🤖 AI Summary
This work addresses the reduced robustness of projection-based reduced-order models (ROMs)—such as Proper Orthogonal Decomposition (POD) and Neural Ordinary Differential Equations (Neural ODEs)—in high-dimensional dynamical systems under input data perturbations. We propose a novel training framework that synergistically integrates variational data assimilation (VDA) with supervised learning. Crucially, the VDA mechanism is embedded into the ROM training pipeline to enable dynamic correction of input disturbances, thereby significantly enhancing model stability and prediction accuracy under noisy conditions. The framework is model-agnostic and seamlessly accommodates diverse ROM paradigms, including POD and Neural ODEs. Experimental evaluation on graph-structured dynamical systems demonstrates a 42% reduction in mean prediction error under perturbations. Cross-model generalization tests further confirm consistent and robust performance improvements across different ROM architectures.
📝 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.
