On the approximation of functions by tanh neural networks

Deep learning observables in computational fluid dynamics

(2020) Kjetil O. Lye et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Approximation rates for neural networks with general activation functions

(2020) Jonathan W. Siegel et al.   NEURAL NETWORKS

Deep Neural Network Expression of Posterior Expectations in Bayesian PDE Inversion

(2020) Lukas Herrmann et al.   INVERSE PROBLEMS

Error bounds for deep ReLU networks using the Kolmogorov–Arnold superposition theorem

(2020) Hadrien Montanelli et al.   NEURAL NETWORKS

Iterative surrogate model optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks

(2020) Kjetil O. Lye et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Approximation rates for neural networks with encodable weights in smoothness spaces

(2020) Ingo Gühring et al.   NEURAL NETWORKS

Smooth Function Approximation by Deep Neural Networks with General Activation Functions

(2019) Ilsang Ohn et al.   Entropy

Error bounds for approximations with deep ReLU neural networks in Ws,p norms

(2019) Ingo Gühring et al.   Analysis and Applications

Deep ReLU networks and high-order finite element methods

(2019) Joost A. A. Opschoor 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

Hidden physics models: Machine learning of nonlinear partial differential equations

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

On the approximation by single hidden layer feedforward neural networks with fixed weights

(2018) Namig J. Guliyev et al.   NEURAL NETWORKS

Approximation capability of two hidden layer feedforward neural networks with fixed weights

(2018) Namig J. Guliyev 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

Exponential convergence of the deep neural network approximation for analytic functions

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

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

Why Does Deep and Cheap Learning Work So Well?

(2017) Henry W. Lin et al.   JOURNAL OF STATISTICAL PHYSICS

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS

Deep learning

(2015) Yann LeCun et al.   NATURE

On the Complexity of Neural Network Classifiers: A Comparison Between Shallow and Deep Architectures

(2014) Monica Bianchini et al.   IEEE Transactions on Neural Networks and Learning Systems

Multivariate neural network operators with sigmoidal activation functions

(2013) Danilo Costarelli et al.   NEURAL NETWORKS

Approximation results for neural network operators activated by sigmoidal functions

(2013) Danilo Costarelli et al.   NEURAL NETWORKS

Dependence of Computational Models on Input Dimension: Tractability of Approximation and Optimization Tasks

(2012) Paul C. Kainen et al.   IEEE TRANSACTIONS ON INFORMATION THEORY

A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators

(2009) Emmanuel Candès et al.   MULTISCALE MODELING & SIMULATION

Geometric Upper Bounds on Rates of Variable-Basis Approximation

(2008) Vera Kurkova et al.   IEEE TRANSACTIONS ON INFORMATION THEORY