{"list":"other","total":59,"rows":[{"id":"1910.03193","title":"DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators","created":"2019-10-08","cited_by_count":2018},{"id":"1708.07469","title":"DGM: A deep learning algorithm for solving partial differential equations","created":"2017-08-24","cited_by_count":678},{"id":"1707.02568","title":"Solving high-dimensional partial differential equations using deep learning","created":"2017-07-09","cited_by_count":556},{"id":"1912.10077","title":"Are Transformers universal approximators of sequence-to-sequence functions?","created":"2019-12-20","cited_by_count":406},{"id":"2005.03180","title":"Model Reduction and Neural Networks for Parametric PDEs","created":"2020-05-07","cited_by_count":258},{"id":"2302.01178","title":"Convolutional Neural Operators for robust and accurate learning of PDEs","created":"2023-02-02","cited_by_count":214},{"id":"1905.08539","title":"Universal Approximation with Deep Narrow Networks","created":"2019-05-21","cited_by_count":200},{"id":"1706.04702","title":"Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations","created":"2017-06-15","cited_by_count":191},{"id":"2205.12944","title":"Learning in Mean Field Games: A Survey","created":"2022-05-25","cited_by_count":61},{"id":"2111.09880","title":"Optimal control of PDEs using physics-informed neural networks","created":"2021-11-18","cited_by_count":52},{"id":"2206.10745","title":"Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning","created":"2022-06-21","cited_by_count":44},{"id":"2303.16317","title":"Operator learning with PCA-Net: upper and lower complexity bounds","created":"2023-03-28","cited_by_count":44},{"id":"2011.15110","title":"Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEs","created":"2020-11-30","cited_by_count":40},{"id":"2102.11379","title":"Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks","created":"2021-02-22","cited_by_count":29},{"id":"1905.00358","title":"Deep Learning Methods for Mean Field Control Problems with Delay","created":"2019-05-01","cited_by_count":25},{"id":"2303.10257","title":"Recent Developments in Machine Learning Methods for Stochastic Control and Games","created":"2023-03-17","cited_by_count":24},{"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},{"id":"2402.19242","title":"Derivative-enhanced Deep Operator Network","created":"2024-02-29","cited_by_count":19},{"id":"2210.15179","title":"Mean-field neural networks: learning mappings on Wasserstein space","created":"2022-10-27","cited_by_count":16},{"id":"2405.20630","title":"Stochastic Optimal Control for Diffusion Bridges in Function Spaces","created":"2024-05-31","cited_by_count":16},{"id":"2403.08220","title":"Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional Bayesian inverse problems","created":"2024-03-13","cited_by_count":13},{"id":"2211.13866","title":"Minimal Width for Universal Property of Deep RNN","created":"2022-11-25","cited_by_count":12},{"id":"2310.02322","title":"Signature Methods in Stochastic Portfolio Theory","created":"2023-10-03","cited_by_count":11},{"id":"1912.01455","title":"Extensions of the Deep Galerkin Method","created":"2019-11-30","cited_by_count":10},{"id":"2212.11518","title":"Mean-field neural networks-based algorithms for McKean-Vlasov control problems *","created":"2022-12-22","cited_by_count":10},{"id":"2305.06000","title":"Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations","created":"2023-05-10","cited_by_count":10},{"id":"2312.14810","title":"Accurate, scalable, and efficient Bayesian optimal experimental design with derivative-informed neural operators","created":"2023-12-22","cited_by_count":10},{"id":"2203.17128","title":"Neural Q-learning for solving PDEs","created":"2022-03-31","cited_by_count":8},{"id":"2411.12726","title":"LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transport","created":"2024-11-19","cited_by_count":7},{"id":"2512.14086","title":"Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization","created":"2025-12-16","cited_by_count":7},{"id":"2505.15602","title":"Deep Learning for Continuous-Time Stochastic Control with