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Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics ?

机译：基于拉格朗日力学的物理知识神经网络建模系统动态 ？

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摘要

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. Additionally, purely data-based models often require large amounts of data and are often difficult to interpret. In this paper, we presentphysics-informed neural ordinary differential equations(PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. This new approach directly incorporates the equations of motion originating from the Lagrange mechanics into a deep neural network structure. Thus, we can integrate prior physics knowledge where it is available and use function approximation—e.g., neural networks—where it is not. The method is tested with a forward model of a real-world physical system with large uncertainties. The resulting model is accurate and data-efficient while ensuring physical plausibility.With this, we demonstrate a method that beneficially merges physical insight with real data. Our findings are of interest for model-based control and system identification of mechanical systems.
机译：识别各种技术系统的仿真和控制需要准确的动态模型。在许多重要的现实世界的应用程序，但是，这两个主要的建模方法往往不能满足要求：第一原理的方法从高偏置苦，而数据驱动的模型往往有较大差异。此外，基于数据的模型通常需要大量数据，并且通常难以解释。在本文中，我们举行了通知的神经常规方程（Pinode），一种混合​​模型，其结合了两个建模技术来克服上述问题。这种新方法直接融入了源自拉格朗日力学的运动方程，进入深度神经网络结构。因此，我们可以集成现有物理知识，在那里它可用，并且使用函数近似值-e.g。，神经网络 - 它不是。该方法用具有大不确定性的实际物理系统的前向模型进行测试。由此产生的模型是准确的，数据有效，同时确保物理合理性。在此，我们演示了一种有利地利用实际数据洞察的方法。我们的研究结果对模型的控制和机械系统的系统识别感兴趣。

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