Target Parameterization in Diffusion Models for Nonlinear Spatiotemporal System Identification

2026-04-19

AI Summary

This work addresses the instability in long-term prediction of high-dimensional, strongly nonlinear spatiotemporal systems—such as turbulence—caused by error accumulation in conventional identification methods. To overcome this challenge, the authors propose a diffusion model–based identification framework that integrates a physics-informed, patch-level Transformer architecture and systematically evaluates different target parameterization strategies. They demonstrate for the first time that predicting the clean state yields superior performance in high-dimensional turbulence modeling: compared to predicting noise or velocity directly, this approach significantly enhances rollout stability over extended time horizons and substantially reduces prediction errors, especially under high token dimensions. The findings establish a more robust and effective paradigm for identifying complex nonlinear spatiotemporal dynamics.

Technology Category

Computer Vision: Diffusion Models for VisionPlanning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsMachine Learning: Large Multimodal Models (LMMs)

Application Category

Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networksUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systemsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Machine learning is becoming increasingly important for nonlinear system identification, including dynamical systems with spatially distributed outputs. However, classical identification and forecasting approaches become markedly less reliable in turbulent-flow regimes, where the dynamics are high-dimensional, strongly nonlinear, and highly sensitive to compounding rollout errors. Diffusion-based models have recently shown improved robustness in this setting and offer probabilistic inference capabilities, but many current implementations inherit target parameterizations from image generation, most commonly noise or velocity prediction. In this work, we revisit this design choice in the context of nonlinear spatiotemporal system identification. We consider a simple, self-contained patch-based transformer that operates directly on physical fields and use turbulent flow simulation as a representative testbed. Our results show that clean-state prediction consistently improves rollout stability and reduces long-horizon error relative to velocity- and noise-based objectives, with the advantage becoming more pronounced as the per-token dimensionality increases. These findings identify target parameterization as a key modeling choice in diffusion-based identification of nonlinear systems with spatial outputs in turbulent regimes.

Problem

• diffusion models
• nonlinear spatiotemporal system identification
• target parameterization
• turbulent flow
• rollout stability

Innovation

• diffusion models
• target parameterization
• spatiotemporal system identification
• clean-state prediction
• turbulent flow