Inverse Design with Dynamic Mode Decomposition

• DOI: 10.48550/arxiv.2502.09490
• Publication Date: 2025-02-13
• Authors: Yunpeng Zhu; Liangliang Cheng; Anping Jing; Haibin Huo; Zi–Qiang Lang; Huixian Zhang; J. Nathan Kutz
• Keywords: Dynamic Mode Decomposition; Mode (computer interface)

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