A mesh-free method for interface problems using the deep learning approach
Zhongjian Wang,Zhiwen Zhang +1 more
TLDR
Wang et al. as discussed by the authors proposed a mesh-free method to solve interface problems using the deep learning approach, where two types of PDEs are considered: an elliptic PDE with a discontinuous and high-contrast coefficient, and a linear elasticity equation with discontinuous stress tensor.About:
This article is published in Journal of Computational Physics.The article was published on 2020-01-01 and is currently open access. It has received 45 citations till now. The article focuses on the topics: Adaptive mesh refinement & Artificial neural network.read more
Citations
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Artificial neural network methods for the solution of second order boundary value problems
TL;DR: A method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy that increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth.
Journal ArticleDOI
The Application of Data-Driven Methods and Physics-Based Learning for Improving Battery Safety
Donal P. Finegan,Juner Zhu,Xuning Feng,Matt Keyser,Marcus Ulmefors,Wei Li,Martin Z. Bazant,Samuel J. Cooper +7 more
TL;DR: This perspective starts with effective strategies for experimentally replicating rare failure scenarios and thus reducing the number of experiments, and proceeds to describe means to acquire high-quality datasets, apply data-driven prediction techniques, and to extract physical insights into the events that lead to failure by incorporating physics into data- driven approaches.
Journal ArticleDOI
Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
Ziqi Liu,Wei Cai,Zhi-Qin John Xu +2 more
TL;DR: In this article, a multi-scale deep neural network (MscaleDNN) is proposed for Poisson-Boltzmann equations with ample frequency contents over complex and singular domains.
Journal ArticleDOI
A physics-guided neural network framework for elastic plates: Comparison of governing equations-based and energy-based approaches
TL;DR: A neural network-based computational framework is established to characterize the finite deformation of elastic plates, which in classic theories is described by the Foppl--von Karman equations with a set of boundary conditions (BCs).
Journal ArticleDOI
Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
TL;DR: The proposed MscaleDNNs are shown to be superior to traditional fully connected DNNs and be an effective mesh-less numerical method for Poisson-Boltzmann equations with ample frequency contents over complex and singular domains.
References
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Proceedings Article
Adam: A Method for Stochastic Optimization
Diederik P. Kingma,Jimmy Ba +1 more
TL;DR: This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.
Journal ArticleDOI
Deep learning
TL;DR: Deep learning is making major advances in solving problems that have resisted the best attempts of the artificial intelligence community for many years, and will have many more successes in the near future because it requires very little engineering by hand and can easily take advantage of increases in the amount of available computation and data.
Book
Deep Learning
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Posted Content
Adam: A Method for Stochastic Optimization
Diederik P. Kingma,Jimmy Ba +1 more
TL;DR: In this article, the adaptive estimates of lower-order moments are used for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimate of lowerorder moments.
Journal ArticleDOI
Multilayer feedforward networks are universal approximators
TL;DR: It is rigorously established that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available.