OGAS uses a parallel diffusion model to bias PDE configuration sampling toward high surrogate difficulty, reducing 99th-percentile errors and error variance versus uniform sampling across tested 2D PDEs.
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An expert's guide to training physics-informed neural networks
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Introduces pinn-gym benchmark demonstrating that low curve error in physics-informed surrogates frequently fails to yield useful design selections across per-material, pooled, and cross-material settings.
PINN gradient conflicts occur in distinct regimes (persistent directional, magnitude imbalance, or low/transient) that each favor different fixes, with per-loss adapters plus reweighting improving results on forward and multi-physics problems.
Windowing and buffer hard-constrained PINNs enforce interface physics by design, yielding higher interface fidelity than soft-constrained baselines on elliptic benchmarks.
Gaussian process regression with physics-aware deep composite kernels models steering vectors continuously over frequency and positions, attaining oracle performance in speech enhancement and binaural rendering with under ten times fewer measurements than dense sampling.
Conditional normalizing flows model the posterior over initial states from short-arc angles-only measurements in cislunar NRHOs and supply warm starts for nonlinear least-squares refinement.
Develops and numerically verifies residual-specific explicit derivative kernels that achieve floating-point agreement with AD while delivering 2-4x speedups and lower memory use in PINN training and CFD adjoint workflows.
SimPhysNet achieves 96.06% accuracy classifying laser welding penetration states using self-supervised contrastive learning with a physics-informed neural network and prototypical networks on only 200 labeled images.
A PINN approach learns galactic gravitational potentials from acceleration data, achieving sub-percent errors on simulations while outperforming analytic models and retaining interpretability via structured priors.
A hybrid MRI-PINN-resolvent framework extracts mean fields from stenotic flow measurements and identifies stationary eigenmodes in the recirculation bubble plus broadband pseudo-resonance in the shear layer.
Elliptic energy loses coercivity on neural ansatzes due to manifold non-closedness and condensation, but state functions remain bounded and converge strongly, with rates proved for Gaussian wave-packet approximations.
Approximates manifold heat kernels via PINNs solving the heat equation to enable diffusion models on arbitrary manifolds including S2, SO(3), and SPD(n).
Hermite-NGP stores derivatives in multi-resolution hash encodings and uses curriculum training to enable analytic differential operators, reporting up to 20x lower error and 2-10x faster convergence than prior neural PDE methods.
Gauss-Newton descent whitens errors by projecting Newton directions or gradients onto the tangent space, replacing JJ^T with the identity and removing parameterization distortions that affect Newton descent.
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
Pi-PINN learns transferable physics-informed representations and solves known or unseen PDEs via closed-form pseudoinverse head adaptation, achieving 100-1000x faster predictions and 10-100x lower error than standard PINNs or data-driven models even with minimal training samples.
A decoupled parametric PINN with conditional modulation and Rosenthal-derived output scaling achieves zero-shot thermal inference across arbitrary metal alloys in laser powder bed fusion.
DC-PINNs embed derivative constraints into PINN optimization using a minimum principle and adaptive balancing, reducing violations and improving fidelity on heat, finance, and fluid benchmarks.
PD-SOVNet combines shared second-order vibration kernels, MIMO coupling, adaptive physical correction, and Mamba temporal modeling to regress 1st-40th order wheel roughness spectra from axle-box vibrations with competitive accuracy on real datasets.
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.
Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.
A modified gated PINN with hard-constraint boundary encoding achieves MAE of 0.27-0.43 kPa against FEM references for time-dependent electro-osmotic radial consolidation cases.
citing papers explorer
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Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training
OGAS uses a parallel diffusion model to bias PDE configuration sampling toward high surrogate difficulty, reducing 99th-percentile errors and error variance versus uniform sampling across tested 2D PDEs.
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Decision-Aware Evaluation of Physics-Informed Surrogates
Introduces pinn-gym benchmark demonstrating that low curve error in physics-informed surrogates frequently fails to yield useful design selections across per-material, pooled, and cross-material settings.
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Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks
PINN gradient conflicts occur in distinct regimes (persistent directional, magnitude imbalance, or low/transient) that each favor different fixes, with per-loss adapters plus reweighting improving results on forward and multi-physics problems.
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Hard-constrained Physics-informed Neural Networks for Interface Problems
Windowing and buffer hard-constrained PINNs enforce interface physics by design, yielding higher interface fidelity than soft-constrained baselines on elliptic benchmarks.
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Gaussian Process Regression of Steering Vectors With Physics-Aware Deep Composite Kernels for Augmented Listening
Gaussian process regression with physics-aware deep composite kernels models steering vectors continuously over frequency and positions, attaining oracle performance in speech enhancement and binaural rendering with under ten times fewer measurements than dense sampling.
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Physics-informed Conditional Normalizing Flows for Angles-only Cislunar Orbit Determination
Conditional normalizing flows model the posterior over initial states from short-arc angles-only measurements in cislunar NRHOs and supply warm starts for nonlinear least-squares refinement.
