03 Parabolic

This chapter introduces time-dependent diffusion problems, where the network must satisfy both PDE residuals in space-time and initial conditions at the starting time.

In This Chapter

• Heat 1D

  The simplest transient diffusion example with a DeepONet-style model.

  Walk through the example

• Heat 2D

  Extend the heat equation to a square domain and inspect time snapshots.

  Walk through the example

• Reaction-Diffusion 2D

  Add a linear reaction term to the transient diffusion dynamics.

  Walk through the example

• Allen-Cahn 2D

  Work with a nonlinear parabolic problem featuring a cubic reaction term.

  Walk through the example

Download Source Files

• heat_1d.py
• heat_2d.py
• reaction_diffusion_2d.py
• allen_cahn_2d.py