CONFIDE: Contextual Finite Differences Modelling of PDEs
This addresses the challenge of modeling PDEs from data for applications in physics and engineering, representing an incremental advancement.
The paper tackles the problem of inferring explicit PDEs from data generated by unseen dynamics using a learned context, achieving results comparable to state-of-the-art approaches through extensive experimentation and ablation studies.
We introduce a method for inferring an explicit PDE from a data sample generated by previously unseen dynamics, based on a learned context. The training phase integrates knowledge of the form of the equation with a differential scheme, while the inference phase yields a PDE that fits the data sample and enables both signal prediction and data explanation. We include results of extensive experimentation, comparing our method to SOTA approaches, together with ablation studies that examine different flavors of our solution.