Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

15 June 2017

Papers citing "Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations"

50 / 248 papers shown

Title
Reverse-BSDE Monte Carlo Jairon H. N. Batista Flávio B. Gonçalves Yuri F. Saporito Rodrigo S. Targino DiffM 31 0 0 11 May 2025
Integration Matters for Learning PDEs with Backwards SDEs Sungje Park Stephen Tu PINN 60 0 0 02 May 2025
FlowKac: An Efficient Neural Fokker-Planck solver using Temporal Normalizing flows and the Feynman Kac-Formula Naoufal El Bekri Lucas Drumetz Franck Vermet 55 0 0 14 Mar 2025
FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equations Zaijun Ye Wansheng Wang 75 0 0 15 Dec 2024
A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations Shu Liu Stanley Osher Wuchen Li 33 0 0 09 Nov 2024
Convergence Guarantees for Neural Network-Based Hamilton-Jacobi Reachability William Hofgard 29 2 0 03 Oct 2024
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method Gareth Hardwick Senwei Liang Haizhao Yang 39 1 0 01 Oct 2024
A Taxonomy of Loss Functions for Stochastic Optimal Control Carles Domingo-Enrich 37 3 0 01 Oct 2024
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in $L^p$ -sense Ariel Neufeld Tuan Anh Nguyen 42 0 0 30 Sep 2024
Frequency-adaptive Multi-scale Deep Neural Networks Jizu Huang Rukang You Tao Zhou AI4CE 33 1 0 28 Sep 2024
Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer Georgios Is. Detorakis 28 0 0 21 Aug 2024
Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations M. L. Shahab Hadi Susanto 27 2 0 29 Jul 2024
Dynamical Measure Transport and Neural PDE Solvers for Sampling Jingtong Sun Julius Berner Lorenz Richter Marius Zeinhofer Johannes Müller Kamyar Azizzadenesheli Anima Anandkumar OT DiffM 42 8 0 10 Jul 2024
Optimal Control of Agent-Based Dynamics under Deep Galerkin Feedback Laws Frederik Kelbel 13 0 0 13 Jun 2024
Solving Poisson Equations using Neural Walk-on-Spheres Hong Chul Nam Julius Berner Anima Anandkumar 37 3 0 05 Jun 2024
Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics Simone Brugiapaglia N. Dexter Samir Karam Weiqi Wang AI4CE DiffM 43 1 0 03 Jun 2024
Convergence of the Deep Galerkin Method for Mean Field Control Problems William Hofgard Jingruo Sun Asaf Cohen AI4CE 37 3 0 22 May 2024
FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model Zezheng Song Jiaxin Yuan Haizhao Yang AI4CE 40 18 0 23 Apr 2024
TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision Zhuo Chen Jacob McCarran Esteban Vizcaino Marin Soljacic Di Luo AI4CE 21 3 0 16 Apr 2024
A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations Lorenc Kapllani Long Teng 31 2 0 12 Apr 2024
Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size Huafu Liao Alpár R. Mészáros Chenchen Mou Chao Zhou 26 2 0 08 Apr 2024
Deep Backward and Galerkin Methods for the Finite State Master Equation Asaf Cohen Mathieu Lauriere Ethan C. Zell 44 2 0 08 Mar 2024
Neural optimal controller for stochastic systems via pathwise HJB operator Zhe Jiao Xiao-zheng Luo Xinlei Yi 30 0 0 23 Feb 2024
Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data YongKyung Oh Dongyoung Lim Sungil Kim AI4TS 43 13 0 22 Feb 2024
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss Yahong Yang Juncai He AI4CE 40 7 0 31 Jan 2024
An Explicit Scheme for Pathwise XVA Computations L. Abbas-Turki Stéphane Crépey Botao Li Bouazza Saadeddine 11 2 0 24 Jan 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 30 0 0 18 Jan 2024
PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws Liu Yang Stanley J. Osher AI4CE 48 19 0 14 Jan 2024
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks Zheyuan Hu Zekun Shi George Karniadakis Kenji Kawaguchi AI4CE PINN 52 24 0 22 Dec 2023
Stochastic Optimal Control Matching Carles Domingo-Enrich Jiequn Han Brandon Amos Joan Bruna Ricky T. Q. Chen DiffM 20 6 0 04 Dec 2023
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs Zheyuan Hu Zhouhao Yang Yezhen Wang George Karniadakis Kenji Kawaguchi 56 10 0 26 Nov 2023
A Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equations E. Putri M. L. Shahab Mohammad Iqbal I. Mukhlash A. Hakam Lutfi Mardianto Hadi Susanto 37 1 0 20 Nov 2023
Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study Rawin Assabumrungrat Kentaro Minami Masanori Hirano 15 1 0 13 Nov 2023
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms Yahong Yang Yulong Lu 40 3 0 08 Nov 2023
Time integration schemes based on neural networks for solving partial differential equations on coarse grids Xinxin Yan Zhideng Zhou Xiaohan Cheng Xiaolei Yang AI4TS AI4CE 23 0 0 16 Oct 2023
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations Lorenc Kapllani Long Teng Matthias Rottmann 24 1 0 05 Oct 2023
An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions Yiran Wang Suchuan Dong 31 35 0 13 Sep 2023
Computing excited states of molecules using normalizing flows Yahya Saleh Álvaro Fernández Corral Emil Vogt Armin Iske J. Küpper A. Yachmenev 38 7 0 31 Aug 2023
$A numerical approach for the fractional Laplacian via deep neural networks$ A numerical approach for the fractional Laplacian via deep neural networks Nicolás Valenzuela 34 3 0 30 Aug 2023
Fine-Tune Language Models as Multi-Modal Differential Equation Solvers Liu Yang Siting Liu Stanley J. Osher 27 0 0 09 Aug 2023
Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables Javier Orera-Echeverria J. Ayensa-Jiménez Manuel Doblaré 25 1 0 07 Aug 2023
From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs Lorenz Richter Leon Sallandt Nikolas Nusken 21 4 0 28 Jul 2023
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks Zheyuan Hu K. Shukla George Karniadakis Kenji Kawaguchi PINN AI4CE 65 87 0 23 Jul 2023
PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations R. Gao Yufeng Wang Min Yang Chuanjun Chen GAN 34 2 0 21 Jul 2023
Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms R. Balkin Héctor D. Ceniceros Ruimeng Hu 21 2 0 12 Jul 2023
Temporal Difference Learning for High-Dimensional PIDEs with Jumps Liwei Lu Hailong Guo Xueqing Yang Yi Zhu AI4CE 23 6 0 06 Jul 2023
Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness C. Hartmann Lorenz Richter AAML 27 2 0 05 Jul 2023
Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes Yuxiao Wen Eric Vanden-Eijnden Benjamin Peherstorfer 24 13 0 27 Jun 2023
Transferability of Winning Lottery Tickets in Neural Network Differential Equation Solvers Edward Prideaux-Ghee 40 0 0 16 Jun 2023
CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions Ben Adcock Juan M. Cardenas N. Dexter 24 6 0 01 Jun 2023