# Modeling chaotic Lorenz ODE System using Scientific Machine Learning

arXiv: https://arxiv.org/abs/2410.06452 · HTML: https://mlsanity.com/paper/2410.06452/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 9 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems](https://mlsanity.com/paper/2010.14685/) (2020)
- [DiffEqFlux.jl - A Julia Library for Neural Differential Equations](https://mlsanity.com/paper/1902.02376/) (2019)
- [Universal Approximation Property of Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.02414/) (2020)
- [Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.00060/) (2021)
- [Universal Battery Performance and Degradation Model for Electric Aircraft](https://mlsanity.com/paper/2008.01527/) (2020)
- [Autonomous Kinetic Modeling of Biomass Pyrolysis using Chemical Reaction Neural Networks](https://mlsanity.com/paper/2105.11397/) (2021)
- [A Universal Ordinary Differential Equation](https://mlsanity.com/paper/1702.08328/) (2017)
- [Hybridizing Physics and Neural ODEs for Predicting Plasma Inductance Dynamics in Tokamak Fusion Reactors](https://mlsanity.com/paper/2310.20079/) (2023)
- [Julia Language in Machine Learning: Algorithms, Applications, and Open Issues](https://mlsanity.com/paper/2003.10146/) (2020)
- [Smart Weather Forecasting Using Machine Learning:A Case Study in Tennessee](https://mlsanity.com/paper/2008.10789/) (2020)

## Built on by (most cited first, 1 of 1)

- [AEGIS: Differentiable Mars Climate Model with Neural Closures](https://mlsanity.com/paper/2610.04081/) (2026)

## Abstract (arXiv)

In climate science, models for global warming and weather prediction face significant challenges due to the limited availability of high-quality data and the difficulty in obtaining it, making data efficiency crucial. In the past few years, Scientific Machine Learning (SciML) models have gained tremendous traction as they can be trained in a data-efficient manner, making them highly suitable for real-world climate applications. Despite this, very little attention has been paid to chaotic climate system modeling utilizing SciML methods. In this paper, we have integrated SciML methods into foundational weather models, where we have enhanced large-scale climate predictions with a physics-informed approach that achieves high accuracy with reduced data. We successfully demonstrate that by combining the interpretability of physical climate models with the computational power of neural networks, SciML models can prove to be a reliable tool for modeling climate. This indicates a shift from the traditional black box-based machine learning modeling of climate systems to physics-informed decision-making, leading to effective climate policy implementation.