Data-Driven Forecasting of High-Dimensional Transient and Stationary Processes via Space-Time Projection

2025-03-31

AI Summary

Addressing the challenge of short-term forecasting for high-dimensional transient and steady-state processes, this paper proposes a hyperparameter-free, interpretable spatiotemporal projection (STP) method. STP introduces a novel unified spatiotemporal dimensionality reduction framework that integrates time-delay embedding with proper orthogonal decomposition (POD), requiring only a single tunable parameter—the truncation rank. Forecasting is achieved purely data-driven by extrapolating spatiotemporal eigenmodes, and forecast reliability is quantified via retrospective accuracy to rigorously estimate the prediction lower bound. Evaluated on supernova turbulence simulations and high-subsonic experimental flow-field data, STP consistently outperforms standard LSTM in prediction accuracy and robustness, while providing physically meaningful, interpretable forecasts grounded in underlying dynamical structures.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon comprising both hindcast and forecast intervals. Forecasts are then generated by projecting the hindcast portion of these modes onto new data, simultaneously leveraging their orthogonality and optimal correlation with the forecast extension. Rooted in Proper Orthogonal Decomposition (POD) theory, dimensionality reduction and time-delay embedding are intrinsic to the approach. For a given ensemble and fixed prediction horizon, the only tunable parameter is the truncation rank--no additional hyperparameters are required. The hindcast accuracy serves as a reliable indicator for short-term forecast accuracy and establishes a lower bound on forecast errors. The efficacy of the method is demonstrated using two datasets: transient, highly anisotropic simulations of supernova explosions in a turbulent interstellar medium, and experimental velocity fields of a turbulent high-subsonic engineering flow. In a comparative study with standard Long Short-Term Memory (LSTM) neural networks--acknowledging that alternative architectures or training strategies may yield different outcomes--the method consistently provided more accurate forecasts. Considering its simplicity and robust performance, STP offers an interpretable and competitive benchmark for forecasting high-dimensional transient and chaotic processes, relying purely on spatiotemporal correlation information.

Problem

• Forecasting high-dimensional transient processes using data-driven methods
• Reducing dimensionality in space-time data without hyperparameters
• Providing accurate benchmarks for chaotic spatiotemporal systems

Innovation

• Space-Time Projection for high-dimensional forecasting
• Uses Proper Orthogonal Decomposition theory
• No hyperparameters, only truncation rank tuning