PICL: Physics Informed Contrastive Learning for Partial Differential Equations

• URL: http://arxiv.org/abs/2401.16327v4
• Date: Tue, 24 Sep 2024 17:31:32 GMT
• Title: PICL: Physics Informed Contrastive Learning for Partial Differential Equations
• Authors: Cooper Lorsung, Amir Barati Farimani,
• Abstract summary: We develop a novel contrastive pretraining framework that improves neural operator generalization across multiple governing equations simultaneously. A combination of physics-informed system evolution and latent-space model output are anchored to input data and used in our distance function. We find that physics-informed contrastive pretraining improves accuracy for the Fourier Neural Operator in fixed-future and autoregressive rollout tasks for the 1D and 2D Heat, Burgers', and linear advection equations.
• Score: 7.136205674624813
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to complex PDEs. While much work has been done evaluating neural operator performance on a wide variety of surrogate modeling tasks, these works normally evaluate performance on a single equation at a time. In this work, we develop a novel contrastive pretraining framework utilizing Generalized Contrastive Loss that improves neural operator generalization across multiple governing equations simultaneously. Governing equation coefficients are used to measure ground-truth similarity between systems. A combination of physics-informed system evolution and latent-space model output are anchored to input data and used in our distance function. We find that physics-informed contrastive pretraining improves accuracy for the Fourier Neural Operator in fixed-future and autoregressive rollout tasks for the 1D and 2D Heat, Burgers', and linear advection equations.

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