# Identifying Ordinary Differential Equations for Data-efficient Model-based Reinforcement Learning

arXiv: https://arxiv.org/abs/2406.19817 · HTML: https://mlsanity.com/paper/2406.19817/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 28 Jun 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [Benchmarking Model-Based Reinforcement Learning](https://mlsanity.com/paper/1907.02057/) (2019)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Safe Reinforcement Learning Using Robust MPC](https://mlsanity.com/paper/1906.04005/) (2019)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Deep Learning and Symbolic Regression for Discovering Parametric Equations](https://mlsanity.com/paper/2207.00529/) (2022)
- [Kalman-Bucy-Informed Neural Network for System Identification](https://mlsanity.com/paper/2210.03424/) (2022)
- [The Use of Gaussian Processes in System Identification](https://mlsanity.com/paper/1907.06066/) (2019)

## Abstract (arXiv)

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that combine physical laws of different disciplines. In this paper, we present a new approach that allows identifying an ordinary differential equation by means of a physics-informed machine learning algorithm. Our method introduces a special neural network that allows exploiting prior human knowledge to a certain degree and extends it autonomously, so that the resulting differential equations describe the system as accurately as possible. We validate the method on a Duffing oscillator with simulation data and, additionally, on a cascaded tank example with real-world data. Subsequently, we use the developed algorithm in a model-based reinforcement learning framework by alternately identifying and controlling a system to a target state. We test the performance by swinging-up an inverted pendulum on a cart.