Modeling Systems with Machine Learning based Differential Equations

• URL: http://arxiv.org/abs/2109.05935v1
• Date: Thu, 9 Sep 2021 19:10:46 GMT
• Title: Modeling Systems with Machine Learning based Differential Equations
• Authors: Pedro Garcia
• Abstract summary: We propose the design of time-continuous models of dynamical systems as solutions of differential equations. Our results suggest that this approach can be an useful technique in the case of synthetic or experimental data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations without additional assumptions or by assuming a preconceived structure in the model, with the help of additional information about the system. In the second case, it is a question of adequately combining theory with observations and subsequently optimizing the mixture. In this work, we proposes the design of time-continuous models of dynamical systems as solutions of differential equations, from non-uniform sampled or noisy observations, using machine learning techniques. The performance of strategy is shown with both, several simulated data sets and experimental data from Hare-Lynx population and Coronavirus 2019 outbreack. Our results suggest that this approach to the modeling systems, can be an useful technique in the case of synthetic or experimental data.

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