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

TL;DR

This paper introduces a score-based generative modeling approach for creating reduced-order models of cyclo-stationary time series, exemplified by climate data, achieving accurate statistical reproduction with significant computational efficiency.

Contribution

The paper presents a novel data-driven method leveraging score-based generative models for reduced-order modeling of cyclo-stationary systems, demonstrated on climate data.

Findings

Accurately reproduces statistical properties and correlations of original data

Generates synthetic climate trajectories in minutes instead of weeks

Maintains physical fidelity across multiple validation metrics

Abstract

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.