Derivatives Are All You Need For Learning Physical Models
Keywords: Physics-informed neural networks, Physics-inspired neural networks, Dynamical systems, Learning physics, Physical systems
TL;DR: We propose DERL, a method that learns physical and dynamicals systems by only learning their derivatives. We also show that distilling derivatives enables transfer of physical knowledge across models.
Abstract: Physics-Informed Neural Networks (PINNs) explicitly incorporate Partial Differential Equations (PDEs) into the loss function, thus learning representations that are inherently consistent with the physical system.
We claim that it is possible to learn physically consistent models without explicit knowledge about the underlying equations. We propose Derivative Learning (DERL) to model a physical system by learning its partial derivatives, as they contain all the necessary information to determine the system's dynamics. Like in PINNs, we also train the learning model on the initial and boundary conditions of the system.
We provide theoretical guarantees that our approach learns the true solution and is consistent with the underlying physical laws, even when using empirical derivatives. DERL outperforms PINNs and other state-of-the-art approaches in tasks ranging from simple dynamical systems to PDEs. Finally, we show that distilling the derivatives enables the transfer of physical information from one model to another. Distillation of higher-order derivatives improves physical consistency. Ultimately, learning and distilling the derivatives of physical systems turns out to be a powerful tool to learn physical models.
Supplementary Material: zip
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 10686
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