Speaker: Per-Olof Persson, UC Berkeley
Title: "High-Order Methods on Unstructured Meshes and AI-Driven Mesh Generation"
Abstract:
High-order accurate methods, such as the discontinuous Galerkin (DG) method, have attracted significant attention due to their low numerical dissipation, natural stabilization through Riemann solvers, compatibility with unstructured meshes of arbitrary curved element types, and rigorous mathematical foundations. This leads to outstanding performance compared to traditional numerical methods for complex applications such as turbulent flows, multiphysics simulations, and wave propagation. This talk will present recent advancements addressing remaining challenges across two complementary fronts: AI-enhanced mesh generation, and novel high-order discretization schemes and solvers.
I will first discuss our work applying deep reinforcement learning (RL) to mesh generation and optimization. We have developed RL frameworks in which agents learn sequences of local topological operations (edge flips, splits, and collapses) to optimize vertex regularity in triangular and quadrilateral meshes. A novel convolution on the half-edge data structure enables policy networks to generalize across mesh sizes and transfer zero-shot to unseen geometries. More recently, we developed approaches that also directly control vertex placement using graph neural networks (GNNs) to optimize element quality and size requirements.
I will then turn to high-order DG methods, outlining the foundational approaches as well as new variants that significantly improve operator sparsity and computational efficiency. The resulting systems are solved using a combination of incomplete solvers and adaptive agglomerated h/p-multigrid. I will also discuss extensions to deforming domains, moving meshes, and fully discrete adjoint methods that enable gradient-based optimization for coupled multiphysics problems such as fluid-structure interaction. Finally, I will introduce our High-Order Implicit Shock Tracking (HOIST) method, which formulates shock tracking as an optimization problem over both the flow solution and the curved element geometry.
Bio:
Per-Olof Persson is a Professor of Mathematics at the University of California, Berkeley, and a Faculty Senior Scientist at the Berkeley Lab. He received his Ph.D. from the Massachusetts Institute of Technology in 2005, where he also developed the widely used DistMesh algorithm for unstructured mesh generation in implicit and deforming geometries. He has also worked for several years on the development of commercial numerical software, such as the finite element package COMSOL Multiphysics. His research focuses on high-order discontinuous Galerkin methods for computational fluid and solid mechanics, spanning efficient discretizations, scalable solvers, and adjoint-based optimization. A second key area of his research is mesh generation, where he has developed methods for space-time and curved meshes, as well as new approaches based on machine learning. His contributions to the field have been recognized with several honors, including a Sloan Research Fellowship, the AFOSR Young Investigator Award, and the SimTech Argyris Award. Additionally, he has delivered keynote addresses at leading conferences such as ICOSAHOM, HONOM, the International Meshing Roundtable, and the GAMM annual meeting.
In person attendance at this seminar is only open to Columbia University affiliates. External guests are welcome to attend remotely. Please contact [email protected] if you need the Zoom link for this seminar.
