通过学习物理系统的偏导数，实现更准确的模型泛化与知识迁移。
Learning and Transferring Physical Models through Derivatives
- 基于偏导数学习物理系统，直接建模动力学规律。
- 在未见过的初值和参数下，对ODE/PDE的泛化性能超越现有方法。
- 支持跨模型迁移物理知识，实现分阶段增量构建模型。
我们提出导数学习（DERL），一种通过学习偏导数来建模物理系统的方法。利用该方法，我们设计了一种知识蒸馏协议，可将预训练模型的知识有效迁移到学生模型中，实现物理模型的逐步构建。理论上证明，即使使用经验导数，DERL仍能学习到符合物理定律的真实系统。实验表明，该方法在将常微分方程推广至未见初值、将参数化偏微分方程推广至未见参数方面均优于当前最佳方法。此外，我们基于DERL设计了跨模型迁移物理知识的方法，通过扩展模型至新的物理域和参数范围，建立了一个多阶段增量构建物理模型的新范式。
原文摘要 · Abstract (English)
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.
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