Learning and Transferring Physical Models through Derivatives

TL;DR

This paper introduces Derivative Learning (DERL), a supervised method for modeling physical systems through derivatives, enabling incremental model building and knowledge transfer with theoretical guarantees and superior generalization performance.

Contribution

DERL is a novel approach that learns physical models via derivatives and facilitates incremental transfer of physical knowledge across models and domains.

Findings

DERL outperforms existing methods in generalizing ODEs to new initial conditions.

DERL effectively transfers physical knowledge across models and parameters.

Theoretical guarantees ensure DERL learns true physical systems even with empirical derivatives.

Abstract

We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that effectively transfers knowledge from a pre-trained model to a student one. We provide theoretical guarantees that DERL can learn the true physical system, being consistent with the underlying physical laws, even when using empirical derivatives. DERL outperforms state-of-the-art methods in generalizing an ODE to unseen initial conditions and a parametric PDE to unseen parameters. We also design a method based on DERL to transfer physical knowledge across models by extending them to new portions of the physical domain and a new range of PDE parameters. This introduces a new pipeline to build physical models incrementally in multiple stages.