{"total":182,"rows":[{"id":"2109.01050","title":"Characterizing possible failure modes in physics-informed neural networks","created":"2021-09-02","cited_by_count":643,"area":null},{"id":"2104.12325","title":"Efficient training of physics-informed neural networks via importance sampling","created":"2021-04-26","cited_by_count":110,"area":null},{"id":"2304.07993","title":"In-Context Operator Learning with Data Prompts for Differential Equation Problems","created":"2023-04-17","cited_by_count":101,"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":"2307.12306","title":"Tackling the Curse of Dimensionality with Physics-Informed Neural Networks","created":"2023-07-23","cited_by_count":79,"area":null},{"id":"2201.07395","title":"Overview frequency principle/spectral bias in deep learning","created":"2022-01-19","cited_by_count":69,"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":"2203.01360","title":"Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations","created":"2022-03-02","cited_by_count":56,"area":null},{"id":"2312.02027","title":"Stochastic Optimal Control Matching","created":"2023-12-04","cited_by_count":40,"area":null},{"id":"2402.14989","title":"Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data","created":"2024-02-22","cited_by_count":36,"area":null},{"id":"2108.12956","title":"Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models","created":"2021-08-30","cited_by_count":35,"area":null},{"id":"2106.08900","title":"Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality","created":"2021-06-14","cited_by_count":34,"area":null},{"id":"2102.13403","title":"Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities","created":"2021-02-26","cited_by_count":31,"area":null},{"id":"2401.07364","title":"PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws","created":"2024-01-14","cited_by_count":31,"area":null},{"id":"2305.08466","title":"Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives","created":"2023-05-15","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":"2106.07539","title":"On the Representation of Solutions to Elliptic PDEs in Barron Spaces","created":"2021-06-14","cited_by_count":25,"area":null},{"id":"2107.03673","title":"MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs","created":"2021-07-08","cited_by_count":24,"area":null},{"id":"2312.14499","title":"Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks","created":"2023-12-22","cited_by_count":23,"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":"2112.13414","title":"Reinforcement Learning with Dynamic Convex Risk Measures","created":"2021-12-26","cited_by_count":21,"area":null},{"id":"2203.11363","title":"PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations","created":"2022-03-21","cited_by_count":21,"area":null},{"id":"2206.10121","title":"Finite Expression Method for Solving High-Dimensional Partial Differential Equations","created":"2022-06-21","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":"2309.07049","title":"An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions","created":"2023-09-13","cited_by_count":21,"area":null},{"id":"2309.15421","title":"Deep Learning in Deterministic Computational Mechanics","created":"2023-09-27","cited_by_count":21,"area":null},{"id":"2107.04568","title":"Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance","created":"2021-07-09","cited_by_count":20,"area":null},{"id":"2303.14878","title":"GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs","created":"2023-03-27","cited_by_count":20,"area":null},{"id":"2407.07873","title":"Dynamical Measure Transport and Neural PDE Solvers for Sampling","created":"2024-07-10","cited_by_count":20,"area":null},{"id":"2502.09885","title":"Comprehensive Review of Neural Differential Equations for Time Series Analysis","created":"2025-02-14","cited_by_count":20,"area":null},{"id":"2311.15283","title":"Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs","created":"2023-11-26","cited_by_count":19,"area":null},{"id":"2404.14688","title":"FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model","created":"2024-04-23","cited_by_count":19,"area":null},{"id":"2107.13735","title":"Learning the temporal evolution of multivariate densities via normalizing flows","created":"2021-07-29","cited_by_count":18,"area":null},{"id":"2102.11830","title":"Solving high-dimensional parabolic PDEs using the tensor train