Learning latent field dynamics of PDEs

We present a new approach to learning surrogate models for simulation of complex physical systems described by partial differential equations. It aims to capture three features of PDEs: locality, time continuity and formation of elementary patterns in the solution by learning a local latent representation and corresponding time evolution. We show that this approach can be leveraged to obtain a class of low dimensional models that are competitive in accuracy and are faster at inference due to time evolution in the reduced representation. Additionally we demonstrate model generalization to larger system sizes without retraining and remark on the challenge of model comparison based on pointwise accuracy.

• Machine Intelligence