- Authors - J. Skyler Sampayan, Tony Guan, and Oren Yang
- Affiliation - ECE 228 - Machine Learning and Physical Applications, Team 3, UC San Diego, Spring 2024
- Motivation - To use learning preconditioners of different neural network architectures to solve linear ill-conditioned partial differential equations (PDE) that is then passed into a conjugate gradient (CG) PDE solver, numerically. The goal is to show that learning preconditioners can decrease computational costs for PDE solvers.
- Background - This repo uses a graphic, recurring, and convolutional neural network architecture-based preconditioner (3 total preconditioners). The PDE solver used is a classical numerical matrix solver, a simple conjugate gradient PDE solver. The methods were tested on 3 ill-conditioned PDEs, the heat, wave, and Poisson equation. Those 3 PDE's with very ill-conditioned matrices where each passed into the 3 difference preconditioners then into the CG solver. The methods were validated against linear classical preconditioners.
- PDE_RNN - Is the Recurring Neural Net (RNN) preconditioner folder authored by J. Sampayan.
- PDE_GNN - Is the Graphics Neural Net (GNN) preconditioner folder authored by T. Guan.
- PDE_CNN - Is the Convolutional Neural Net (CNN) preconditioner folder authored by O. Yang.
├─ Root
├─ README.md
├─ PDE_CNN
├─ PDE_CNN.ipynb
├─ PDE_GNN
├─ PDE_GNN.ipynb
├─ PDE_RNN
├─ PDE_RNN.ipynb
Numpy
Pandas
Matplotlib
Torch Geometric
- Li, Y., Chen, H., & Sun, L. (2023). Learning Preconditioners for Conjugate Gradient PDE Solvers. Proceedings of the 40th International Conference on Machine Learning. PMLR 202. Retrieved from https://sites.google.com/view/neuralPCG.
- Belbute-Peres, F., Economon, T., & Kolter, Z. (2023). Neural Network Preconditioners for Solving the Dirac Equation in Lattice Gauge Theory. Under review at ICLR 2023. Retrieved from https://arxiv.org/abs/2208.02728.