From Noise to Laws: Regularized Time-Series Forecasting via Denoised Dynamic Graphs

2025-09-27

arXiv.org

AI Summary

Long-term multivariate time series forecasting faces challenges including heterogeneous noise corruption, difficulty in modeling time-varying cross-variable dependencies, and instability in long-horizon predictions. To address these, we propose PRISM: a physics-regularized, interpretable, and stable forecasting framework. First, it employs a score-based diffusion model for robust input denoising. Second, it constructs a dynamic correlation-thresholded graph to explicitly capture time-varying topological structures. Third, it introduces a physics-guided regularized prediction head to enforce physical consistency and stability. We theoretically prove that PRISM’s prediction dynamics are contractive and its graph encoding module satisfies Lipschitz boundedness. Evaluated on six standard benchmarks, PRISM consistently achieves state-of-the-art performance—significantly reducing MSE and MAE—demonstrating superior accuracy, robustness to noise, and interpretability in long-term forecasting.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Long-horizon multivariate time-series forecasting is challenging because realistic predictions must (i) denoise heterogeneous signals, (ii) track time-varying cross-series dependencies, and (iii) remain stable and physically plausible over long rollout horizons. We present PRISM, which couples a score-based diffusion preconditioner with a dynamic, correlation-thresholded graph encoder and a forecast head regularized by generic physics penalties. We prove contraction of the induced horizon dynamics under mild conditions and derive Lipschitz bounds for graph blocks, explaining the model's robustness. On six standard benchmarks , PRISM achieves consistent SOTA with strong MSE and MAE gains.

Problem

• Denoise heterogeneous signals in multivariate time-series
• Track time-varying cross-series dependencies dynamically
• Ensure long-term forecast stability with physics regularization

Innovation

• Score-based diffusion preconditioner denoises signals
• Dynamic correlation-thresholded graph encoder tracks dependencies
• Physics-regularized forecast head ensures stable predictions