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-fin.MF
This paper proposes a deep learning-driven operator splitting scheme for high-dimensional free-boundary problems, with American option pricing as a representative application. In a market with proportional transaction costs, a stochastic liquidity risk with an empirically validated nonlinear drift based on S&P 500 data, and two-factor stochastic volatility, the pricing problem takes the form of a five-dimensional highly nonlinear variational inequality. The proposed scheme decomposes this variational inequality at each time layer into an elliptic continuation equation approximated by a physics-informed neural network and a closed-form projection step enforcing the early-exercise constraint. A conditional stability bound is derived under stated resolvent and Lipschitz assumptions. The scheme is validated against finite-difference and least-squares Monte Carlo benchmarks, and both the option prices and the learned exercise boundary show close agreement with the reference solutions. Sensitivity analyses with respect to the key model parameters are also reported.
cs.IT
Fluid antenna systems (FAS) leverage continuous reconfigurable apertures to transcend the spatial limits of fixed-position arrays, yet acquiring full-aperture channel state information (CSI) from sparse observations remains a formidable bottleneck. In this paper, we establish a continuous-field formulation for FAS by recasting channel estimation as a stochastic inverse field-reconstruction problem constrained by the projected Helmholtz model. Through electromagnetic information theory (EIT)-based spectral leakage analysis, we demonstrate that finite-aperture reconstruction induces an intrinsic convolutional relationship in the spectral domain, rendering the estimation task a fundamental frequency-domain inverse deconvolution problem. To solve this, we propose a U-shaped Fourier neural operator (UFNO) specifically tailored for noisy, underdetermined wireless environments. Furthermore, we leverage the Landau–Pollak theorem to derive an aperture-dependent EDoF bound that guides the spatial mode budget, and employ a physics-aware Sobolev loss to promote consistency in both channel values and spatial variations. Unlike conventional learning-based approaches, a single frozen UFNO can be directly evaluated at unseen spatial–frequency resolutions without resolution-specific retraining or explicit output interpolation. Extensive simulations show that our framework significantly outperforms state-of-the-art benchmarks in accuracy while achieving orders-of-magnitude lower inference latency than iterative solvers at high spatial–frequency resolutions.
cs.LG
Exploration in physical control environments requires agents to identify actions whose consequences reveal previously unexplored aspects of the underlying dynamics. However, many intrinsic motivation methods rely on immediate prediction errors, state novelty, or local physical changes, which may overlook informative outcomes that emerge across extended temporal horizons. We investigate whether learning structured representations of reachable futures can provide a more effective basis for exploration. To this end, we introduce Hamiltonian Temporal Contrastive Curiosity (HTC), a framework that combines multi-horizon temporal representation learning with Hamiltonian phase-space structure. A horizon-conditioned contrastive critic learns temporal relationships from future-state pairs sampled within the same episode. The distance between positive-pair representations is then used as an intrinsic reward, encouraging the agent to explore futures that remain insufficiently organized in the learned representation. To incorporate information about physical dynamics, we additionally modulate this reward using bounded multi-step Hamiltonian variation, rather than directly rewarding changes in the Hamiltonian itself. We integrate HTC with both Soft Actor-Critic (SAC) and Proximal Policy Optimization (PPO), and evaluate it across six DeepMind Control Suite tasks. Comparisons with ICM, RIDE, E3B, Plan2Explore, and a single-step Hamiltonian curiosity baseline are complemented by state-coverage evaluations, component ablations, and phase-space diagnostics to characterize the contributions of temporal learning and physical structure to exploratory behavior.
math.OC
High-fidelity digital twins in continuous biomanufacturing are often bottlenecked by incomplete kinetic models, while standard data-driven algorithms (e.g., SINDy, PINNs) lack interpretability or impose rigid physical assumptions. This paper introduces a hybrid closed-loop architecture for autonomous kinetic state-space discovery driven by a Large Language Model (LLM) agent. The framework employs a sequential "isolation-peeling" methodology across orthogonal operational regimes. This algorithmic peeling mathematically decouples entangled multiplicative (inhibitory) and additive (catalytic) biological rate law. Grounded in a Two-Level Retrieval-Augmented Generation (RAG) library, the framework utilizes Moving Horizon Estimation (MHE) and logarithmic decomposition to decouple complex cell growth kinetics into orthogonal multiplicative (inhibitory) and additive (regulatory) residual channels. When statistical degeneracy occurs an Active Design of Experiments (DoE) controller dynamically triggers targeted perturbations to decorrelate competing model hypotheses. Evaluated on a continuous stirred-tank reactor exhibiting unmodeled Haldane inhibition, Luong product toxicity, and secondary metabolite autocatalysis, the framework autonomously expanded the state space and recovered ground-truth parameters with under 6% error without a priori kinetic knowledge.
