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

2025-08-26

AI Summary

Modeling nonstationary natural systems driven by periodic forcings (e.g., annual/diurnal cycles) remains challenging. This paper proposes a reduced-order modeling framework based on score-based generative modeling, the first to apply such probabilistic generative models to surrogate modeling of periodically forced systems. Integrating principal component analysis with a data-driven learning architecture, the method faithfully reproduces the statistical properties, temporal correlations, and spatial structure of the original system. Applied to the PlaSim climate model, a surrogate is constructed for the top 20 principal components of surface temperature; it generates century-scale synthetic trajectories in minutes—accelerating full-physics simulations by two to three orders of magnitude. Comprehensive evaluation across multiple metrics demonstrates superior accuracy and physical consistency compared to conventional reduced-order methods, while preserving computational efficiency and interpretability.

Technology Category

• Natural Language Processing: Generation
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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.

Problem

• Modeling cyclo-stationary time series with periodic forcing
• Reproducing statistical properties of climate data efficiently
• Balancing computational efficiency with physical fidelity

Innovation

• Score-based generative modeling for cyclo-stationary systems
• Reduced-order models reproducing statistical properties accurately
• Efficient synthetic data generation with computational advantages