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Abstract <p>The relationship between neural ordinary differential equations and inverse problems of dynamics is identified. This relationship opens up opportunities for the use of inverse problems of dynamics when building and training neural ordinary differential equations, and vice versa, for the application of neural ordinary differential equations in solving inverse problems of dynamics. A complete algorithm for training the neural ordinary differential equation model with given dataset of trajectory points is presented. The case of training a neural ordinary differential equation model based on a Cassini oval-shaped trajectory is considered. The dataset for training the neural ordinary differential equation model is generated using the system of nonlinear ordinary differential equations obtained by analytically building differential equations with given properties of motion (a given curve). The study presents a computational experiment that demonstrates the convergence of the neural network training process, as evidenced by MAE (mean absolute error) metrics.</p>

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Building a Neural Ordinary Differential Equation Using Methods for Solving Inverse Problems of Dynamics

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • S. G. Shorokhov

摘要

Abstract

The relationship between neural ordinary differential equations and inverse problems of dynamics is identified. This relationship opens up opportunities for the use of inverse problems of dynamics when building and training neural ordinary differential equations, and vice versa, for the application of neural ordinary differential equations in solving inverse problems of dynamics. A complete algorithm for training the neural ordinary differential equation model with given dataset of trajectory points is presented. The case of training a neural ordinary differential equation model based on a Cassini oval-shaped trajectory is considered. The dataset for training the neural ordinary differential equation model is generated using the system of nonlinear ordinary differential equations obtained by analytically building differential equations with given properties of motion (a given curve). The study presents a computational experiment that demonstrates the convergence of the neural network training process, as evidenced by MAE (mean absolute error) metrics.