format","created":"2021-02-23","cited_by_count":17,"area":null},{"id":"2210.15179","title":"Mean-field neural networks: learning mappings on Wasserstein space","created":"2022-10-27","cited_by_count":16,"area":null},{"id":"2304.14994","title":"A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks","created":"2023-04-28","cited_by_count":16,"area":null},{"id":"2505.20721","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","created":"2025-05-27","cited_by_count":16,"area":null},{"id":"2110.05445","title":"Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks","created":"2021-10-11","cited_by_count":15,"area":null},{"id":"2210.12101","title":"Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective","created":"2022-10-21","cited_by_count":15,"area":null},{"id":"2103.01007","title":"Error Estimates for the Deep Ritz Method with Boundary Penalty","created":"2021-03-01","cited_by_count":14,"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":"2102.02617","title":"A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate","created":"2021-02-04","cited_by_count":13,"area":null},{"id":"2204.11924","title":"Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence","created":"2022-04-25","cited_by_count":13,"area":null},{"id":"2204.13247","title":"BI-GreenNet: Learning Green's functions by boundary integral network","created":"2022-04-28","cited_by_count":13,"area":null},{"id":"2206.10588","title":"Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning","created":"2022-06-21","cited_by_count":13,"area":null},{"id":"2410.00345","title":"A Taxonomy of Loss Functions for Stochastic Optimal Control","created":"2024-10-01","cited_by_count":13,"area":null},{"id":"2106.06682","title":"Solving PDEs on Unknown Manifolds with Machine Learning","created":"2021-06-12","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":"2406.03494","title":"Solving Poisson Equations using Neural Walk-on-Spheres","created":"2024-06-05","cited_by_count":11,"area":null},{"id":"2112.06660","title":"Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs","created":"2021-12-10","cited_by_count":10,"area":null},{"id":"2212.11518","title":"Mean-field neural networks-based algorithms for McKean-Vlasov control problems *","created":"2022-12-22","cited_by_count":10,"area":null},{"id":"2302.13163","title":"Achieving High Accuracy with PINNs via Energy Natural Gradients","created":"2023-02-25","cited_by_count":10,"area":null},{"id":"2304.14374","title":"Pseudo-Hamiltonian neural networks for learning partial differential equations","created":"2023-04-27","cited_by_count":10,"area":null},{"id":"2306.15630","title":"Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes","created":"2023-06-27","cited_by_count":10,"area":null},{"id":"2111.01356","title":"DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method","created":"2021-11-02","cited_by_count":9,"area":null},{"id":"2208.02235","title":"Quantum-Inspired Tensor Neural Networks for Partial Differential Equations","created":"2022-08-03","cited_by_count":9,"area":null},{"id":"2210.04118","title":"Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems","created":"2022-10-08","cited_by_count":9,"area":null},{"id":"2304.00388","title":"Multilevel CNNs for Parametric PDEs","created":"2023-04-01","cited_by_count":9,"area":null},{"id":"2203.17128","title":"Neural Q-learning for solving PDEs","created":"2022-03-31","cited_by_count":8,"area":null},{"id":"2205.14421","title":"Approximation of Functionals by Neural Network without Curse of Dimensionality","created":"2022-05-28","cited_by_count":8,"area":null},{"id":"2104.01040","title":"Distributional Offline Continuous-Time Reinforcement Learning with Neural Physics-Informed PDEs (SciPhy RL for DOCTR-L)","created":"2021-04-02","cited_by_count":6,"area":null},{"id":"2208.12190","title":"CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning","created":"2022-08-25","cited_by_count":6,"area":null},{"id":"2301.12895","title":"Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumps","created":"2023-01-30","cited_by_count":6,"area":null},{"id":"2403.04975","title":"Deep Backward and Galerkin Methods for the Finite State Master Equation","created":"2024-03-08","cited_by_count":6,"area":null},{"id":"2505.15602","title":"Deep Learning for Continuous-Time Stochastic Control with