Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting

2024-10-04

arXiv.org

AI Summary

This work addresses spatiotemporal probabilistic forecasting, revealing the high sensitivity of forecast performance to probabilistic path selection in flow matching. To this end, we propose a lightweight, differentiable probabilistic path model tailored for spatiotemporal dynamical systems, integrating latent-space time-series modeling with an efficient ODE solver. Unlike conventional linear or fixed-path designs, our approach significantly improves prediction accuracy and training stability. Experiments across multiple dynamical-system benchmarks demonstrate faster convergence, reduced sampling steps (only 4–8 steps required at inference), and enhanced generalization. The model achieves a favorable trade-off between computational efficiency and representational capacity, exhibiting strong potential for real-world deployment.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on forecasting performance remains under-explored. In this work, we demonstrate that forecasting spatio-temporal data with flow matching is highly sensitive to the selection of the probability path model. Motivated by this insight, we propose a novel probability path model designed to improve forecasting performance. Our empirical results across various dynamical system benchmarks show that our model achieves faster convergence during training and improved predictive performance compared to existing probability path models. Importantly, our approach is efficient during inference, requiring only a few sampling steps. This makes our proposed model practical for real-world applications and opens new avenues for probabilistic forecasting.

Problem

• Temporal-Spatial Prediction
• Probability Path
• Stream Matching Design

Innovation

• Probabilistic Path Flow Matching
• Reduced Computational Complexity
• Enhanced Predictive Performance