Greedy training algorithms for neural networks and applications to PDEs (Q2699382)

scientific article; zbMATH DE number 7679188

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English	Greedy training algorithms for neural networks and applications to PDEs	scientific article; zbMATH DE number 7679188

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instance of

scholarly article

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title

Greedy training algorithms for neural networks and applications to PDEs (English)

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Journal of Computational Physics

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publication date

26 April 2023

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full work available at URL

https://arxiv.org/abs/2107.04466

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zbMATH Keywords

neural networks

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partial differential equations

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greedy algorithms

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generalization accuracy

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describes a project that uses

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Active Neuron Least Squares: A Training Method for Multivariate Rectified Neural Networks

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A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids

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Breaking the Curse of Dimensionality with Convex Neural Networks

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Universal approximation bounds for superpositions of a sigmoidal function

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Approximation and learning by greedy algorithms

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10.1162/153244303321897690

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Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

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Greedy algorithms for high-dimensional non-symmetric linear problems

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Solving the quantum many-body problem with artificial neural networks

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A homotopy training algorithm for fully connected neural networks

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Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs

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Q4273944

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Some remarks on greedy algorithms

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Neural network approximation

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Neural‐network‐based approximations for solving partial differential equations

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Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators

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Solving high-dimensional partial differential equations using deep learning

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The collected works of Wassily Hoeffding. Ed. by N. I. Fisher and P. K. Sen

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A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training

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Solving parametric PDE problems with artificial neural networks

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Approximation by Combinations of ReLU and Squared ReLU Ridge Functions With <inline-formula> <tex-math notation="LaTeX">$\ell^1$ </tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\ell^0$ </tex-math> </inline-formula> Controls

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Q5053337

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Error estimates for DeepONets: a deep learning framework in infinite dimensions

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Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations

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Efficient agnostic learning of neural networks with bounded fan-in

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A finite difference method and analysis for 2D nonlinear Poisson-Boltzmann equations

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Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks

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Q4320142

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Deep Network Approximation for Smooth Functions

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The Barron space and the flow-induced function spaces for neural network models

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Matching pursuits with time-frequency dictionaries

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Physics-informed neural networks for high-speed flows

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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Q4626279

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fPINNs: Fractional Physics-Informed Neural Networks

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Q4998934

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What Kinds of Functions Do Deep Neural Networks Learn? Insights from Variational Spline Theory

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Q3952642

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

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Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

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Understanding Machine Learning

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Optimal approximation rate of ReLU networks in terms of width and depth

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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

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Approximation rates for neural networks with general activation functions

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Optimal Convergence Rates for the Orthogonal Greedy Algorithm

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DGM: a deep learning algorithm for solving partial differential equations

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Q5680973

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Greedy Approximation

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Greedy approximation

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High-Dimensional Statistics

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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Representation formulas and pointwise properties for Barron functions

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Finite Neuron Method and Convergence Analysis

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Error bounds for approximations with deep ReLU networks

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Sequential greedy approximation for certain convex optimization problems

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Gradient descent optimizes over-parameterized deep ReLU networks

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2023.112084

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Sitelinks

Mathematics(1 entry)

mardi Publication:2699382