Paper Title:

Lie Point Symmetry and Physics Informed Networks

Published on:

7 November 2023

Primary Category:

Machine Learning

Paper Authors:

Tara Akhound-Sadegh,

Laurence Perreault-Levasseur,

Johannes Brandstetter,

Max Welling,

Siamak Ravanbakhsh

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Proposes novel method to integrate symmetries into physics-informed neural networks

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Derives mathematical framework to impose symmetries via loss function

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Shows symmetry loss complements physics loss used in PINN models

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Empirically demonstrates large improvements in sample efficiency

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Opens door to leveraging symmetries in neural PDE solvers

Using symmetries to improve neural network PDE solvers

This paper explores integrating mathematical symmetries into physics-informed neural networks to improve their ability to solve partial differential equations. It proposes a novel loss function that encodes symmetries, complementing the physics loss. Empirically, this greatly boosts sample efficiency and generalization.

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