Deep ReLU networks and high-order finite element methods

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

Deep Neural Networks for Rotation-Invariance Approximation and Learning

(2019) Charles K. Chui et al.   Analysis and Applications

Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ

(2018) Christoph Schwab et al.   Analysis and Applications

Provable approximation properties for deep neural networks

(2018) Uri Shaham et al.   APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS

Anisotropic radial basis function methods for continental size ice sheet simulations

(2018) Gong Cheng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficiency of deep networks for radially symmetric functions

(2018) Brendan McCane et al.   NEUROCOMPUTING

DGM: A deep learning algorithm for solving partial differential equations

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

Optimal approximation of piecewise smooth functions using deep ReLU neural networks

(2018) Philipp Petersen et al.   NEURAL NETWORKS

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

Exponential convergence of the deep neural network approximation for analytic functions

(2018) Weinan E et al.   Science China-Mathematics

Generalization and Expressivity for Deep Nets

(2018) Shao-Bo Lin   IEEE Transactions on Neural Networks and Learning Systems

Exponential Convergence of hp-FEM for Elliptic Problems in Polyhedra: Mixed Boundary Conditions and Anisotropic Polynomial Degrees

(2017) Dominik Schötzau et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS

Deep learning

(2015) Yann LeCun et al.   NATURE

Exponential convergence ofhpquadrature for integral operators with Gevrey kernels

(2010) Alexey Chernov et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE