The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using neural networks for learning dynamics from observed time-series data. In this work, we survey ten recently proposed energy-conserving neural network models, including HNN, LNN, DeLaN, SymODEN, CHNN, CLNN and their variants. We provide a compact derivation of the theory behind these models and explain their similarities and differences. Their performance are compared in 4 physical systems. We point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers.

翻译：近年来，将物理信息归纳偏置融入深度学习框架的研究日益受到关注。其中，大量文献致力于探索如何在利用神经网络从观测时间序列数据学习动力学时强制满足能量守恒约束。本文系统综述了十种近期提出的能量守恒神经网络模型，包括HNN、LNN、DeLaN、SymODEN、CHNN、CLNN及其变体。我们给出了这些模型背后理论的简洁推导，阐明了它们的相似性与差异性，并在4个物理系统中对其性能进行了比较。此外，我们指出了利用部分能量守恒模型设计基于能量的控制器的潜在可能性。