Nature Communications (Mar 2025)

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,
  • Zhun Wei

DOI
https://doi.org/10.1038/s41467-025-57516-z
Journal volume & issue
Vol. 16, no. 1
pp. 1 – 13

Abstract

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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.