aware framework that is structured into three modules: (a) Module A, a multi-target forward quality model; (b) Module B, a sparse inverse reconstructor; and (c) Module C, a feasibility-constrained ranking layer. Then it has been validated in an industrial textile dyeing context with recipe-grouped cross-validation under multi-illuminant quality assessment comprising process and production information, target reflectance, K/S values, and spectral descriptors. Histogram Gradient Boosting (HGB) with spectral-only features (, K/S) and Gradient Boosting Regressor (GBDT) with recipe-process features outperforms other configurations with out-of-Fold MAE of 0.1655 and 0.1523 in the forward quality model. For inverse reconstruction, a component-wise median blend achieved a recipe-vector MAE of 0.0295. Exploratory conditional treatment effect (CATE) suggests an observational association that alkali adjustment reduces error for red and pale shades (CATE = -0.196). This framework provides a human-in-the-loop decision-support tool that minimizes costly laboratory trials across industrial formulation domains.
cs.RO
Close-proximity multi-arm manipulation requires collision models that are both geometrically accurate and differentiable enough for real-time optimization. Classical geometry checkers provide reliable distances but are difficult to use inside gradient-based model predictive control, while conservative proxy models can restrict tightly coupled motion. We present PI-UDF, a physics-informed unified differentiable framework for body-to-body collision distance prediction between articulated robots. PI-UDF combines analytical forward kinematics with learnable link-geometry embeddings and a shared residual network to predict pairwise inter-arm distances directly from robot configurations. To improve safety-critical fidelity, we combine quota-driven boundary mining with an asymmetric boundary-crossing penalty that emphasizes false-safe sign errors near the collision boundary. The learned distance field is integrated into nonlinear MPC as a differentiable inter-arm clearance term. We validate the framework on a real dual-Franka platform through high-speed close-proximity 14-DoF dual-arm swapping, sustained single-arm dynamic evasion, and dynamic-evasion planning configurations with frozen, predicted, and target-switching treatments of the moving arm. Hardware experiments and offline Drake/FCL replay show that PI-UDF provides a differentiable inter-arm clearance estimate suitable for closed-loop collision-aware collaborative robot motion generation.
math.NA
We propose a novel numerical method for transport-dominated problems using Physics-Informed Neural Networks (PINNs). In such problems, the solution can develop large gradients and fine structures over time. This is particularly challenging for classical PINNs, which represent the solution itself. In our approach, rather than the solution, we choose to approximate the flow map of the equation. The solution is then recovered by pulling back the exact initial condition, so that its fine structures are produced by the map rather than represented by the network. Our method is constructed by approximating the flow map of the equation with multiple PINNs, one per time subinterval, and composing them using the semigroup property of the flow, so that each network only has to represent a map close to the identity. To highlight the advantages of our method compared to classical PINNs or classical numerical schemes, we present numerical results on the linear advection equation, the incompressible Euler equation in vorticity formulation, the Vlasov-Poisson equation, and finally a drift-kinetic equation.
cs.LG
Bayesian physics-informed neural networks (B-PINNs) are a popular framework for parameter and state inference from sparse or noisy observations. They are commonly formulated via a collider structure, in which physical and trajectory parameters are assumed to be a priori independent and become coupled through virtual likelihoods on differential-equation residuals that enforce physical consistency. We show that this modeling choice can induce severe systematic bias in the posterior over physical parameters: even when the prior is favorably centered on the ground-truth parameters, the resulting posterior can drift away and concentrate far from them. As a remedy, we advocate a hierarchical chain model in which physics generates trajectories, which in turn generate observations. The chain model does not suffer from this posterior bias, but it poses a harder, so-called doubly intractable, inference problem due to a physics-dependent normalization constant. This challenge can be resolved by discretizing the underlying stochastic dynamics, after which the chain posterior can be sampled exactly with particle MCMC. We identify two distinct mechanisms characterizing the collider bias, derive analytical approximations of their magnitudes, and establish diagnostic criteria for predicting when standard B-PINNs remain reliable. Experiments confirm the predicted bias and show that the chain formulation successfully avoids it.