Jumps","created":"2025-05-21","cited_by_count":6},{"id":"2410.18153","title":"Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees","created":"2024-10-23","cited_by_count":5},{"id":"2603.03211","title":"Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization","created":"2026-03-03","cited_by_count":5},{"id":"2603.04525","title":"The Volterra signature","created":"2026-03-04","cited_by_count":5},{"id":"2110.11265","title":"Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations","created":"2021-10-21","cited_by_count":4},{"id":"2504.08730","title":"Dimension reduction for derivative-informed operator learning: An analysis of approximation errors","created":"2025-04-11","cited_by_count":4},{"id":"2511.01125","title":"One model to solve them all: 2BSDE families via neural operators","created":"2025-11-03","cited_by_count":4},{"id":"2602.05898","title":"Universal approximation with signatures of non-geometric rough paths","created":"2026-02-05","cited_by_count":4},{"id":"2309.07091","title":"Optimal adaptive control with separable drift uncertainty","created":"2023-09-13","cited_by_count":3},{"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},{"id":"2511.23295","title":"Signature approach for pricing and hedging path-dependent options with frictions","created":"2025-11-28","cited_by_count":3},{"id":"2302.08809","title":"Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models","created":"2023-02-17","cited_by_count":2},{"id":"2408.07688","title":"Finite Dimensional Projections of HJB Equations in the Wasserstein Space","created":"2024-08-14","cited_by_count":2},{"id":"2408.12404","title":"Optimal control of partial differential equations in PyTorch using automatic differentiation and neural network surrogates","created":"2024-08-22","cited_by_count":2},{"id":"2511.09701","title":"Optimal control of Volterra integral diffusions and application to contract theory","created":"2025-11-12","cited_by_count":2},{"id":"2511.21646","title":"Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications","created":"2025-11-26","cited_by_count":2},{"id":"2602.17578","title":"Optimal control of stochastic Volterra integral equations with completely monotone kernels and stochastic differential equations on Hilbert spaces with unbounded control and diffusion operators","created":"2026-02-19","cited_by_count":2},{"id":"1907.04006","title":"Variational Optimization Based Reinforcement Learning for Infinite Dimensional Stochastic Systems","created":"2019-07-09","cited_by_count":1},{"id":"2102.09851","title":"Linear-quadratic stochastic delayed control and deep learning resolution","created":"2021-02-19","cited_by_count":1},{"id":"2301.11926","title":"Neural Network Approximation of Optimal Controls for Stochastic Reaction-Diffusion Equations","created":"2023-01-25","cited_by_count":1},{"id":"2301.11959","title":"Approximation of Optimal Feedback Controls for Stochastic Reaction-Diffusion Equations","created":"2023-01-27","cited_by_count":1},{"id":"2306.06016","title":"Lifting partial smoothing to solve HJB equations and stochastic control problems","created":"2023-06-09","cited_by_count":1},{"id":"2308.14506","title":"Stochastic optimal control problems with delays in the state and in the control via viscosity solutions and applications to optimal advertising and optimal investment problems","created":"2023-08-28","cited_by_count":1},{"id":"2309.05029","title":"Optimal control of stochastic delay differential equations: Optimal feedback controls","created":"2023-09-10","cited_by_count":1},{"id":"2310.03181","title":"Stochastic optimal control in Hilbert spaces: $C^{1,1}$ regularity of the value function and optimal synthesis via viscosity solutions","created":"2023-10-04","cited_by_count":1},{"id":"2502.12957","title":"A measure-valued HJB perspective on Bayesian optimal adaptive control","created":"2025-02-18","cited_by_count":1},{"id":"2503.07514","title":"Global maximum principle for optimal control of stochastic Volterra equations with singular kernels: An infinite dimensional approach","created":"2025-03-10","cited_by_count":1},{"id":"2505.05521","title":"Model-Based Closed-Loop Control Algorithm for Stochastic Partial Differential Equation Control","created":"2025-05-08","cited_by_count":1},{"id":"2601.01248","title":"Stochastic Control Methods for Optimization","created":"2026-01-03","cited_by_count":1}],"next_cursor":null}