{"total":57,"rows":[{"id":"2201.05624","title":"Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next","created":"2022-01-14","cited_by_count":608,"area":null},{"id":"2211.08064","title":"Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications","created":"2022-11-15","cited_by_count":92,"area":null},{"id":"2205.11393","title":"Generic bounds on the approximation error for physics-informed (and) operator learning","created":"2022-05-23","cited_by_count":65,"area":null},{"id":"2203.09346","title":"Error estimates for physics informed neural networks approximating the Navier-Stokes equations","created":"2022-03-17","cited_by_count":63,"area":null},{"id":"2109.09444","title":"When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?","created":"2021-09-20","cited_by_count":58,"area":null},{"id":"2211.08939","title":"Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology","created":"2022-11-16","cited_by_count":44,"area":null},{"id":"2501.16371","title":"Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks","created":"2025-01-22","cited_by_count":42,"area":null},{"id":"2405.04230","title":"Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be?","created":"2024-05-07","cited_by_count":31,"area":null},{"id":"2207.08483","title":"wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws","created":"2022-07-18","cited_by_count":29,"area":null},{"id":"2310.05801","title":"An operator preconditioning perspective on training in physics-informed machine learning","created":"2023-10-09","cited_by_count":27,"area":null},{"id":"2112.03749","title":"Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems","created":"2021-12-07","cited_by_count":21,"area":null},{"id":"2305.04962","title":"Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs","created":"2023-05-08","cited_by_count":21,"area":null},{"id":"2306.02816","title":"MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks","created":"2023-06-05","cited_by_count":17,"area":null},{"id":"2402.00152","title":"Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss","created":"2024-01-31","cited_by_count":14,"area":null},{"id":"2402.00531","title":"Preconditioning for Physics-Informed Neural Networks","created":"2024-02-01","cited_by_count":13,"area":null},{"id":"2406.03494","title":"Solving Poisson Equations using Neural Walk-on-Spheres","created":"2024-06-05","cited_by_count":11,"area":null},{"id":"2503.17379","title":"Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study","created":"2025-03-14","cited_by_count":11,"area":null},{"id":"2302.07557","title":"On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it","created":"2023-02-15","cited_by_count":10,"area":null},{"id":"2405.14099","title":"Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations","created":"2024-05-23","cited_by_count":9,"area":null},{"id":"2401.12806","title":"Binary structured physics-informed neural networks for solving equations with rapidly changing solutions","created":"2024-01-23","cited_by_count":8,"area":null},{"id":"2508.05141","title":"Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms","created":"2025-08-07","cited_by_count":6,"area":null},{"id":"2303.11205","title":"Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs","created":"2023-02-11","cited_by_count":5,"area":null},{"id":"2402.11283","title":"Deep adaptive sampling for surrogate modeling without labeled data","created":"2024-02-17","cited_by_count":5,"area":null},{"id":"2311.04779","title":"Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms","created":"2023-11-08","cited_by_count":4,"area":null},{"id":"2409.20383","title":"Beyond Derivative Pathology of PINNs: Variable Splitting Strategy with Convergence Analysis","created":"2024-09-30","cited_by_count":4,"area":null},{"id":"2505.06459","title":"Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles","created":"2025-05-09","cited_by_count":3,"area":null},{"id":"2211.11716","title":"Neural tangent kernel analysis of PINN for advection-diffusion equation","created":"2022-11-21","cited_by_count":2,"area":null},{"id":"2406.01539","title":"Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics","created":"2024-06-03","cited_by_count":2,"area":null},{"id":"2407.08868","title":"Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems","created":"2024-07-11","cited_by_count":2,"area":null},{"id":"2411.13848","title":"Exact