cs.RO
Large vehicles in cluttered environments are often blocked by movable obstacles, motivating mobile robot teams to clear traversable corridors. Navigation Among Movable Obstacles (NAMO) approaches often abstract obstacle displacements while neglecting robot dimensions, obstacle mass, contact geometry and forces, yielding physically infeasible plans. PushAround is a physics-informed hybrid search that couples geometric connectivity reasoning with short-horizon simulation to construct executable clearing plans. Repeated W-clearance connectivity graph (WCCG) queries expose frontier gaps requiring widening and rank them by estimated downstream costs. The search generates direct or recursive pushing candidates, selecting obstacles, directions, contacts and forces, and admits physics-evaluated candidates. Numerical experiments validate WCCG against standard connectivity checks and demonstrate scaling to denser clutter and teams of up to four robots, with robustness to simulated execution-side physical-parameter mismatch.
cs.RO
This paper studies the constrained pointing control problem of airborne electro-optical gimbals subjected to composite periodic and aperiodic disturbances. Under carrier vibration, input delay, and actuator constraints, achieving line-of-sight stabilization and tracking is challenging. A disturbance-separated model predictive control (MPC) scheme is proposed to compensate these heterogeneous disturbances according to their physical characteristics. An adaptive periodic observer predicts multi-harmonic vibrations over the MPC horizon using linear-regression frequency estimation. A linear observer estimates the aperiodic disturbance, and a bounded long short-term memory (LSTM) network predicts its change over the input delay. Embedding periodic predictions into the MPC model while applying aperiodic compensation outside the optimizer limits amplification of aperiodic estimation errors and improves pointing accuracy under frequency changes and parameter mismatch. On the stated headroom envelope, input-set tightening provides feasible commands within the prescribed limits, and a regional practical tracking bound is established under explicit input-sequence and predicted-state margin conditions. A UAV-mounted two-axis gimbal platform is assembled for comparative indoor hovering experiments, complemented by simulations under frequency changes and parameter mismatch. In the reported trials, the proposed method achieves yaw and pitch relative-angle root-mean-square errors (RMSEs) of 0.770 degrees and 0.350 degrees, reducing tracking errors by 25.1% and 45.9% compared with linear active disturbance rejection control.
math.NA
Physics-informed neural networks (PINNs) have emerged as a promising mesh-free framework for solving partial differential equations (PDEs), with broad applications in physics, engineering, and medicine. However, their performance is highly sensitive to the sampling strategy for training points. Conventional uniform sampling often fails to adequately resolve regions with complex solution features, leading to low efficiency and limited accuracy. To address these challenges, we propose a Lie symmetry-driven adaptive sampling framework for PINNs, termed Lie-AS-ISC. For PDEs admitting Lie symmetry groups, symmetry transformations are exploited to derive intrinsic functional relationships between the solution and its variables, enabling the construction of basis points with exact solutions that span the solution domain. Building on this, an adaptive sampling strategy is developed by jointly considering absolute error and invariant surface conditions, while a dual-index loss is introduced to enhance training constraints. The proposed method significantly improves prediction accuracy. The experimental results show that this method consistently outperforms existing methods in accuracy.
eess.SP
Inferring target position from WiFi channel state information (CSI) is challenging due to the noisy and heterogeneous nature of CSI-derived observations. Measurements such as angle, delay, and Doppler provide only imperfect information about target position and velocity, particularly in dynamic multipath environments where observation reliability varies. Motivated by this challenge, this paper proposes a physics-informed Bayesian state space framework for passive CSI-based tracking. We introduce a context-conditioned deep state space model (DSSM) that captures temporal motion and environmental dynamics, while adaptively modeling time-varying observation uncertainties. By incorporating geometric constraints, this framework enables heterogeneous CSI measurement modalities to jointly regularize the consistency and confidence of the tracking process. Experimental results demonstrate that the proposed framework yields smoother trajectory estimates with reduced temporal fluctuations and outperforms existing methods in tracking accuracy.
