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Using symmetries to improve neural network PDE solvers

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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Key Details

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

Derives mathematical framework to impose symmetries via loss function

Shows symmetry loss complements physics loss used in PINN models

Empirically demonstrates large improvements in sample efficiency

Opens door to leveraging symmetries in neural PDE solvers

AI generated summary

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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