PICL: Physics Informed Contrastive Learning for Partial Differential Equations
This work addresses the challenge of limited generalization in PDE surrogate models for researchers in computational physics and machine learning, though it appears incremental as it builds on existing neural operator methods.
The authors tackled the problem of improving neural operator generalization across multiple partial differential equations (PDEs) simultaneously, developing a physics-informed contrastive learning framework that enhanced accuracy for tasks like fixed-future and autoregressive rollouts on 1D and 2D Heat, Burgers', and linear advection equations.
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.