Improving Surrogate Model Robustness to Perturbations for Dynamical Systems Through Machine Learning and Data Assimilation
This addresses robustness issues in reduced-order modeling for complex dynamical systems, though it appears incremental as it builds on existing techniques.
The paper tackles the problem of surrogate models for dynamical systems being vulnerable to input perturbations by proposing a framework combining machine learning and data assimilation. The result is substantially improved accuracy under perturbations, with consistent enhancements demonstrated across different surrogate models including neural ODEs.
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal Decomposition (POD) can be used in such cases. However, these reduced order models are susceptible to perturbations in the input. We propose a novel framework that combines machine learning and data assimilation techniques to improving surrogate models to handle perturbations in input data effectively. Through rigorous experiments on dynamical systems modelled on graphs, we demonstrate that our framework substantially improves the accuracy of surrogate models under input perturbations. Furthermore, we evaluate the framework's efficacy on alternative surrogate models, including neural ODEs, and the empirical results consistently show enhanced performance.