Improving Surrogate Model Robustness to Perturbations for Dynamical Systems Through Machine Learning and Data Assimilation

TL;DR

This paper introduces a new framework combining machine learning and data assimilation to enhance the robustness of surrogate models against input perturbations in dynamical systems, validated through experiments on graph-based models.

Contribution

The paper presents a novel framework that improves surrogate model robustness to input perturbations by integrating machine learning with data assimilation techniques.

Findings

Significant accuracy improvements under input perturbations

Effective across multiple surrogate models including neural ODEs

Consistent performance enhancement demonstrated in experiments

Abstract

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.