HyperPINNs and a New Benchmark Dataset for Learned Physics Models

Speaker Name
Filipe de Avila Belbute-Peres, Anudhyan Boral, and R. Lily Hu
Speaker Organization
Google Research
Start Time
End Time
Location
Virtual Event

Join us on Zoom: https://ucsc.zoom.us/j/99620840826?pwd=YTNXK05PVFUyaXlWR0RXbGJkdmVjQT09

Description: We present several empirical studies of the generalization ability of physics-informed neural network (PINNs) models across parameterized differential equations.

First, we investigate a new way of extending the standard PINNs to provide the solutions to PDEs or ODEs. In contrast to the standard approaches of either retraining the PINNs or expanding the state space of the original differential equations, we propose HyperPINN, a two-part hierarchical neural network that consists of a PINN-generator that outputs the parameters for a regular PINN which then generates the solutions. We demonstrate with promising results on both a PDE and an ODE that the PINN-generator generalizes across parameterization of the differential equations and can output regular PINNs that approximate the solutions well.

Second, we briefly describe a forthcoming benchmark dataset that is designed for investigating in-depth the generalization properties of PINN-based models. We use high-performance computing to simulate cylinder wakes under multiple parameterization and geometric configurations. Our initial results show that machine learning models have difficulty generalizing both across diverse parameter configurations and also extrapolating in space-time for a fixed parameter set. We hope this dataset and our initial results will interest and inspire the SciML community to study and propose new methodologies of machine learning models to address these challenges.

The talk is based on the joint work of Filipe de Avila Belbute-Peres(CMU) and co-authors at Google Research. The first part of the talk is based on our NeurIPS 2021 Workshop paper (https://arxiv.org/abs/2111.01008).

Bios:
Filipe de Avila Belbute-Peres is a Ph.D. student at Carnegie Mellon University advised by Zico Kolter, and currently working part time at Google Research. His work centers around incorporating physics knowledge into deep learning models, with the goal of creating more robust and efficient methods.

Anudhyan Boral is an engineer at Google Research with experience working on numerics and large scale machine learning. He has a Masters from Harvard University in Computer Science.

R. Lily Hu is a researcher and engineer at Google Research. She conducted research in machine learning for the physical sciences and sustainability. She earned a M.S./Ph.D. from the University of California, Berkeley and a BASci from the University of Toronto.