Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches

TL;DR

This paper compares embedded and staged data-driven closure learning for dynamical systems, showing that while embedded approaches offer higher accuracy, staged methods using data assimilation achieve comparable qualitative results with significantly lower computational cost and greater robustness. The staged approach avoids repeated simulator calls during training, making it more efficient for real-world applications.

Why It Matters

Efficient closure modeling is critical for real-time simulations and design optimization in complex systems like epidemiological models. By reducing computational overhead without sacrificing much accuracy, staged approaches enable scalable deployment of data-driven models in resource-constrained environments.

Key Findings

• Embedded closure training achieves the highest average accuracy but is computationally expensive and prone to numerical instability.
• Staged approaches using data assimilation yield comparable qualitative behavior with only a moderate increase in error and drastically fewer model evaluations.
• The staged method demonstrates improved optimization robustness and is better suited for practical deployment in iterative design workflows.