# Stochastic generative methods for stable and accurate closure modeling of chaotic dynamical systems

arXiv: https://arxiv.org/abs/2504.09750 · HTML: https://mlsanity.com/paper/2504.09750/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems](https://mlsanity.com/paper/2312.10527/) (2023)
- [Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning](https://mlsanity.com/paper/2106.09004/) (2021)
- [A scalable generative model for dynamical system reconstruction from neuroimaging data](https://mlsanity.com/paper/2411.02949/) (2024)

## Abstract (arXiv)

Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean modeling motivates the use of stochastic SGS models for chaotic dynamics. Further, developing stochastic generative models of underlying dynamics is a rapidly expanding field. In this work, we aim to incorporate stochastic integration toward closure modeling for chaotic dynamical systems. Further, we want to explore the potential stabilizing effect that stochastic models could have on linearized chaotic systems. We propose parametric and generative approaches for closure modeling using stochastic differential equations (SDEs). We derive and implement a quadratic diffusion model based on the fluctuations, demonstrating increased accuracy from bridging theoretical models with generative approaches. Results are demonstrated on the Lorenz-63 dynamical system.