Greedy training algorithms for neural networks and applications to PDEs
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Publication:2699382
DOI10.1016/j.jcp.2023.112084OpenAlexW4360603778MaRDI QIDQ2699382
Jonathan W. Siegel, Xianlin Jin, Qingguo Hong, Wenrui Hao, Jin-Chao Xu
Publication date: 26 April 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.04466
Artificial intelligence (68Txx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Approximations and expansions (41Axx)
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- Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations
- A finite difference method and analysis for 2D nonlinear Poisson-Boltzmann equations
- A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids
- A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
- The collected works of Wassily Hoeffding. Ed. by N. I. Fisher and P. K. Sen
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Some remarks on greedy algorithms
- Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators
- Approximation rates for neural networks with general activation functions
- DGM: a deep learning algorithm for solving partial differential equations
- Optimal approximation rate of ReLU networks in terms of width and depth
- Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
- Representation formulas and pointwise properties for Barron functions
- The Barron space and the flow-induced function spaces for neural network models
- Physics-informed neural networks for high-speed flows
- Gradient descent optimizes over-parameterized deep ReLU networks
- Error bounds for approximations with deep ReLU networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Approximation and learning by greedy algorithms
- Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference
- Greedy Approximation
- Greedy algorithms for high-dimensional non-symmetric linear problems
- Greedy approximation
- Universal approximation bounds for superpositions of a sigmoidal function
- Neural‐network‐based approximations for solving partial differential equations
- Efficient agnostic learning of neural networks with bounded fan-in
- 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
- High-Dimensional Statistics
- Solving the quantum many-body problem with artificial neural networks
- Sequential greedy approximation for certain convex optimization problems
- 10.1162/153244303321897690
- Matching pursuits with time-frequency dictionaries
- Solving high-dimensional partial differential equations using deep learning
- Solving parametric PDE problems with artificial neural networks
- Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks
- 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
- What Kinds of Functions Do Deep Neural Networks Learn? Insights from Variational Spline Theory
- Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
- Error estimates for DeepONets: a deep learning framework in infinite dimensions
- Optimal Convergence Rates for the Orthogonal Greedy Algorithm
- Active Neuron Least Squares: A Training Method for Multivariate Rectified Neural Networks
- Deep Network Approximation for Smooth Functions
- A homotopy training algorithm for fully connected neural networks
- Finite Neuron Method and Convergence Analysis
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- fPINNs: Fractional Physics-Informed Neural Networks
- Breaking the Curse of Dimensionality with Convex Neural Networks
- Understanding Machine Learning
- Neural network approximation
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