Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences
From MaRDI portal
Publication:5001377
DOI10.1137/20M1344883MaRDI QIDQ5001377
T. Konstantin Rusch, Siddhartha Mishra
Publication date: 19 July 2021
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.12564
Artificial neural networks and deep learning (68T07) Algorithms for approximation of functions (65D15) Numerical quadrature and cubature formulas (65D32) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)
Related Items
Compliance minimisation of smoothly varying multiscale structures using asymptotic analysis and machine learning ⋮ A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations ⋮ Deep Neural Network Surrogates for Nonsmooth Quantities of Interest in Shape Uncertainty Quantification ⋮ On the approximation of functions by tanh neural networks ⋮ Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms ⋮ Convergence Analysis of a Quasi-Monte CarloBased Deep Learning Algorithm for Solving Partial Differential Equations ⋮ wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws ⋮ Approximation bounds for convolutional neural networks in operator learning ⋮ Finite Neuron Method and Convergence Analysis ⋮ A physics-informed multi-fidelity approach for the estimation of differential equations parameters in low-data or large-noise regimes ⋮ Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
- Deep learning observables in computational fluid dynamics
- Hidden physics models: machine learning of nonlinear partial differential equations
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Efficient basket Monte Carlo option pricing via a simple analytical approximation
- A priori estimates of the population risk for two-layer neural networks
- A machine learning framework for data driven acceleration of computations of differential equations
- An artificial neural network as a troubled-cell indicator
- On the mathematical foundations of learning
- Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations
- Handbook of Uncertainty Quantification
- Multilevel Monte Carlo Path Simulation
- Monte Carlo Variance of Scrambled Net Quadrature
- Solving high-dimensional partial differential equations using deep learning
- A multi-level procedure for enhancing accuracy of machine learning algorithms
- Multidimensional Variation for Quasi-Monte Carlo
- High-dimensional integration: The quasi-Monte Carlo way
- Advanced Lectures on Machine Learning
- Understanding Machine Learning
- Reduced Basis Methods for Partial Differential Equations
- On the distribution of points in a cube and the approximate evaluation of integrals
- Transformations and Hardy--Krause Variation