Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches
Abstract
Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require rapid evaluations for fast design iterations. Closure models address this challenge by approximating unresolved effects in reduced or incomplete dynamical systems. Data-driven closures offer a flexible mechanism for improving model accuracy and applicability, but approaches that embed the closure within a computational model for construction and training phases can be computationally expensive and cause numerical instabilities in the computational model during training. To avoid the challenges posed by embedded approaches, staged approaches to closure-model learning have been developed. The first stage uses data assimilation to infer state and closure trajectories from observations. The second stage trains a machine learning closure model offline using the assimilated data, thereby avoiding repeated simulator calls during training. In this work, we investigate the cost and accuracy tradeoffs between embedded and staged data-driven closure modeling approaches for a synthetic epidemiological SIQR model with a nonlinear state-dependent quarantine closure. The results illustrate a practical accuracy-efficiency trade-off: for this exemplar, embedded training provides the strongest average accuracy, while the staged approach yields comparable qualitative behavior with a moderate increase in error, substantially fewer model evaluations, and improved optimization robustness.
Related
- Further Approaches of Dynamical Low-Rank Approximation for SDEs
- Comparison of two approaches to weighted topological entropy
- Topologically free minimal actions without dynamical comparison
- The Dynamical Radius of Comparison for C*-Dynamical Systems
- Skewness and Kurtosis for Heavy-Tailed Distributions: A Comparison of Mean Absolute Deviation and L-Moment Approaches for Pareto and Extreme-Value Families
BibTeX
@misc{bandy2026efficient,
title = {{Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches}},
author = {Rileigh Bandy and Teresa Portone and Mohammad Khalil and Eric Crislip and Kyle Neal},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03612},
eprint = {2611.03612},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03612},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches
AU - Rileigh Bandy
AU - Teresa Portone
AU - Mohammad Khalil
AU - Eric Crislip
AU - Kyle Neal
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03612
UR - https://arxiv.org/abs/2611.03612
AB - Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require rapid evaluations for fast design iterations. Closure models address this challenge by approximating unresolved effects in reduced or incomplete dynamical systems. Data-driven closures offer a flexible mechanism for improving model accuracy and applicability, but approaches that embed the closure within a computational model for construction and training phases can be computationally expensive and cause numerical instabilities in the computational model during training. To avoid the challenges posed by embedded approaches, staged approaches to closure-model learning have been developed. The first stage uses data assimilation to infer state and closure trajectories from observations. The second stage trains a machine learning closure model offline using the assimilated data, thereby avoiding repeated simulator calls during training. In this work, we investigate the cost and accuracy tradeoffs between embedded and staged data-driven closure modeling approaches for a synthetic epidemiological SIQR model with a nonlinear state-dependent quarantine closure. The results illustrate a practical accuracy-efficiency trade-off: for this exemplar, embedded training provides the strongest average accuracy, while the staged approach yields comparable qualitative behavior with a moderate increase in error, substantially fewer model evaluations, and improved optimization robustness.
ER -