Analytic continuation of noisy data using Adams Bashforth residual neural network

DOI10.3934/dcdss.2021088OpenAlexW3193221323MaRDI QIDQ2129155

Thomas Maier, Xuping Xie, Feng Bao, Clayton G. Webster

Publication date: 22 April 2022

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.10430

zbMATH Keywords

stochastic optimizationinverse problemneural networkanalytic continuationmachine learning

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Optimal stochastic control (93E20) Analytic continuation of functions of one complex variable (30B40) Problems with incomplete information (optimization) (49N30)

Related Items

On mathematical modeling in image reconstruction and beyond

Uses Software

• ImageNet
• Maxent
• torchdiffeq
• PDE-Net
• AlexNet
• NETT

Cites Work

• Learning light transport the reinforced way
• Implementation of the maximum entropy method for analytic continuation
• Exponential convergence of the deep neural network approximation for analytic functions
• Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
• Projected regression method for solving Fredholm integral equations arising in the analytic continuation problem of quantum physics
• Stable architectures for deep neural networks
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• NETT: solving inverse problems with deep neural networks
• Model Reduction with Memory and the Machine Learning of Dynamical Systems
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