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Center for Nonlinear Studies |
This talk starts by spanning a short bridge between the modeling of simulated physical processes, equivariant graph neural networks, and neural network based PDE solvers. All these topics fall under the category of dynamical systems, the primary subject of which is the description of particles and fields evolving over time. Although distinct at first glance, these topics share many common challenges. The main part of the talk discusses the motivation of introducing graph neural network based PDE solvers, and discusses the chicken-egg data generation problem which arises when training neural PDE solvers. We relate our methods and challenges to respective numerical counterparts and to various state of the art models. Eventually, we will give an outlook on future work.
Papers:
- Message Passing Neural PDE Solvers (ICLR 2022 spotlight, main paper)
- Lie Point Symmetrie Data Augmentation for Neural PDE Solvers (ICML 2022 spotlight, second main paper)
- Geometric and Physical Quantities Improve E(3) Equivariant Message Passing (ICLR 2022 spotlight, sidenote)
- Boundary Graph Neural Networks for 3d simulations (sidenote)
Bio:Johannes Brandstetter did his PhD studying Higgs boson decays at the CMS experiment at the Large Hadron Collider at CERN. In 2018, he joined Sepp Hochreiter’s group in Linz, Austria. In 2021, he become the first ELLIS PostDoc at Max Welling’s lab at the University of Amsterdam. Since 2022, he is a Senior Researcher at the newly founded Microsoft Lab in Amsterdam. His current research interests comprise Geometric Deep Learning, equivariant graph neural networks, neural PDE solving, and dynamical systems in general.
Host: Wenting Li, Arvind Mohan