On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations

Classification with a disordered dopant-atom network in silicon

(2020) Tao Chen et al.   NATURE

Evolution of circuits for machine learning

(2020) Cyrus F. Hirjibehedin   NATURE

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

(2019) Christian Beck et al.   JOURNAL OF NONLINEAR SCIENCE

Machine Learning for Semi Linear PDEs

(2019) Quentin Chan-Wai-Nam et al.   JOURNAL OF SCIENTIFIC COMPUTING

Adversarial uncertainty quantification in physics-informed neural networks

(2019) Yibo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

(2019) Dongkun Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Solving many-electron Schrödinger equation using deep neural networks

(2019) Jiequn Han et al.   JOURNAL OF COMPUTATIONAL PHYSICS

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

(2019) Zichao Long et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Polynomial Approximation of High-Dimensional Hamilton--Jacobi--Bellman Equations and Applications to Feedback Control of Semilinear Parabolic PDEs

(2018) Dante Kalise et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A unified deep artificial neural network approach to partial differential equations in complex geometries

(2018) Jens Berg et al.   NEUROCOMPUTING

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Error Analysis for POD Approximations of Infinite Horizon Problems via the Dynamic Programming Approach

(2017) A. Alla et al.   SIAM JOURNAL ON CONTROL AND OPTIMIZATION

Suboptimal Feedback Control of PDEs by Solving HJB Equations on Adaptive Sparse Grids

(2016) Jochen Garcke et al.   JOURNAL OF SCIENTIFIC COMPUTING

Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

(2015) Tao Kong et al.   Communications in Computational Physics

On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton--Jacobi Equations

(2015) Jérôme Darbon   SIAM Journal on Imaging Sciences

A Constrained Backpropagation Approach for the Adaptive Solution of Partial Differential Equations

(2013) Keith Rudd et al.   IEEE Transactions on Neural Networks and Learning Systems

An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations

(2012) Olivier Bokanowski et al.   JOURNAL OF SCIENTIFIC COMPUTING

Some Recent Aspects of Differential Game Theory

(2010) R. Buckdahn et al.   Dynamic Games and Applications

Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions

(2009) K.S. McFall et al.   IEEE TRANSACTIONS ON NEURAL NETWORKS

Efficient computation of optimal actions

(2009) Emanuel Todorov   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs

(2009) William M. McEneaney et al.   SIAM JOURNAL ON CONTROL AND OPTIMIZATION

The Max-Plus Finite Element Method for Solving Deterministic Optimal Control Problems: Basic Properties and Convergence Analysis

(2008) Marianne Akian et al.   SIAM JOURNAL ON CONTROL AND OPTIMIZATION