{"total":65,"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":"2207.05748","title":"Physics-Informed Deep Neural Operator Networks","created":"2022-07-08","cited_by_count":113,"area":null},{"id":"2402.15715","title":"Operator Learning: Algorithms and Analysis","created":"2024-02-24","cited_by_count":85,"area":null},{"id":"2312.14688","title":"A Mathematical Guide to Operator Learning","created":"2023-12-22","cited_by_count":76,"area":null},{"id":"2212.06347","title":"Reliable extrapolation of deep neural operators informed by physics or sparse observations","created":"2022-12-13","cited_by_count":62,"area":null},{"id":"2306.10619","title":"Towards Stability of Autoregressive Neural Operators","created":"2023-06-18","cited_by_count":59,"area":null},{"id":"2405.13998","title":"CViT: Continuous Vision Transformer for Operator Learning","created":"2024-05-22","cited_by_count":51,"area":null},{"id":"2303.16317","title":"Operator learning with PCA-Net: upper and lower complexity bounds","created":"2023-03-28","cited_by_count":44,"area":null},{"id":"2402.10926","title":"Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning","created":"2024-01-30","cited_by_count":39,"area":null},{"id":"2301.11509","title":"Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation","created":"2023-01-27","cited_by_count":32,"area":null},{"id":"2404.07662","title":"PINNACLE: PINN Adaptive ColLocation and Experimental points selection","created":"2024-04-11","cited_by_count":32,"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":"2312.15949","title":"HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork","created":"2023-12-26","cited_by_count":26,"area":null},{"id":"2312.05410","title":"Rethinking materials simulations: Blending direct numerical simulations with neural operators","created":"2023-12-08","cited_by_count":25,"area":null},{"id":"2303.10257","title":"Recent Developments in Machine Learning Methods for Stochastic Control and Games","created":"2023-03-17","cited_by_count":24,"area":null},{"id":"2305.17170","title":"Error Bounds for Learning with Vector-Valued Random Features","created":"2023-05-26","cited_by_count":23,"area":null},{"id":"2209.14977","title":"Transformer Meets Boundary Value Inverse Problems","created":"2022-09-29","cited_by_count":22,"area":null},{"id":"2308.07051","title":"Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems","created":"2023-08-14","cited_by_count":13,"area":null},{"id":"2506.10973","title":"Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning","created":"2025-06-12","cited_by_count":12,"area":null},{"id":"2306.00945","title":"CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions","created":"2023-06-01","cited_by_count":11,"area":null},{"id":"2410.23440","title":"The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures","created":"2024-10-30","cited_by_count":11,"area":null},{"id":"2305.10157","title":"Efficient Error Certification for Physics-Informed Neural Networks","created":"2023-05-17","cited_by_count":10,"area":null},{"id":"2210.03426","title":"Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs","created":"2022-10-07","cited_by_count":8,"area":null},{"id":"2504.11383","title":"Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modeling","created":"2025-04-15","cited_by_count":8,"area":null},{"id":"2308.14789","title":"Scattering with Neural Operators","created":"2023-08-28","cited_by_count":7,"area":null},{"id":"2404.07943","title":"A Pretraining-Finetuning Computational Framework for Material Homogenization","created":"2024-03-18","cited_by_count":7,"area":null},{"id":"2409.04779","title":"Component Fourier Neural Operator for Singularly Perturbed Differential Equations","created":"2024-09-07","cited_by_count":7,"area":null},{"id":"2503.01036","title":"Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis","created":"2025-03-02","cited_by_count":7,"area":null},{"id":"2306.09389","title":"ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equations","created":"2023-06-15","cited_by_count":6,"area":null},{"id":"2308.06338","title":"Size Lowerbounds for Deep Operator Networks","created":"2023-08-11","cited_by_count":6,"area":null},{"id":"2408.13222","title":"An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning","created":"2024-08-23","cited_by_count":6,"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":"2508.07994","title":"Prediction error certification for PINNs: Theory, computation, and application to Stokes flow","created":"2025-08-11","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":"2510.20017","title":"Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators","created":"2025-10-22","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":"2307.06167","title":"Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solving","created":"2023-07-12","cited_by_count":2,"area":null},{"id":"2401.05211","title":"Error estimation for physics-informed neural networks with implicit Runge-Kutta methods","created":"2024-01-10","cited_by_count":2,"area":null},{"id":"2404.03586","title":"Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning","created":"2024-04-04","cited_by_count":2,"area":null},{"id":"2507.06967","title":"Noisy PDE Training Requires Bigger PINNs","created":"2025-07-09","cited_by_count":2,"area":null},{"id":"2303.17109","title":"Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models","created":"2023-03-30","cited_by_count":1,"area":null},{"id":"2403.12764","title":"Neural Parameter Regression for Explicit Representations of PDE Solution Operators","created":"2024-03-19","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":"2503.16777","title":"Physics-Informed Deep B-Spline Networks","created":"2025-03-21","cited_by_count":1,"area":null},{"id":"2506.19396","title":"Maximal Update Parametrization and Zero-Shot Hyperparameter Transfer for Fourier Neural Operators","created":"2025-06-24","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":"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":"2602.12706","title":"Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations","created":"2026-02-13","cited_by_count":1,"area":null},{"id":"2605.08517","title":"A Deep Risk Estimator for Known Operator Learning","created":"2026-05-08","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":"2307.06362","title":"Spectral-Bias and Kernel-Task Alignment in Physically Informed Neural Networks","created":"2023-07-12","cited_by_count":0,"area":null},{"id":"2402.09018","title":"Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEs","created":"2024-02-14","cited_by_count":0,"area":null},{"id":"2405.13731","title":"Control, Transport and Sampling: Towards Better Loss Design","created":"2024-05-22","cited_by_count":0,"area":null},{"id":"2406.02723","title":"Predicting AI Agent Behavior through Approximation of the Perron-Frobenius Operator","created":"2024-06-04","cited_by_count":0,"area":null},{"id":"2410.20951","title":"Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?","created":"2024-10-28","cited_by_count":0,"area":null},{"id":"2504.00910","title":"Provably Accurate Adaptive Sampling for Collocation Points in Physics-informed Neural Networks","created":"2025-04-01","cited_by_count":0,"area":null},{"id":"2603.15526","title":"Building Trust in PINNs: Error Estimation through Finite Difference Methods","created":"2026-03-16","cited_by_count":0,"area":null},{"id":"2603.23072","title":"Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations","created":"2026-03-24","cited_by_count":0,"area":null},{"id":"2605.15399","title":"Breakeven complexity: A new perspective on neural partial differential equation solvers","created":"2026-05-14","cited_by_count":0,"area":null},{"id":"2605.26341","title":"A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning","created":"2026-05-25","cited_by_count":0,"area":null},{"id":"2606.02475","title":"Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers","created":"2026-06-01","cited_by_count":0,"area":null},{"id":"2606.06171","title":"Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks","created":"2026-06-04","cited_by_count":0,"area":null},{"id":"2606.12050","title":"Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds","created":"2026-06-10","cited_by_count":0,"area":null},{"id":"2609.16853","title":"Can Deep Learning Achieve Cross-Physics Mapping?","created":"2026-09-15","cited_by_count":0,"area":null}],"next_cursor":null}