# Modeling Systems with Machine Learning based Differential Equations

arXiv: https://arxiv.org/abs/2109.05935 · HTML: https://mlsanity.com/paper/2109.05935/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 25 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 2 of 2)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)

## Abstract (arXiv)

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.