cs.CE
Physics-informed neural solvers often struggle with multiscale behavior and sharp gradients due to the use of global approximation spaces and nonconvex training. We introduce AB-PIELM, an adaptive-basis physics-informed extreme learning machine that combines domain decomposition with joint optimisation of spatial and spectral hyperparameters while retaining deterministic normal-equation training. The method adapts both the number and placement of subdomains and the locality of radial basis functions, enabling problem-dependent allocation of representational capacity without modifying the underlying solver. Experiments on oscillatory function approximation and singularly perturbed advection-diffusion equations demonstrate accurate solutions across a wide range of stiffness regimes while using substantially fewer neurons than existing neural and PIELM-based approaches. The learned hyperparameters are interpretable, concentrating resolution near sharp gradients. The framework also supports inverse problems, successfully recovering diffusion coefficients from sparse noisy observations using Bayesian optimisation. These results indicate that adaptive-basis PIELM formulations provide an efficient and stable alternative to gradient-trained neural PDE solvers and naturally extend to broader classes of differential equations.
nucl-th
We have employed Bayesian inference to extract the centroid energies and widths from the isovector giant dipole resonance (IVGDR) data for the IVGDR built on the ground states of nuclei.These IVGDR properties were modeled by explicitly incorporating the structural effects like isospin asymmetry, nuclear deformation and shell correction. The resulting parametrizations reproduce the IVGDR systematics with remarkable precision for both spherical and axially deformed nuclei. Subsequently, the extracted IVGDR parameters were used to constrain the coefficients of the nuclear symmetry energy, which are found to be in good agreement with recent measurements of nuclear dipole polarizability. Furthermore, these symmetry-energy coefficients were employed to predict the dipole polarizability within different self-consistent mean-field models and to investigate its correlation with the neutron-skin thickness. The present findings provide valuable input for large-scale calculations of radiative capture processes relevant to nuclear astrophysics and for improving our understanding of astrophysical scenarios under extreme conditions.
cs.LG
Multi-domain physics-informed neural networks (PINNs) flexibly model medium-specific representations to solve fluid–solid conjugate heat transfer (CHT). However, standard multi-domain PINNs enforce governing equations and interface conditions on separately sampled domain supports, which can yield plausible temperature fields but inaccurate end-to-end energy transfer and outlet temperatures. We propose Cova-PINN, a multi-domain PINN framework that aligns conservation support with thermal interaction paths in complex geometries. Cova-PINN jointly optimizes cross-domain composite control-volume balances at the local scale and paired-wall closure at the global exchanger scale. We evaluate Cova-PINN on four triply periodic minimal surface (TPMS) heat exchangers and a geometrically distinct DualMS design against CHT-specific, optimization-oriented, and complex-geometry PINN baselines under a common protocol. Relative to the closest baseline, MUSA-PINN-CHT, Cova-PINN reduces average outlet-temperature and device-level closure errors across the four TPMS topologies by and , respectively, while also improving full-field and heat-duty accuracy, with consistent gains on DualMS.
cs.LG
Physics-Informed Neural Networks (PINNs) are a widely used data-free method for solving Partial Differential Equations (PDEs) using machine learning. With recent advances in Generative Adversarial Networks (GANs), adversarial learning has shown strong capabilities for modeling complex data-driven problems; however, the use of GANs in deterministic physics-informed PDE solutions remains limited. In this work, we first identify limitations of standard PINNs for solving PDEs, including spectral bias, loss imbalance, and optimizer stagnation. We then propose Generative Adversarial Physics-Informed Neural Networks (Gen-PINNs), a unified deterministic residual-adversarial framework designed to improve data-free solutions of PDEs with sharp or shock-front behavior. The generator learns the underlying PDE solution using dynamically weighted physics-informed loss components, while separate discriminators evaluate complementary PDE residual features against ideal zero-residual states. The framework further develops and adapts several methodological components, including a Fourier representation for resolving high-frequency spatial content, an orthonormal spectral diagnostic for quantifying frequency-dependent solution errors, and a modified gradient-based dynamic weighting system for physics, initial-condition, boundary-condition, and adversarial loss objectives. Gen-PINNs is tested against standard PINNs on nonlinear and higher-order PDEs, including the Burgers, Allen-Cahn, and Kuramoto-Sivashinsky equations. The results demonstrate substantial improvements in accuracy and convergence across sharp-front, stiff, and higher-order PDE solutions, highlighting the potential of deterministic residual-adversarial learning as an effective approach for solving challenging nonlinear PDEs.
