The Error Analysis of Numerical Integrators for Deep Neural Network Modeling of Differential Equations
The Error Analysis of Numerical Integrators for Deep Neural Network Modeling of Differential Equations
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发表时间：
2020
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通讯作者：
Shunpei Terakawa;Takashi Matsubara;Takaharu Yaguchi
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作者：
Shunpei Terakawa;Takashi Matsubara;Takaharu Yaguchi
最近，使用神经网络学习运动方程以从数据中描述动力学已经引起了人们的关注。在这样的训练过程中，使用数值积分将数据与神经网络模型的解进行比较；然而，数值积分导致的离散化误差会导致模型无法正确训练。在本研究中，我们提出了一个理论框架来研究数值积分对建模误差的影响，并对龙格-库塔方法进行误差分析
Recently, learning equations of motion to describe dynamics from data using neural networks has been attracting attention. During such training, numerical integration is used to compare the data with the solution of the neural network model; however, discretization errors due to numerical integration prevent the model from being trained correctly. In this study, we propose a theoretical framework for investigating the effect of numerical integration on modeling errors and perform the error analysis of the Runge-Kutta methods