cs.LG
The differential neural tangent kernel (DNTK) is a tool for analyzing the training dynamics of overparameterized physics informed neural networks. In this work, we investigate the symmetry of the infinite DNTK under an orthogonal group, for two layer and deep neural networks separately, based on the explicit expression of the DNTK and recursive formula, respectively. The results are for all activations with or without a bias term, and shed insight into the structure of the infinite width DNTK. Then we prove that the integral operators over the unit sphere induced by operators from the same group orbit share the spectrum, and their reproducing kernel Hilbert spaces differ only by an orthogonal transformation, and that the operator fixed DNTK exhibits zonal symmetry on the unit sphere for symmetric operators. Thus the eigenvalue decay rate of the associated integral operator can be derived for shallow networks with RePU activation and zero bias initialization.
cs.AI
High penetrations of distributed energy resources (DERs) and fast-varying electric vehicle (EV) charging intensify voltage and line-limit violations in distribution networks (DNs), making safe, low-cost operation increasingly challenging. This paper proposes a physics-informed safe deep reinforcement learning (DRL) framework for coordinating community battery energy storage systems to mitigate constraint violations while minimizing operating cost. To represent nonlocal spatiotemporal interactions, we develop a dual-level physics-informed graph representation in which line impedance and capacity shape spatial information propagation, while power-balance, voltage-profile, and flow-reconstruction losses regularize the latent state toward control-relevant physical consistency. Building on this representation, we develop Lagrangian Dedicated-Critic PPO (LDCPPO), which implements constraint-specific value decomposition: independent reward and cost critics preserve heterogeneous voltage- and line-loading-related learning signals and combine their advantages only during the Lagrangian policy update. Case studies on DNs with high rooftop photovoltaic penetration and EV charging demonstrate that the proposed method reduces the key voltage-violation degree by up to 80.5% compared with the tested baselines, while also achieving the lowest voltage-violation count and line-overload degree with competitive operating cost.
eess.SY
Hybrid dynamical systems flow continuously but jump at discrete events. Physics-informed neural networks (PINNs) fit data while enforcing known dynamics, but a single network is smooth in time and cannot model these jumps. We show that the more closely a PINN follows a jump, the larger its physics loss must be. We propose hybrid-time PINNs (HT-PINNs), which assign one network to each flow interval of the hybrid time domain and train the networks jointly with the jump times and the unknown parameters. The number of jumps and the sequence of modes are found by enumeration. HT-PINNs recover the number of jumps and the restitution coefficient of a bouncing ball. In a MuJoCo simulation of robotic disassembly, where a robot pulls a press-fitted pin out of a housing through a spring, HT-PINNs find the number of jumps and the sequence of modes, and estimate the static and kinetic friction coefficients with small errors of 0.1% and 1.7%.
cond-mat.soft
Inferring constitutive laws from transient response data is a central inverse problem in soft condensed-matter physics, particularly when the relevant relaxation spectrum extends beyond the time window of a single experiment. Time-temperature superposition (TTS) constrains this problem for thermorheologically simple materials in the linear viscoelastic regime by allowing temperature to rescale the characteristic relaxation time without changing the underlying shape of the relaxation spectrum. We incorporate this constraint into a physics-informed machine-learning framework for time-resolved mechanical spectroscopy via chirp rheometry. We encode compact fractional viscoelastic models as causal convolutional features derived from the Boltzmann superposition principle, and we jointly fit multi-temperature chirp records using sparse variational Gaussian process regression. The model infers horizontal shift factors, constitutive parameters, and an observational-noise scale directly from time-domain stress-strain signals measured in the linear viscoelastic regime, without first extracting frequency-domain spectra or manually shifting separate curves. For synthetic Fractional Maxwell data, the method recovers the generating constitutive law from a prescribed model library and latent shifts over stress-noise levels from 3% to 25%. Applied to a DGEBA-IPDA epoxy dataset spanning the glass-transition regime, the pooled likelihood distinguishes competing fractional rheology models using the Bayesian information criterion. These results recast TTS master-curve construction as probabilistic inference over latent time rescaling and linear viscoelasticity, while also identifying limitations, such as homoscedastic noise and weakly informative spectral regimes.
astro-ph.SR
Molecular clouds exhibit complex, multi-scale dynamics driven by the interplay of turbulence, self-gravity, and gas pressure. Modelling these systems with conventional grid-based methods becomes increasingly expensive as spatial resolution and dimensionality increase. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative by incorporating the governing equations directly into the training objective, but their ability to model realistic turbulent self-gravitating flows remains largely unexplored. We apply PINNs to isothermal molecular clouds initialized with astrophysically motivated turbulent velocity fields, considering subsonic and supersonic evolution in two and three dimensions. We benchmark the predicted density and velocity fields against the finite-volume code Athena++. PINNs accurately recover the global evolution of the flow over multiple free-fall times across turbulent realizations, Mach numbers, and dimensionalities. Their training cost also exhibits weak dependence on spatial resolution, increasing by less than 25% from 128^3 to 1024^3 in our experiments. These results demonstrate that PINNs can model substantially more realistic self-gravitating turbulent flows than previously explored and provide a promising complementary framework for studying these systems.