cs.CE
Modeling heterogeneous materials remains a challenge for physics-informed neural networks such as the deep energy method (DEM). The DEM and its variants, here collectively referred to as the neural energy method (NEM), offer a differentiable variational framework. However, their conventional collocation-based implementation (C-NEM) often suffers from physically inadmissible displacement oscillations, integration errors, and high computational costs from automatic differentiation. This work introduces the mesh-based neural energy method (M-NEM), extending the NEM through a mesh-based discretization of the displacement field. By interpolating nodal displacements via shape functions, the M-NEM imposes a kinematic constraint that suppresses oscillations. Furthermore, the method replaces automatic differentiation with algebraic shape function derivatives for strain computation and employs high-order Gaussian quadrature for accurate energy integration. On a directly comparable benchmark problem, the M-NEM reduces stress errors by up to three orders of magnitude relative to the C-NEM while being one to two orders of magnitude faster. On two further benchmarks involving extreme stiffness contrasts, only the M-NEM converges. A comparative study of neural architectures reveals that radial basis function neural networks (RBFNNs) yield optimal performance within the M-NEM, resolving sharp gradients at material interfaces with higher accuracy than multi-layer perceptrons (MLPs) with random Fourier feature (RFF) mapping and faster convergence than Kolmogorov-Arnold networks (KANs).
physics.flu-dyn
Physics-informed neural networks (PINNs) provide a mesh-free framework for multiphysics modeling, yet fluid flow in axisymmetric cylindrical coordinates remains largely unexplored because the governing operators are singular at the axis and momentum and energy are strongly coupled through advection and buoyancy. We introduce SAGE-PINN, a Singularity-free Axisymmetric Geometry-Encoded Physics-Informed Neural Network for this class of problems. SAGE-PINN removes the coordinate singularity by construction: the parity-preserving variable and a modified stream-function representation eliminate explicit terms from the trained residuals and satisfy mass conservation identically. Boundary-fitted analytical ansätze enforce the boundary conditions exactly, while staged momentum-thermal-joint training, residual normalization, Péclet- and Richardson-number continuation, and a physics-scaled drift guard stabilize the coupled optimization. The framework is trained without labelled data, using only physics and boundary constraints, and its predictions are validated against finite-element reference solutions for steady nanofluid flow and heat transfer through a stenosed artery over a wide range of flow and thermal regimes, without case-specific tuning. Mass conservation remains at single-precision round-off, and over the central operating range the axial velocity and temperature are reproduced within and relative error, respectively. The main deterioration occurs only in the limiting regimes of strongly buoyancy-influenced slow flow and highly advection-dominated heat transfer. Embedding cylindrical geometry, conservation structure, and boundary physics directly into the network provides a robust route to PINN simulation of axisymmetric multiphysics flows.
cs.LG
Traffic flow modeling is essential for understanding and predicting the collective dynamics of vehicles on road networks. Cellular automata provide a simple, interpretable yet powerful framework for representing these dynamics via local interaction rules, while retaining the ability to reproduce complex macroscopic traffic phenomena. However, learning local transition rules from data while preserving physically meaningful constraints remains challenging, particularly for stochastic models. In this work, we propose a physics-informed neural cellular automaton (PI-NCA) for data-driven traffic flow modeling. Building on the standard neural cellular automaton (NCA), we design a neural architecture that is physically consistent with the road topology and guarantees conservation of the total number of vehicles, thereby constraining the learned transition rules to physically admissible dynamics. We further extend this framework to stochastic dynamics by parameterizing probabilistic transition rules while preserving the same physics-informed constraints. We evaluate the proposed models on multiple traffic scenarios generated by the well-established Nagel-Schreckenberg and Kerner-Klenov-Wolf cellular automata. The results demonstrate that the PI-NCA successfully learns the dynamics of both traffic models and consistently outperforms a standard NCA, while the stochastic extension captures probabilistic transition rules without compromising the imposed physical constraints.