and approximate error bounds for physics-informed neural networks","created":"2024-11-21","cited_by_count":2,"area":null},{"id":"2506.18773","title":"DPG loss functions for learning parameter-to-solution maps by neural networks","created":"2025-06-23","cited_by_count":2,"area":null},{"id":"2402.07153","title":"Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations","created":"2024-02-11","cited_by_count":1,"area":null},{"id":"2402.07621","title":"Correctness Verification of Neural Networks Approximating Differential Equations","created":"2024-02-12","cited_by_count":1,"area":null},{"id":"2405.11451","title":"Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz Method","created":"2024-05-19","cited_by_count":1,"area":null},{"id":"2406.02645","title":"Astral: training physics-informed neural networks with error majorants","created":"2024-06-04","cited_by_count":1,"area":null},{"id":"2410.22371","title":"Error Bounds for Physics-Informed Neural Networks in Fokker-Planck PDEs","created":"2024-10-28","cited_by_count":1,"area":null},{"id":"2501.18879","title":"Understanding Generalization in Physics Informed Models through Affine Variety Dimensions","created":"2025-01-31","cited_by_count":1,"area":null},{"id":"2503.16777","title":"Physics-Informed Deep B-Spline Networks","created":"2025-03-21","cited_by_count":1,"area":null},{"id":"2507.06038","title":"Fredholm Neural Networks for inverse problems in elliptic PDEs","created":"2025-07-08","cited_by_count":1,"area":null},{"id":"2509.20733","title":"PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization","created":"2025-09-25","cited_by_count":1,"area":null},{"id":"2510.23149","title":"Complexity Dependent Error Rates for Physics-informed Statistical Learning via the Small-ball Method","created":"2025-10-27","cited_by_count":1,"area":null},{"id":"2511.00886","title":"HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs","created":"2025-11-02","cited_by_count":1,"area":null},{"id":"2601.06388","title":"Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEs","created":"2026-01-10","cited_by_count":1,"area":null},{"id":"2601.13256","title":"Deep Neural networks for solving high-dimensional parabolic partial differential equations","created":"2026-01-19","cited_by_count":1,"area":null},{"id":"2603.09693","title":"Physics-informed neural operator for parametric phase-field modelling of interfacial degradation and microstructural evolution","created":"2026-03-10","cited_by_count":1,"area":null},{"id":"2606.23179","title":"EML Trees Are Universal Approximators","created":"2026-06-22","cited_by_count":1,"area":null},{"id":"2308.16272","title":"A numerical approach for the fractional Laplacian via deep neural networks","created":"2023-08-30","cited_by_count":0,"area":null},{"id":"2407.02010","title":"Feynman-Kac Operator Expectation Estimator","created":"2024-07-02","cited_by_count":0,"area":null},{"id":"2408.09756","title":"Parallel-in-Time Solutions with Random Projection Neural Networks","created":"2024-08-19","cited_by_count":0,"area":null},{"id":"2506.11395","title":"Convergence of physics-informed neural networks modeling time-harmonic wave fields","created":"2025-05-18","cited_by_count":0,"area":null},{"id":"2509.17293","title":"Physics-Informed Operator Learning for Hemodynamic Modeling","created":"2025-09-22","cited_by_count":0,"area":null},{"id":"2602.07970","title":"Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity","created":"2026-02-08","cited_by_count":0,"area":null},{"id":"2605.08672","title":"Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs","created":"2026-05-09","cited_by_count":0,"area":null},{"id":"2607.06369","title":"Feature Learning for the High Dimensional Stationary Sch\\\"odinger Equation with Deep Ritz Method","created":"2026-07-07","cited_by_count":0,"area":null},{"id":"2607.27781","title":"Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation","created":"2026-07-30","cited_by_count":0,"area":null},{"id":"2608.15187","title":"MiNO: Cotangent-bundle propagator learning for PDEs","created":"2026-08-15","cited_by_count":0,"area":null},{"id":"2610.05767","title":"Global error estimators for parametric monotone nonlinearities and neural approximations","created":"2026-10-05","cited_by_count":0,"area":null}],"next_cursor":null}