Learning and Transferring Physical Models through Derivatives

• URL: http://arxiv.org/abs/2505.01391v2
• Date: Sat, 04 Oct 2025 12:59:12 GMT
• Title: Learning and Transferring Physical Models through Derivatives
• Authors: Alessandro Trenta, Andrea Cossu, Davide Bacciu,
• Abstract summary: We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives.<n>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.
• Score: 61.227256589854726
• License: http://creativecommons.org/licenses/by/4.0/
• 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. We believe this is the first attempt at building physical models incrementally in multiple stages.

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