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 present a comparative analysis of the energy-conserving neural networks - for example, deep Lagrangian network, Hamiltonian neural network, etc. - wherein the underlying physics is encoded in their computation graph. We focus on ten neural network models and explain the similarities and differences between the models. We compare their performance in 4 different physical systems. Our result highlights that using a high-dimensional coordinate system and then imposing restrictions via explicit constraints can lead to higher accuracy in the learned dynamics. We also point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers.
翻译:在过去几年里,人们越来越有兴趣将物理学知情的感性偏向纳入深层学习框架,特别是越来越多的文献一直在探索如何在利用神经网络从观察到的时间序列数据中学习动力学的同时实施节能,同时利用神经网络从观察到的时间序列数据中学习动力学。在这项工作中,我们提出了对节能神经网络的比较分析,例如深Lagrangian网络、汉密尔顿神经网络等,这些网络的基本物理学在其计算图中被编码。我们侧重于10个神经网络模型,并解释这些模型之间的异同。我们用4个不同的物理系统来比较这些模型的性能。我们的结果突出表明,使用高维协调系统,然后通过明确的限制施加限制,可以提高所学动力学的准确性。我们还指出了利用这些节能模型来设计以能源为基础的控制器的可能性。