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

arXiv: https://arxiv.org/abs/2307.09762 · HTML: https://mlsanity.com/paper/2307.09762/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 19 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [Graph Sparsification by Universal Greedy Algorithms](https://mlsanity.com/paper/2007.07161/) (2020)

## Abstract (arXiv)

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.