# Reduced-Order Modeling of Cyclo-Stationary Time Series Using Score-Based Generative Methods

arXiv: https://arxiv.org/abs/2508.19448 · HTML: https://mlsanity.com/paper/2508.19448/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 56 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 6 of 6)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations](https://mlsanity.com/paper/1709.00037/) (2017)
- [What's the score? Automated Denoising Score Matching for Nonlinear Diffusions](https://mlsanity.com/paper/2407.07998/) (2024)
- [Probing forced responses and causality in data-driven climate emulators: conceptual limitations and the role of reduced-order models](https://mlsanity.com/paper/2506.22552/) (2025)
- [Response Theory via Generative Score Modeling](https://mlsanity.com/paper/2402.01029/) (2024)
- [Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling](https://mlsanity.com/paper/2504.13333/) (2025)

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

- [Conditional Score-Based Modeling of Effective Langevin Dynamics](https://mlsanity.com/paper/2604.23952/) (2026)

## Abstract (arXiv)

Many natural systems exhibit cyclo-stationary behavior characterized by periodic forcing such as annual and diurnal cycles. We present a data-driven method leveraging recent advances in score-based generative modeling to construct reduced-order models for such cyclo-stationary time series. Our approach accurately reproduces the statistical properties and temporal correlations of the original data, enabling efficient generation of synthetic trajectories. We demonstrate the performance of the method through application to the Planet Simulator (PlaSim) climate model, constructing a reduced-order model for the 20 leading principal components of surface temperature driven by the annual cycle. The resulting surrogate model accurately reproduces the marginal and joint probability distributions, autocorrelation functions, and spatial coherence of the original climate system across multiple validation metrics. The approach offers substantial computational advantages, enabling generation of centuries of synthetic climate data in minutes compared to weeks required for equivalent full model simulations. This work opens new possibilities for efficient modeling of periodically forced systems across diverse scientific domains, providing a principled framework for balancing computational efficiency with physical fidelity in reduced-order modeling applications.