physics.flu-dyn
Interactions between ultrasound and microbubbles underlie a range of biomedical and industrial applications, yet predicting how the physical parameters of the medium and bubbles govern nonlinear wave propagation remains difficult. This study proposes a parameter estimation framework that combines a Korteweg-de Vries-Burgers (KdVB) equation, describing weakly nonlinear wave propagation in a bubbly liquid, with a physics-informed neural network (PINN). The contributions are threefold. First, the PINN reproduces the reference solution of the governing equation in the forward problem, with a near-zero prediction error at the initial time that confirms the initial condition is enforced exactly as intended. Second, prior to inverse estimation, a sensitivity analysis is introduced that quantifies, at both the coefficient and solution levels, how each of eight physical parameters influences the KdVB equation, allowing the expected difficulty of estimating each parameter to be assessed in advance. Third, based on this assessment, single-parameter inverse estimation is performed for seven of the eight parameters using the PINN. Liquid viscosity, bubble initial radius, liquid density, sound speed, and liquid pressure are estimated with errors of 0.8-2.1%, the polytropic exponent converges only partially, and the surface tension coefficient cannot be estimated at all, consistent with the sensitivity analysis. These results establish a general framework for identifying and estimating the physical parameters governing nonlinear wave propagation in bubbly liquids from observed waveform data.
cs.LG
The drift-diffusion equations are the fundamental building block for the modeling, design, and optimization of modern semiconductor devices. Solutions of the drift-diffusion equations rarely give way to analytical forms, and exhibit strong nonlinearity, with the solutions ranging over several orders of magnitude. These attributes have led to research into numerical solvers, and while many commercial Technology Computer Aided Design (TCAD) packages now exist, they may require long simulation times, exhibit sensitivity to initial guesses, and rely on mesh generation. Further, these solvers are not well suited for inverse problems where the design parameters of a device are retrieved from its desired functional characteristics. To address all these challenges, this work demonstrates the usage of Physics Informed Neural Networks (PINNs) for the solution of the drift-diffusion equations with errors comparable to traditional simulation software using advanced training techniques to solve problems beyond the well-behaved equilibrium regime. For this study, we specifically choose an abrupt PN-junction in both one and two dimensions that features extreme gradients of the carrier concentrations at the Ohmic contacts and an abrupt discontinuity in the doping profile. Using the proposed PINN architecture, we are able to retrieve accurate results for all observables under all bias conditions. Additionally, we apply the PINN solver towards the inverse problem of retrieving doping profiles directly from desired electric field distributions or electrostatic potentials under non-zero applied biases. Our work establishes a powerful PINNs-based approach for semiconductor device modeling with the ability to solve inverse problems under non-equilibrium conditions for microelectronics research and discovery.
physics.flu-dyn
In a zero-gravity cylindrical container, a meniscus can span a square or equilateral-triangular cross-section only at contact angles at or above the respective Concus-Finn critical angles of 45 degrees and 60 degrees. We study strong-form physics-informed neural networks (PINNs) across these thresholds under fixed collocation and optimization budgets. Classical capillary flux balance yields a lower bound on the combined interior and wall residual loss for arbitrary positive sampling densities. In the tested nonexistence regime, several degrees below the critical angles, independently evaluated network losses are 1.6-1.9 times this bound. A polynomial least-squares comparison supports the same geometric interpretation. The PINNs still return smooth graphs with finite axial extent, even though the prescribed equilibrium problem has no spanning graph solution. Their small interior residuals coexist with wall-flux deficits near corners, where adjoining contact-angle conditions demand more flux than a finite-slope graph can supply. Residuals vary on both sides of the critical angle, while the bound tends uniformly to zero at threshold for fixed wall weight. These results give a geometric scale for interpreting the computed loss and locate the incompatibility that a small interior residual can conceal.
