- 数据分析与问题求解讨论班

Physics-Informed Neural Networks: Software Tools, a DeepXDE Case Study, and Future Directions

组织者

张晓明

演讲者

马蕾

时间

2026年07月16日 15:00 至 16:00

地点

A3-1-301

线上

Zoom 204 323 0165 (BIMSA)

摘要

Physics-informed neural networks provide a data-driven approach to solving differential equations by incorporating physical laws, boundary conditions, and initial conditions into neural network training. This talk introduces the practical use of PINNs from the perspective of scientific software. We first demonstrate the complete PINN workflow in DeepXDE through the viscous Burgers equation, including problem definition, sampling, network construction, loss formulation, optimization, and accuracy evaluation. The predicted solution is compared with a reference solution to illustrate both the overall performance and the difficulty of resolving regions with sharp changes. We then review representative scientific machine-learning libraries, including DeepXDE, PhysicsNeMo, NeuroDiffEq, TorchPhysics, SciANN, NeuralPDE.jl, ADCME, TensorDiffEq, NeuralUQ, and DUE, highlighting their different capabilities and application scenarios. Finally, the talk discusses four major challenges that must be addressed before PINNs can become more reliable scientific computing tools: training stability, representation of multiscale and rapidly changing solutions, computational efficiency, and integration with traditional numerical methods.