arxiv_ml 85% Match Research Paper Time series analysts,Data scientists,Machine learning researchers,Forecasting practitioners 2 weeks ago

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

generative-ai › diffusion

📄 Abstract

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.

Authors (3)

Hongwei Ma

Junbin Gao

Minh-ngoc Tran

Submitted

September 27, 2025

arXiv Category

cs.LG

arXiv PDF

Key Contributions

Introduces PRISM, a framework for long-horizon multivariate time-series forecasting that couples a score-based diffusion preconditioner with a dynamic graph encoder and physics penalties. It addresses denoising, time-varying dependencies, and prediction stability, achieving SOTA performance on benchmarks.

Business Value

Enables more accurate and reliable long-term predictions in critical domains like finance, energy, and climate, leading to better decision-making and risk management.

Paper Metadata

Innovation Type

Algorithmic

Deployment Feasibility

Feasible, as it builds upon established techniques like diffusion models and graph networks, but requires significant data and computational resources for training.

Limitations Addressed

Difficulty in denoising heterogeneous signals,Challenges in tracking time-varying cross-series dependencies,Instability and lack of physical plausibility in long-horizon forecasts

Performance Gains

Consistent SOTA with strong MSE and MAE gains.

Technical Tags

time-series forecastingmultivariate time-seriesdenoisingdynamic graphsscore-based diffusiongraph encoderphysics-informedlong-horizon forecastingcross-series dependenciesrobustness

Research Topics

Time Series AnalysisForecastingGenerative ModelsGraph Neural NetworksPhysics-Informed AI

Methods & Architectures

PRISM frameworkScore-based diffusion preconditionerDynamic correlation-thresholded graph encoderPhysics penaltiesLipschitz bounds Diffusion modelsGraph Neural NetworksEncoder-Decoder architectures

Applications & Tasks

Time Series Forecasting Scientific Modeling Financial Markets Climate Science Long-horizon multivariate time-series forecastingDenoising heterogeneous signalsTracking time-varying cross-series dependenciesEnsuring stable and physically plausible predictions ForecastingPredictionTime-series analysis

Datasets & Benchmarks

Benchmarks

six standard benchmarks

MSEMAE

Related Fields

Time Series AnalysisMachine LearningGraph Neural NetworksGenerative ModelsPhysics-Informed Machine Learning

Keywords

Time Series ForecastingMultivariateDiffusion ModelsGraph Neural NetworksDenoisingLong-HorizonPhysics-InformedPredictionDependenciesRobustnessGenerative AI

Academic Context

#Time Series Analysis#Forecasting#Generative Models#Graph Neural Networks#Physics-Informed AI

Commercial Potential

Potential Products

Advanced forecasting softwareRisk management toolsPredictive maintenance systems

Target Industries

FinanceEnergyClimate ScienceSupply Chain ManagementManufacturing

Use Case Examples

Predicting stock market trends over extended periodsForecasting energy demandModeling climate change impacts

Competitive Edge

Outperforms existing methods by integrating denoising, dynamic dependency modeling, and physics constraints, leading to superior accuracy and robustness in long-horizon forecasting.

Market Opportunity

The market for accurate forecasting solutions is substantial across numerous industries.

Revenue Models

SaaS for forecasting platformslicensing of the PRISM framework.

Resource Requirements

Compute Needs

High, particularly for training the diffusion model and graph encoder on large multivariate time-series data.

Data Requirements

Requires extensive multivariate time-series data with clear dependencies and potentially physical constraints.

Deployment Constraints

Data availability and quality,Computational resources for inference

Scalability

Scalability depends on the efficiency of the graph encoder and the diffusion process. The dynamic graph approach may offer advantages in handling evolving dependencies.

Production Readiness

Maturity Level

Research

Time to Market

Medium-term, depending on benchmark validation and practical application integration.

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