{"total":26,"rows":[{"id":"2302.01178","title":"Convolutional Neural Operators for robust and accurate learning of PDEs","created":"2023-02-02","cited_by_count":214,"area":null},{"id":"2405.19101","title":"Poseidon: Efficient Foundation Models for PDEs","created":"2024-05-29","cited_by_count":200,"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":"2104.08938","title":"On the approximation of functions by tanh neural networks","created":"2021-04-18","cited_by_count":81,"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":"2106.14473","title":"Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs","created":"2021-06-28","cited_by_count":57,"area":null},{"id":"2210.01074","title":"Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities","created":"2022-10-03","cited_by_count":30,"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":"2402.06031","title":"An operator learning perspective on parameter-to-observable maps","created":"2024-02-08","cited_by_count":22,"area":null},{"id":"2305.19663","title":"Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains","created":"2023-05-31","cited_by_count":21,"area":null},{"id":"2107.10428","title":"Deep Adaptive Arbitrary Polynomial Chaos Expansion: A Mini-data-driven Semi-supervised Method for Uncertainty Quantification","created":"2021-07-22","cited_by_count":6,"area":null},{"id":"2110.14443","title":"Failure-averse Active Learning for Physics-constrained Systems","created":"2021-10-27","cited_by_count":5,"area":null},{"id":"2302.01518","title":"LSA-PINN: Linear Boundary Connectivity Loss for Solving PDEs on Complex Geometry","created":"2023-02-03","cited_by_count":4,"area":null},{"id":"2302.11173","title":"VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problems","created":"2023-02-22","cited_by_count":4,"area":null},{"id":"2307.00296","title":"Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems","created":"2023-07-01","cited_by_count":4,"area":null},{"id":"2407.07674","title":"Feasibility Study on Active Learning of Smart Surrogates for Scientific Simulations","created":"2024-07-10","cited_by_count":4,"area":null},{"id":"2505.21626","title":"Learning where to learn: Training data distribution optimization for scientific machine learning","created":"2025-05-27","cited_by_count":3,"area":null},{"id":"2207.07362","title":"Error analysis for deep neural network approximations of parametric hyperbolic conservation laws","created":"2022-07-15","cited_by_count":2,"area":null},{"id":"2505.12556","title":"Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers","created":"2025-05-18","cited_by_count":2,"area":null},{"id":"2403.14848","title":"Learning WENO for entropy stable schemes to solve conservation laws","created":"2024-03-21","cited_by_count":1,"area":null},{"id":"2503.19717","title":"Invertible Koopman neural operator for data-driven modeling of partial differential equations","created":"2025-03-25","cited_by_count":1,"area":null},{"id":"2302.08309","title":"The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach","created":"2023-02-16","cited_by_count":0,"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":"2503.04024","title":"An optimal Petrov-Galerkin framework for operator networks","created":"2025-03-06","cited_by_count":0,"area":null},{"id":"2506.03835","title":"Learning task-specific predictive models for scientific computing","created":"2025-06-04","cited_by_count":0,"area":null}],"next_cursor":null}