PICL: Physics informed contrastive learning for partial differential equations

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 performed 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 is 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.