Learning and Transferring Physical Models through Derivatives
This addresses the challenge of incremental physical modeling for scientific computing, though it appears incremental in approach.
The authors tackled the problem of modeling physical systems by learning partial derivatives, proposing Derivative Learning (DERL) to generalize ODEs and PDEs to unseen conditions, outperforming state-of-the-art methods.
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. We believe this is the first attempt at building physical models incrementally in multiple stages.