Hi, and welcome to my homepage! I am a Ph.D. candidate at the University of Illinois Urbana-Champaign. I am advised by Matthew West, and broadly speaking, I work on optimizing PDE solvers using machine learning. In particular, I have used techniques such as unsupervised and reinforcement learning (RL), along with graph neural networks (GNN), to optimize numerical PDE solvers.

In a study published at NeurIPS 2021, I utilized RL and GNN to optimize coarse grid selection in algebraic multigrid (AMG, a famous numerical PDE solver), with theoretical guarantees for convergence of the obtained method. Feel free to check out the paper here.

In another study published at NeurIPS 2022, I utilized unsupervised learning and GNN to learn and optimize domain decomposition PDE solvers (DDMs). The unsupervised loss function introduced in this study provides a theoretical guarantee to converge to the global optimum in limits. Feel free to check out the paper here.

Hierarchy of grids obtained from a PDE passing through GNNs.

I have recently been working on a follow-up study on learning domain decomposition solvers, and have developed a new GNN architecture to learn to optimize multilevel DDMs. I have also improved the unsupervised loss function to adapt to a multilevel training scheme, which also enjoys a theoretical guarantee to converge to the global optimum in limits. This work has been accepted at ICML 2023, and its preprint is available here.