Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
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Publication:5162368
DOI10.4208/cicp.OA-2020-0179zbMath1473.65348arXiv2007.11207MaRDI QIDQ5162368
Zhi-Qin John Xu, Ziqi Liu, Wei Cai
Publication date: 2 November 2021
Published in: Communications in Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.11207
Artificial neural networks and deep learning (68T07) Numerical methods for partial differential equations, boundary value problems (65N99) PDEs in connection with computer science (35Q68)
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Uses Software
Cites Work
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Provable approximation properties for deep neural networks
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Accurate evaluation of electrostatics for macromolecules in solution
- A mesh-free method for interface problems using the deep learning approach
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Relu Deep Neural Networks and Linear Finite Elements
- Ten Lectures on Wavelets
- Preface
- Solving high-dimensional partial differential equations using deep learning
- Deep Potential: A General Representation of a Many-Body Potential Energy Surface
- Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields using Convolutional Neural Networks
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