DeepXDE: A Deep Learning Library for Solving Differential Equations
summary
DeepXDE is a Python library that implements physics‑informed neural networks using TensorFlow and automatic differentiation to embed PDEs (Laplacian, Helmholtz, diffusion‑reaction) into loss functions, and it also constructs quadrature matrices to solve integral equations. It recovers hidden parameters (learns D and kf) and tolerates up to 20% noise in measurements, uses residual-based adaptive refinement to cut domain training points from ~10,000 to ~2,000, and handles complex domains via constructive solid geometry. Code is on GitHub.
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chapters (14)
- 0:00Introduction to DeepXDE
- 1:05Physics-informed neural networks
- 7:32Advantages of PINNs
- 10:03Approximation and optimization
- 16:49Residual-based adaptive refinement
- 20:31DeepXDE usage overview
- 21:12Solving Poisson equation
- 27:25Time-dependent problems
- 29:16Systems of PDEs
- 30:01Integral equations
- 31:50Inverse problems
- 34:00Handling complex geometry
- 38:59Key features summary
- 41:55Q&A and stability discussion
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