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

A research position paper argues that time series modeling needs to adopt dynamical systems (DS) theory to move beyond current foundation model approaches. By reconstructing underlying system equations from data, DS-informed models could deliver superior long-term forecasting, lower computational costs, and theoretical guarantees about performance limits and generalization.

The article presents a methodological critique of contemporary time series modeling, arguing that the field's focus on data-driven foundation models overlooks fundamental principles from dynamical systems theory. Rather than treating time series as isolated patterns to predict, DS reconstruction (DSR) approaches treat observed data as manifestations of underlying physical or engineered systems with governing equations. This distinction carries profound implications: models built on DS principles can predict long-term statistical behavior—often more relevant than point forecasts—while providing domain-independent theoretical frameworks for understanding generation mechanisms.

The motivation stems from decades of statistical and machine learning progress, yet uncertainty persists about whether current advances represent genuine progress or engineering refinement. By incorporating DS theory, researchers gain access to theoretical upper bounds on model performance, mechanisms for generalizing into unseen regimes like tipping points, and potential control strategies for systems. These advantages directly address real limitations: computational and memory inefficiency in current foundation models, poor extrapolation beyond training distributions, and lack of interpretability about system behavior.

For the AI research community, this position paper signals growing recognition that scaling data and parameters alone may have diminishing returns. Organizations developing time series models for finance, climate, engineering, or infrastructure face pressure to improve forecasting accuracy while reducing resource consumption. The dynamical systems perspective offers a principled alternative that could reshape model architectures and training methodologies. Researchers building production systems should evaluate whether incorporating DS-informed constraints—such as conservation laws or stability conditions—improves both performance and generalization. This shift represents a maturation of the field toward theoretically grounded approaches that balance empirical performance with interpretability.

• →Time series models incorporating dynamical systems theory can achieve better long-term forecasting and lower computational overhead than current foundation models.
• →Reconstructing underlying system equations from data enables prediction of long-term statistics, which matters more than short-term forecasts in many practical applications.
• →Dynamical systems theory provides theoretical upper bounds on model performance and insights into generalization across unseen regimes like tipping points.
• →Current time series modeling trends may prioritize scale over fundamental principles, missing opportunities for efficiency and interpretability.
• →Integrating domain-independent DS insights into time series architectures could inform control strategies and improve extrapolation beyond training distributions.