Modeling Systems with Machine Learning based Differential Equations

TL;DR

This paper introduces a machine learning approach to model dynamical systems through differential equations, effectively handling noisy and irregular data, and demonstrates its utility with biological and epidemiological examples.

Contribution

It presents a novel method for constructing continuous-time models from imperfect observational data using machine learning, bridging theory and empirical observations.

Findings

Effective modeling of noisy and irregular data.

Successful application to biological and epidemiological data.

Potential for broad use in synthetic and experimental systems.

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.