DeepXDE: A Deep Learning Library for Solving Differential Equations
Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis
Massachusetts Institute of Technology Brown University Xiamen University Pacific Northwest National Laboratory
阅读操作
确认中在文库中上传 PDF 后可生成中文音频讲解。
摘要与影响
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs), which embed a PDE into the loss of the neural network using automatic differentiation. The PINN algorithm is simple, and it can be applied to different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. Moreover, from an implementation point of view, PINNs solve inverse problems as easily as forward problems. We propose a new residual-based adaptive refinement (RAR) method to improve the training efficiency of PINNs. For pedagogical reasons, we compare the PINN algorithm to a standard finite element method. We also present a Python library for PINNs, DeepXDE, which is designed to serve both as an educational tool to be used in the classroom as well as a research tool for solving problems in computational science and engineering. Specifically, DeepXDE can solve forward problems given initial and boundary conditions, as well as inverse problems given some extra measurements. DeepXDE supports complex-geometry domains based on the technique of constructive solid geometry and enables the user code to be compact, resembling closely the mathematical formulation. We introduce the usage of DeepXDE and its customizability, and we also demonstrate the capability of PINNs and the user-friendliness of DeepXDE for five different examples. More broadly, DeepXDE contributes to the more rapid development of the emerging scientific machine learning field.
逐年被引趋势
关键指标
同类平均 = 1
同领域 · 同年份 · 同类型
Google Scholar 与 OpenAlex 的被引统计范围不同,数值存在差异属正常。
AI 辅助阅读
依据:摘要
可就本文提问;依据不足时会说明。
学术脉络
学科主题
物理Model Reduction and Neural Networks
Probabilistic and Robust Engineering Design · Magnetic Properties and Applications
参考文献 62
此处列出前 3 条
引用本文 2,530
按被引量排序,此处列出前 3 条