This repository explores hybrid numerical and machine learning approaches to solve the Allen-Cahn equation, a stiff parabolic partial differential equation (PDE) used to model phase separation and microstructural evolution.
- Numerical Baseline (FDM): Implemented a multi-core optimized Finite Difference Method (explicit Euler scheme) to generate highly accurate, physically consistent phase-coarsening data.
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ML Surrogate Model (U-Net): Designed and trained a Convolutional Neural Network (U-Net) to act as an autoregressive surrogate solver. The model learns the transient phase-field dynamics, mapping the system state at
$t$ to$t+\Delta t$ .
The U-Net was trained on frames generated from randomly seeded initial conditions. Below is the model's performance on a completely unseen test seed. The surrogate model successfully predicts the interfacial dynamics autoregressively without solving the underlying PDEs.
allen_cahn_fdm.py: Base FDM solver for data generation and verification.allen_cahn_unet.py: Multi-core data pipeline, U-Net architecture, training loop, and autoregressive evaluation.