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Lie Point Symmetry and Physics Informed Networks
Tara Akhound-Sadegh · Laurence Perreault-Levasseur · Johannes Brandstetter · Max Welling · Siamak Ravanbakhsh

Fri Jul 28 02:10 PM -- 03:00 PM (PDT) @
in 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML) »
Event URL: https://openreview.net/forum?id=VlUf77e9cR »

Physics-informed neural networks (PINNs) are computationally efficient alternatives to traditional partial differential equation (PDE) solvers.However, their reliability is dependent on the accuracy of the trained neural network. We introduce a mechanism for leveraging the symmetries of a given PDE to improve the neural solver. In particular, we propose a loss function that informs the network about Lie point symmetries in the same way that PINN models try to enforce the underlying PDE. Intuitively, our symmetry loss tries to ensure that infinitesimal generators of the Lie group preserve solutions of the PDE. This means that once the network learns a solution, it also learns the neighbouring solutions generated by Lie point symmetries.Our results show that symmetry is an effective inductive bias for PINNs and lead to a significant increase in sample efficiency.

Author Information

Tara Akhound-Sadegh (McGill-Mila)
Laurence Perreault-Levasseur (Université de Montréal and Mila)

Laurence Perreault Levasseur is an assistant professor at university of Montreal and Mila. She specializes in the development of machine learning methods for the analysis of cosmological data, with an emphasis on strong lensing data analysis. She is particularly interested in difficult inference problems, in particular in high dimension. She is the Canada research chair in Computational Cosmology and and Artificial Intelligence

Johannes Brandstetter (Microsoft)
Max Welling (University of Amsterdam & Qualcomm)
Siamak Ravanbakhsh (McGill - Mila)

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