Inverse Design with Dynamic Mode Decomposition

TL;DR

This paper presents a fast, robust, and interpretable inverse design method using dynamic mode decomposition, enabling efficient optimization in engineering with high accuracy and scalability, suitable for complex physical systems.

Contribution

The paper introduces ID-DMD, a novel inverse design algorithm based on dynamic mode decomposition that is faster, more accurate, and more scalable than existing methods.

Findings

ID-DMD outperforms competing methods in accuracy by an order of magnitude.

ID-DMD is 3-5 orders faster than existing approaches on complex problems.

The method is robust to noise and provides uncertainty quantification.

Abstract

We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a low-rank subspace spanning multiple experiments in parameter space. The proposed inverse design dynamic mode composition (ID-DMD) algorithm leverages the computed low-dimensional subspace to enable fast digital design and optimization on laptop-level computing, including the potential to prescribe the dynamics themselves. Moreover, the method is robust to noise, physically interpretable, and can provide uncertainty quantification metrics. The architecture can also efficiently scale to large-scale design problems using randomized algorithms in the ID-DMD. The simplicity of the method and its implementation are highly attractive in practice, and the ID-DMD has been demonstrated to be an order of magnitude more accurate than competing methods while simultaneously being 3-5 orders faster on challenging engineering design problems ranging from structural vibrations to fluid dynamics. Due to its speed, robustness, interpretability, and ease-of-use, ID-DMD in comparison with other leading machine learning methods represents a significant advancement in data-driven methods for inverse design and optimization, promising a paradigm shift in how to approach inverse design in practice.