Diffusion-Reaction Robin BC

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This example compares a variational PINN against a classical FEM reference under mixed Dirichlet and Robin boundary conditions.

Problem Setup

The PDE is a diffusion-reaction or Helmholtz-like problem on a 2D domain with boundary integrals contributing Robin terms.

Step 1: Build a Weak Form With Boundary Terms

The script includes boundary quadrature contributions directly in the variational residual.

Step 2: Train the VPINN

Instead of minimizing a pointwise PDE residual, the network minimizes a weak-form objective.

Step 3: Compare Against FEM

A finer FEM solve is used as a reference to assess how well the variational PINN captures the solution.

What To Notice

• Robin conditions fit naturally into a weak-form workflow.
• This script is a strong reference for FEM versus VPINN comparisons.
• Boundary quadrature tags are one of the key implementation ideas.

Download full script Back to 08 FEM and Variational PINNs

Script Snippet