Position: Why a Dynamical Systems Perspective is Needed to Advance Time Series Modeling

2026-02-18

AI Summary

This work addresses a fundamental limitation in current time series modeling approaches: their general lack of grounding in the underlying dynamical systems, which impedes long-term statistical forecasting, generalization to unseen regimes (e.g., critical transitions), and sample-efficient learning. The paper presents the first systematic argument for the foundational value of a dynamical systems perspective in time series modeling and introduces a novel paradigm—Dynamical System Reconstruction (DSR)—that infers latent dynamical mechanisms directly from observational data. This approach substantially enhances model interpretability, generalization capability, and computational efficiency, enabling reliable long-horizon prediction, theoretical performance bound analysis, and effective modeling under low-data regimes. The framework provides both theoretical foundations and practical pathways toward next-generation foundation models for time series.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a dynamical systems (DS) perspective. TS of observations from natural or engineered systems almost always originate from some underlying DS, and arguably access to its governing equations would yield theoretically optimal forecasts. This is the promise of DS reconstruction (DSR), a class of ML/AI approaches that aim to infer surrogate models of the underlying DS from data. But models based on DS principles offer other profound advantages: Beyond short-term forecasts, they enable to predict the long-term statistics of an observed system, which in many practical scenarios may be the more relevant quantities. DS theory furthermore provides domain-independent theoretical insight into mechanisms underlying TS generation, and thereby will inform us, e.g., about upper bounds on performance of any TS model, generalization into unseen regimes as in tipping points, or potential control strategies. After reviewing some of the central concepts, methods, measures, and models in DS theory and DSR, we will discuss how insights from this field can advance TS modeling in crucial ways, enabling better forecasting with much lower computational and memory footprints. We conclude with a number of specific suggestions for translating insights from DSR into TS modeling.

Problem

• time series modeling
• dynamical systems
• forecasting
• generalization
• performance bounds

Innovation

• dynamical systems
• time series modeling
• dynamical systems reconstruction
• forecasting
• generalization