Adjoint-based optimization with quantized local reduced-order models for spatiotemporally chaotic systems

TL;DR

This paper presents a new efficient reduced order modeling approach combining quantized local models with adjoint optimization, successfully reconstructing chaotic system trajectories faster than full models.

Contribution

It introduces a novel combination of quantized local reduced models with adjoint optimization for chaotic systems, enabling faster and accurate trajectory reconstruction.

Findings

Achieves 3.5x speed-up over full-order models.

Successfully reconstructs trajectories up to 0.25 Lyapunov times.

Demonstrates effectiveness on the chaotic Kuramoto-Sivashinsky equation.

Abstract

We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based optimization. We employ the methodology in a variational data assimilation problem for the chaotic Kuramoto-Sivashinsky equation and show that it successfully reconstructs the full trajectory for up to 0.25 Lyapunov times given full state measurements at the final time. The proposed algorithm provides 3.5 times speed-up when compared to the full-order model. The proposed method opens up new possibilities for the reduced order modelling of spatiotemporally chaotic systems.