  We propose a theoretical framework for investigating a modeling error caused
by numerical integration in the learning process of dynamics. 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 formulate the modeling
error using the Dahlquist test equation that is commonly used in the analysis
of numerical methods and apply it to some of the Runge--Kutta methods.
