NeuTSFlow: Modeling Continuous Functions Behind Time Series Forecasting

TL;DR

NeuTSFlow introduces a novel approach to time series forecasting by modeling the continuous functions underlying data, leveraging neural operators and flow matching to improve accuracy and robustness over traditional discrete methods.

Contribution

It proposes a new framework that models the transition between historical and future function families in continuous space using neural operators and flow matching.

Findings

Outperforms traditional methods in accuracy.

Demonstrates robustness across diverse tasks.

Validates the function-family perspective.

Abstract

Time series forecasting is a fundamental task with broad applications, yet conventional methods often treat data as discrete sequences, overlooking their origin as noisy samples of continuous processes. Crucially, discrete noisy observations cannot uniquely determine a continuous function; instead, they correspond to a family of plausible functions. Mathematically, time series can be viewed as noisy observations of a continuous function family governed by a shared probability measure. Thus, the forecasting task can be framed as learning the transition from the historical function family to the future function family. This reframing introduces two key challenges: (1) How can we leverage discrete historical and future observations to learn the relationships between their underlying continuous functions? (2) How can we model the transition path in function space from the historical function family to the future function family? To address these challenges, we propose NeuTSFlow, a novel framework that leverages Neural Operators to facilitate flow matching for learning path of measure between historical and future function families. By parameterizing the velocity field of the flow in infinite-dimensional function spaces, NeuTSFlow moves beyond traditional methods that focus on dependencies at discrete points, directly modeling function-level features instead. Experiments on diverse forecasting tasks demonstrate NeuTSFlow's superior accuracy and robustness, validating the effectiveness of the function-family perspective.