  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.
