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"

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An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations Dan Crisan Alexander Lobbe S. Ortiz-Latorre 14 4 0 10 Jan 2022
Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons Zijian Zhou Li Wang Zhenya Yan 16 1 0 28 Dec 2021
Reinforcement Learning with Dynamic Convex Risk Measures Anthony Coache S. Jaimungal 34 27 0 26 Dec 2021
Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs Xi-An Li Z. Xu Lei Zhang 24 27 0 10 Dec 2021
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 31 27 0 07 Dec 2021
Data-driven Hedging of Stock Index Options via Deep Learning Jie Chen Lingfei Li AIFin 13 4 0 05 Nov 2021
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method Zhongjian Wang Jack Xin Zhiwen Zhang 39 15 0 02 Nov 2021
Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models Ahmet Demirkaya Tales Imbiriba Kylee J Lockwood S. Rampersad Elie Alhajjar G. Guidoboni Zachary C Danziger Deniz Erdogmus 28 5 0 12 Oct 2021
Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks Sagi Shaier M. Raissi P. Seshaiyer PINN AI4CE 21 25 0 11 Oct 2021
Deep Learning for Principal-Agent Mean Field Games S. Campbell Yichao Chen Arvind Shrivats S. Jaimungal 13 16 0 03 Oct 2021
Characterizing possible failure modes in physics-informed neural networks Aditi S. Krishnapriyan A. Gholami Shandian Zhe Robert M. Kirby Michael W. Mahoney PINN AI4CE 51 614 0 02 Sep 2021
Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models Ling Guo Hao Wu Tao Zhou AI4CE 14 45 0 30 Aug 2021
Deep Signature FBSDE Algorithm Qiaochu Feng Man Luo Zhao-qin Zhang 9 8 0 24 Aug 2021
Learning the temporal evolution of multivariate densities via normalizing flows Yubin Lu R. Maulik Ting Gao Felix Dietrich Ioannis G. Kevrekidis Jinqiao Duan 13 22 0 29 Jul 2021
Data-informed Deep Optimization Lulu Zhang Z. Xu Yaoyu Zhang AI4CE 35 3 0 17 Jul 2021
Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance René Carmona Mathieu Laurière AI4CE 20 26 0 09 Jul 2021
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs Lulu Zhang Tao Luo Yaoyu Zhang Weinan E Z. Xu Zheng Ma AI4CE 27 33 0 08 Jul 2021
Exploration noise for learning linear-quadratic mean field games François Delarue A. Vasileiadis MLT 34 11 0 02 Jul 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs Tim De Ryck Siddhartha Mishra PINN 21 100 0 28 Jun 2021
Lagrangian dual framework for conservative neural network solutions of kinetic equations H. Hwang Hwijae Son 17 7 0 23 Jun 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 38 27 0 14 Jun 2021
Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality Lukas Gonon 21 35 0 14 Jun 2021
Solving PDEs on Unknown Manifolds with Machine Learning Senwei Liang Shixiao W. Jiang J. Harlim Haizhao Yang AI4CE 42 16 0 12 Jun 2021
HiDeNN-PGD: reduced-order hierarchical deep learning neural networks Lei Zhang Ye Lu Shaoqiang Tang Wing Kam Liu AI4CE 12 28 0 13 May 2021
A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks Haoya Li Lexing Ying 24 10 0 07 May 2021
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Jérome Darbon P. Dower Tingwei Meng 8 22 0 07 May 2021
Efficient training of physics-informed neural networks via importance sampling M. A. Nabian R. J. Gladstone Hadi Meidani DiffM PINN 71 223 0 26 Apr 2021
On the approximation of functions by tanh neural networks Tim De Ryck S. Lanthaler Siddhartha Mishra 26 138 0 18 Apr 2021
Distributional Offline Continuous-Time Reinforcement Learning with Neural Physics-Informed PDEs (SciPhy RL for DOCTR-L) I. Halperin OffRL 20 7 0 02 Apr 2021
dNNsolve: an efficient NN-based PDE solver V. Guidetti F. Muia Y. Welling A. Westphal 27 6 0 15 Mar 2021
Error Estimates for the Deep Ritz Method with Boundary Penalty Johannes Müller Marius Zeinhofer 37 16 0 01 Mar 2021
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities Mengwu Guo Andrea Manzoni Maurice Amendt Paolo Conti J. Hesthaven 85 95 0 26 Feb 2021
Solving high-dimensional parabolic PDEs using the tensor train format Lorenz Richter Leon Sallandt Nikolas Nusken 14 49 0 23 Feb 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 27 433 0 04 Feb 2021
Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification L. Scarabosio 16 9 0 18 Jan 2021
Recurrent Neural Networks for Stochastic Control Problems with Delay Jiequn Han Ruimeng Hu 19 18 0 05 Jan 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 28 30 0 15 Dec 2020
Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm Yao Xuan R. Balkin Jiequn Han Ruimeng Hu Héctor D. Ceniceros 19 9 0 12 Dec 2020
Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes Raffaele Marino N. Macris 24 16 0 09 Dec 2020
Meshless physics-informed deep learning method for three-dimensional solid mechanics Diab W. Abueidda Q. Lu S. Koric AI4CE 31 113 0 02 Dec 2020
Some observations on high-dimensional partial differential equations with Barron data E. Weinan Stephan Wojtowytsch AI4CE 6 15 0 02 Dec 2020
Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 11 11 0 02 Dec 2020
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning Julius Berner Markus Dablander Philipp Grohs 11 46 0 09 Nov 2020
Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates X. Zhuang Hongwei Guo N. Alajlan Timon Rabczuk AI4CE 11 311 0 09 Oct 2020
Actor-Critic Algorithm for High-dimensional Partial Differential Equations Xiaohan Zhang 19 3 0 07 Oct 2020
Analysis of three dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis Hongwei Guo X. Zhuang Pengwan Chen N. Alajlan Timon Rabczuk 27 58 0 03 Oct 2020
Stochastic analysis of heterogeneous porous material with modified neural architecture search (NAS) based physics-informed neural networks using transfer learning Hongwei Guo X. Zhuang Timon Rabczuk 20 82 0 03 Oct 2020
Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations Lorenc Kapllani Long Teng 16 11 0 03 Oct 2020
Physics Informed Neural Networks for Simulating Radiative Transfer Siddhartha Mishra Roberto Molinaro PINN 18 104 0 25 Sep 2020