Modeling Systems with Machine Learning based Differential Equations
This work addresses the challenge of combining theory and observations for dynamical system modeling, which is incremental as it applies existing machine learning techniques to differential equations.
The authors tackled the problem of modeling dynamical systems from noisy or non-uniformly sampled time series data by proposing a machine learning approach based on differential equations. They demonstrated the method's performance on simulated datasets and real-world examples like the Hare-Lynx population and COVID-19 outbreak, suggesting it is useful for synthetic or experimental data.
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.