Frequency transfer and inverse design for metasurface under multi-physics coupling by Euler latent dynamic and data-analytical regularizations

Enze Zhu, Zheng Zong, Erji Li, Yang Lu, Jingwei Zhang, Hao Xie, Ying Li, Wen-Yan Yin () and Zhun Wei ()
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Enze Zhu: Zhejiang University
Zheng Zong: Zhejiang University
Erji Li: Zhejiang University
Yang Lu: Zhejiang University
Jingwei Zhang: Zhejiang University
Hao Xie: Zhejiang University
Ying Li: Zhejiang University
Wen-Yan Yin: Zhejiang University
Zhun Wei: Zhejiang University

Nature Communications, 2025, vol. 16, issue 1, 1-13

Abstract: Abstract Frequency transfer is a key challenge in machine learning as it allows researchers to go beyond in-range analyses of spectrum properties towards out-of-the-range predictions. Traditionally, to predict properties at a specific frequency, targeted spectrum is included in training data for a deep neural network (DNN). However, due to limitations of measurement or computation source, training data at some frequencies are hardly accessible, especially for multi-physics problems. In this work, we propose a multi-physics deep learning framework (MDLF) consisting of a multi-fidelity DeepONet, a Euler latent dynamic network, and a data-analytical inversion network. Without the knowledge about multi-physics response, MDLF is successfully generalized to unseen frequency bands for both parametric and free-form metasurface by dynamically utilizing a Euler latent space and single-physics information. Moreover, an inversion method is introduced to incorporate hybrid a priori in inverse design of metasurface. Under EM-thermal coupling, we verify the proposed MDLF numerically and experimentally.

Date: 2025
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DOI: 10.1038/s41467-025-57516-z

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