DeepXDE Physics-Informed Neural Network FrameworkNew

Why DeepXDE

DeepXDE (Lu et al., arXiv 1907.04502) is the most widely used open-source library for physics-informed learning. Its value is uniform abstraction: you describe the PDE, geometry, boundary/initial conditions and observation data, and the same API handles forward problems, inverse parameter identification, and multiphysics coupling.

Core capabilities

• PINN: flexible residual specification for nearly arbitrary PDEs
• DeepONet / Mionet: operator learning with multi-input support
• Fractional differential equations (time and space fractional Laplacian)
• Multi-backend: PyTorch / TensorFlow / JAX / PaddlePaddle
• Utility modules: point cloud sampling, callbacks, model save/restore

Suggested path

1. Run the official Poisson 1D example; understand the loss = physics residual + boundary + data
2. Reproduce Burgers forward problem; tune point counts and network depth
3. Inverse problem: recover the diffusion coefficient from sparse observations
4. Operator learning: compare DeepONet vs FNO on the same Darcy dataset

Where it fits

• Prototype: fastest way to test a physics-informed idea
• Benchmark: reference implementation in many papers
• Limitation: very large 3D industrial problems still favor dedicated frameworks like PhysicsNeMo or NVIDIA Warp