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Verified residual-specific explicit derivative kernels for physics-informed learning and discretized PDE adjoints
Develops and numerically verifies residual-specific explicit derivative kernels that achieve floating-point agreement with AD while delivering 2-4x speedups and lower memory use in PINN training and CFD adjoint workflows.
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A welding penetration prediction model for laser welding process based on self-supervised learning using physics-informed neural networks
SimPhysNet achieves 96.06% accuracy classifying laser welding penetration states using self-supervised contrastive learning with a physics-informed neural network and prototypical networks on only 200 labeled images.
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Reconstructing Galactic Gravitational Potentials from Stellar Kinematics with Physics-Informed Neural Networks
A PINN approach learns galactic gravitational potentials from acceleration data, achieving sub-percent errors on simulations while outperforming analytic models and retaining interpretability via structured priors.
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Uncovering Turbulent Dynamics in Stenotic Flows from 4D-flow MRI Measurements via Resolvent Analysis and Data Assimilation
A hybrid MRI-PINN-resolvent framework extracts mean fields from stenotic flow measurements and identifies stationary eigenmodes in the recirculation bubble plus broadband pseudo-resonance in the shear layer.
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The Coercivity Gap in Neural PDE Solvers: Parameter Escape and Functional Convergence
Elliptic energy loses coercivity on neural ansatzes due to manifold non-closedness and condensation, but state functions remain bounded and converge strongly, with rates proved for Gaussian wave-packet approximations.
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Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks
Approximates manifold heat kernels via PINNs solving the heat equation to enable diffusion models on arbitrary manifolds including S2, SO(3), and SPD(n).
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Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs
Hermite-NGP stores derivatives in multi-resolution hash encodings and uses curriculum training to enable analytic differential operators, reporting up to 20x lower error and 2-10x faster convergence than prior neural PDE methods.
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Error whitening: Why Gauss-Newton outperforms Newton
Gauss-Newton descent whitens errors by projecting Newton directions or gradients onto the tangent space, replacing JJ^T with the identity and removing parameterization distortions that affect Newton descent.
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Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
-
When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
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Transferable Physics-Informed Representations via Closed-Form Head Adaptation
Pi-PINN learns transferable physics-informed representations and solves known or unseen PDEs via closed-form pseudoinverse head adaptation, achieving 100-1000x faster predictions and 10-100x lower error than standard PINNs or data-driven models even with minimal training samples.
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Material-Agnostic Zero-Shot Thermal Inference for Metal Additive Manufacturing via a Parametric PINN Framework
A decoupled parametric PINN with conditional modulation and Rosenthal-derived output scaling achieves zero-shot thermal inference across arbitrary metal alloys in laser powder bed fusion.
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Physics-Informed Neural Networks for Solving Derivative-Constrained PDEs
DC-PINNs embed derivative constraints into PINN optimization using a minimum principle and adaptive balancing, reducing violations and improving fidelity on heat, finance, and fluid benchmarks.
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PD-SOVNet: A Physics-Driven Second-Order Vibration Operator Network for Estimating Wheel Polygonal Roughness from Axle-Box Vibrations
PD-SOVNet combines shared second-order vibration kernels, MIMO coupling, adaptive physical correction, and Mamba temporal modeling to regress 1st-40th order wheel roughness spectra from axle-box vibrations with competitive accuracy on real datasets.
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Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
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Deep Learning Alternatives of the Kolmogorov Superposition Theorem
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.
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Random Neural Network Expressivity for Non-Linear Partial Differential Equations
Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.
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Physics-Informed Neural Networks for Radial Consolidation of Combined Electroosmotic, Vacuum and Surcharge Preloading Considering Smear Effects
A modified gated PINN with hard-constraint boundary encoding achieves MAE of 0.27-0.43 kPa against FEM references for time-dependent electro-osmotic radial consolidation cases.
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AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training
AdamFLIP treats PDE constraint residuals in PINNs as a controlled dynamical system, computes Lagrange multipliers via feedback linearization to drive residuals to zero, and applies Adam-style adaptation to the resulting gradient for scalable hard-constrained training.
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Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations
DeepGaLA is a neural-network surrogate for differential equation solvers that provides uncertainty-aware predictions to enable scalable Bayesian inference for inverse PDE problems.
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A Deep Learning Approach to Describing the Plasma Sheath
PINNs trained on fluid sheath equations produce parametric surrogate models that predict plasma sheath profiles across ion species, temperature ratios, and collisionalities, validated against Runge-Kutta solvers.
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Deep-Learning based surrogate models for plasma exhaust simulations -- SOLPS-NN
SOLPS-NN is a fully connected neural network surrogate trained on SOLPS-ITER simulations that predicts spatial plasma profiles and indicates access to detachment with experimental trends.
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Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle
The paper supplies explicit hand-derived gradient formulas and a full training cycle for PINNs on a simple ODE, achieving 4.29e-4 relative L2 error against the analytic solution using only the physics loss.
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Beyond Data-Driven: How Physics-Informed Neural Networks are Reshaping Multi-Physics Design and Discovery
A review assessing PINN advances for forward modeling, inverse design, and equation discovery across multi-physics domains.