Comparing efficient methods for learning models in dynamic systems
Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches
Machine Learning
Summary
Simulating complex systems can be difficult and slow, so scientists use simpler models that guess missing parts. The authors compare two ways to teach computers to improve these guesses using data. One way trains the model inside the simulation but can be slow and unstable. The other way first figures out hidden data from observations, then trains separately, making it faster and more stable but slightly less accurate. They tested both methods on a disease-spread model showing the trade-off between speed and accuracy.
What this means in practice
- •For computational modelers: Train improved dynamic system models more efficiently by separating data assimilation and model training phases to reduce simulation calls during training.
- •For epidemiological modelers: Use staged data-driven closure learning to model disease spread with quarantine measures, balancing accuracy and computational cost.
Authors
Rileigh Bandy, Teresa Portone, Mohammad Khalil, Eric Crislip, Kyle Neal
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.