cs.LG
Physics-informed neural PDE solvers adapt their parameters to satisfy governing equations, yet their representational structure typically remains fixed throughout training. This rigidity is poorly matched to PDE solutions with strongly heterogeneous complexity across space and space–time, leaving capacity insufficient where the physics is difficult and redundant where it is simple. We introduce physics-informed neural plasticity, a paradigm in which the representation itself reshapes during optimization in response to unresolved physics. We instantiate this principle with Representation Capacity Adaptation for PDEs (ReCAP), a Gaussian-localized solver that dynamically redistributes capacity through local enrichment, residual-directed splitting, gate-based pruning, and function-aware merging. ReCAP uses responsibility-weighted error indicators and the geometry of residual energy to determine where and how to refine. To limit the disturbance introduced by splitting, we introduce quiet-child refinement, which initializes new components by transporting the parent representation while controlling instantaneous functional perturbation. We further establish conditional a posteriori reliability and structural-stability guarantees linking localized physics residuals to solution error and stable refinement. Across five challenging 3D and 4D PDE benchmarks against 11 physics-informed solvers, ReCAP achieves the lowest relative error on every problem, reducing error by – relative to the strongest competing result. These results suggest that physics-informed solvers need not merely learn their parameters—they can learn how their representational capacity should be organized.
math.NA
We derive error bounds from empirical squared residuals for two non-monotone, mesh-free approximations of Hamilton–Jacobi–Bellman equations on unbounded spatial domains: collocation with Wendland kernels under a native space norm constraint, and physics-informed neural networks with smooth activations under a Sobolev-norm constraint. The main step is to recover the pointwise residual control needed for viscosity-solution error estimates from the empirical loss, while quantifying the discretization or sampling error. For the kernel method, we prove uniform convergence on compact sets under classical and native space regularity and derive an a posteriori quantitative error bound for the unique bounded continuous viscosity solution. For the neural-network method, we prove uniform convergence on compact sets in probability and give a quantitative high-probability error bound under classical Sobolev regularity. The bounds are governed by the fill distance for kernels and by the network and sample sizes for neural networks. The proofs combine empirical-to-population estimates, an interpolation inequality that turns an residual into a sup norm bound, and a controlled diffusion estimate for the error caused by truncating the domain. The regularity assumptions used to obtain convergence from approximation properties are additional to viscosity wellposedness. Numerical experiments in one and two space dimensions illustrate the methods and the estimates.
cs.LG
Accurate thermal modeling is essential in metal additive manufacturing (AM) for understanding the process-structure-property chain. Physics-informed neural networks (PINNs) offer effective surrogate thermal modeling by minimizing physics-based residual losses at collocation points. However, prior works typically rely on manually-crafted, static collocation sampling strategies, which are neither principled nor scalable across process conditions, hindering their generalization capability. In this work, we provide theoretical analysis through empirical risk minimization, showing that process condition-aware adaptive sampling is strictly more favorable than conventional static sampling for generalization. Building on this insight, we propose an adaptive sampling strategy within a two-stage framework: (1) a conditional Flow Matching model that learns approximate high-residual distributions across different process conditions, and (2) a mixed sampling strategy combining this distribution with a domain-informed base distribution to generate adaptive collocation points for refining the PINN predictor. Experiments on metal AM numerical benchmarks demonstrate that our method consistently outperforms state-of-the-art PINN baselines, achieving an average 62.1% reduction in relative error under an identical collocation budget, by capturing process-dependent heat dissipation regions often overlooked in the literature. To the authors' knowledge, this is the first adaptive sampling strategy for PINNs in metal AM, contributing to the enhanced generalization and broader applicability.