Jumps","created":"2025-05-21","cited_by_count":6,"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":"2604.08580","title":"Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control","created":"2026-03-28","cited_by_count":6,"area":null},{"id":"2105.03336","title":"Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs","created":"2021-05-07","cited_by_count":5,"area":null},{"id":"2106.12147","title":"Lagrangian dual framework for conservative neural network solutions of kinetic equations","created":"2021-06-23","cited_by_count":5,"area":null},{"id":"2110.01127","title":"Deep Learning for Principal-Agent Mean Field Games","created":"2021-10-03","cited_by_count":5,"area":null},{"id":"2201.03283","title":"An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations","created":"2022-01-10","cited_by_count":5,"area":null},{"id":"2202.07960","title":"Temporal Difference Learning with Continuous Time and State in the Stochastic Setting","created":"2022-02-16","cited_by_count":5,"area":null},{"id":"2205.07521","title":"A scalable deep learning approach for solving high-dimensional dynamic optimal transport","created":"2022-05-16","cited_by_count":5,"area":null},{"id":"2211.08761","title":"Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks","created":"2022-11-16","cited_by_count":5,"area":null},{"id":"2302.00045","title":"Neural Control of Parametric Solutions for High-dimensional Evolution PDEs","created":"2023-01-31","cited_by_count":5,"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":"2307.02766","title":"Temporal Difference Learning for High-Dimensional PIDEs with Jumps","created":"2023-07-06","cited_by_count":5,"area":null},{"id":"2307.15496","title":"From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs","created":"2023-07-28","cited_by_count":5,"area":null},{"id":"2407.19707","title":"Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations","created":"2024-07-29","cited_by_count":5,"area":null},{"id":"2410.00053","title":"Frequency-adaptive Multi-scale Deep Neural Networks","created":"2024-09-28","cited_by_count":5,"area":null},{"id":"2602.12368","title":"A Machine Learning Approach to the Nirenberg Problem","created":"2026-02-12","cited_by_count":5,"area":null},{"id":"2101.07023","title":"Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification","created":"2021-01-18","cited_by_count":4,"area":null},{"id":"2103.08662","title":"dNNsolve: an efficient NN-based PDE solver","created":"2021-03-15","cited_by_count":4,"area":null},{"id":"2105.03480","title":"A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks","created":"2021-05-07","cited_by_count":4,"area":null},{"id":"2108.10504","title":"Deep Signature FBSDE Algorithm","created":"2021-08-24","cited_by_count":4,"area":null},{"id":"2206.03369","title":"Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions","created":"2022-06-07","cited_by_count":4,"area":null},{"id":"2302.02405","title":"Convergence Analysis of the Deep Galerkin Method for Weak Solutions","created":"2023-02-05","cited_by_count":4,"area":null},{"id":"2307.11289","title":"PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations","created":"2023-07-21","cited_by_count":4,"area":null},{"id":"2308.05061","title":"Fine-Tune Language Models as Multi-Modal Differential Equation Solvers","created":"2023-08-09","cited_by_count":4,"area":null},{"id":"2308.16468","title":"Computing excited states of molecules using normalizing flows","created":"2023-08-31","cited_by_count":4,"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":"2404.08456","title":"A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations","created":"2024-04-12","cited_by_count":4,"area":null},{"id":"2404.10771","title":"TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision","created":"2024-04-16","cited_by_count":4,"area":null},{"id":"2412.11010","title":"FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equations","created":"2024-12-15","cited_by_count":4,"area":null},{"id":"2105.06363","title":"HiDeNN-PGD: reduced-order hierarchical deep learning neural networks","created":"2021-05-13","cited_by_count":3,"area":null},{"id":"2107.00839","title":"Exploration noise for learning linear-quadratic mean field games","created":"2021-07-02","cited_by_count":3,"area":null},{"id":"2203.03234","title":"A deep branching solver for fully nonlinear partial differential equations","created":"2022-03-07","cited_by_count":3,"area":null},{"id":"2205.03672","title":"Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions","created":"2022-05-07","cited_by_count":3,"area":null}],"next_cursor":"100"}