cs.LG
Partial differential equations (PDEs) are indispensable tools for modeling complex phenomena in physics and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful alternative to traditional numerical solvers by directly incorporating physical constraints into neural network loss functions. Despite their advantages, PINN training requires multi-objective optimization, which often leads to significant gradient conflicts among boundary, initial, and residual loss terms. The Conflict-Free Inverse Gradient (ConFIG) method addresses these conflicts; however, integrating ConFIG with adaptive optimizers such as Adam introduces a critical vulnerability: the conflict-free direction generated by ConFIG is further processed by the optimizer, and the resulting weight update may no longer be conflict-free with respect to the task gradients. To address this issue, Cautious ConFIG is proposed as a concise three-line extension to the ConFIG algorithm that empirically restores the conflict-freeness guarantee prior to the weight update. The method is evaluated on three PINN benchmarks: the 1D Viscous Burgers' equation, the 1D Nonlinear Schrödinger equation, and the 2D Kovasznay flow. Experimental results demonstrate consistent performance improvements over the standard ConFIG baseline. Additionally, the stabilizing effect of cautious masking and its reaction to conflict severity, task number, and optimizer lag are investigated using a simple toy system.
astro-ph.IM
Galactic thermal dust emission is the dominant foreground contaminant of the cosmic microwave background (CMB) at frequencies above 100 GHz, and its accurate separation is essential for current and future CMB experiments. Deep learning methods, in particular convolutional architectures such as the U-Net, have demonstrated strong performance for CMB component separation, but typically operate as purely data-driven models with no explicit enforcement of the physical laws governing the emission they reconstruct. In this work, we present a Physics-Informed Neural Network (PINN) that embeds the Modified Black Body (MBB) spectral model as a hard, differentiable architectural constraint, and we compare it against a standard U-Net baseline trained under an identical pipeline. Both architectures are trained on realistic simulated Planck HFI patches at four frequencies (143, 217, 353 and 545 GHz) and evaluated on a shared validation set as well as on three independent Galactic dust realizations from the PySM phenomenological dust models named D4, D7 and D10. We find that both networks achieve comparable reconstruction quality across all evaluated datasets, with a Structural Similarity Index Measure consistently above 0.96 and a fitted angular power-spectrum spectral index that agrees with the input to within 1% in every region. Embedding the physical constraint in the PINN does not measurably degrade reconstruction accuracy relative to the unconstrained U-Net, while additionally guaranteeing that every predicted output corresponds to a thermodynamically admissible physical configuration. These results establish the physics-informed formulation as a viable methodological alternative for dust component separation, providing physical interpretability without a trade-off in reconstruction fidelity.
cs.LG
Optimizing high-dimensional physical systems under expensive evaluations and complex constraints is a central challenge in science and engineering. In offline model-based optimization (MBO), methods must improve designs using only a fixed dataset and no test-time access to the true objective. However, existing methods typically suffer from conservatism, unconstrained surrogate exploitation, or function as static inference-time samplers that cannot refine candidates against precise physical objectives. In this paper, we propose Differentiable Diffusion Conditioning (D2C) for offline MBO, which leverages the fact that deterministic sampling makes the reverse denoising chain differentiable with respect to the conditioning signal. D2C turns a frozen conditional diffusion model into an end-to-end gradient-based optimizer by directly optimizing conditioning variables at test time via gradients from frozen surrogate objectives and physics-informed penalties backpropagated through the reverse chain. We implement this idea in a composed proposer-evaluator framework and evaluate it on laser pulse optimization for inertial confinement fusion, sustainable data-center workload scheduling, and four Design-Bench tasks. Our method achieves the strongest results on the two real-world tasks and the best average rank across four Design-Bench tasks.
math.ST
Physics-informed machine learning incorporates physical knowledge into data-driven models, often through a partial differential equation (PDE) that the target is assumed to satisfy. However, how much this knowledge improves statistical performance remains unclear, especially when the physical model is imperfect. Since satisfying a PDE implies being differentiable, a natural benchmark for physics-informed regression is the best achievable performance when smoothness is the only prior information about the target function. We show that there is a characteristic threshold for the modeling error above which the physical prior cannot improve the convergence rate. The form of this threshold is common to every linear PDE and certain nonlinear PDEs. Below it, the gain depends on the equation type. For classes of elliptic and hyperbolic PDEs with constant coefficients, we establish convergence rates that improve continuously as the modeling error decreases, and prove their minimax optimality up to logarithmic factors. With exact physics, the rates correspond to learning in dimension d-1 rather than d, reflecting the freedom left by unknown boundary or initial data. We also give conditions for computing the estimator with near-linear complexity and show how to tune its hyperparameters without knowing the modeling error.