This repository implements a complete operator-learning pipeline for the PDE:
- div(a(x) grad u(x)) = -f(x) (implemented as -div(a grad u)=f) on Ω = (0,1)^2 with homogeneous Dirichlet boundary conditions u=0 on ∂Ω.
Input: coefficient field a(x,y)
Output: solution field u(x,y)
We provide:
- Dataset generation with a Gaussian random field prior for w and a pointwise transform a=T(w)
- A finite-elements solver for variable-coefficient diffusion in divergence form
- DeepONet training (sensor-based operator learning)
- FNO training (grid-based Fourier neural operator)
- Evaluation utilities
python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt