Deep empirical neural network for optical phase retrieval over a scattering medium

Huaisheng Tu, Haotian Liu, Tuqiang Pan, Wuping Xie, Zihao Ma, Fan Zhang, Pengbai Xu, Leiming Wu, Ou Xu, Yi Xu () and Yuwen Qin ()
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Huaisheng Tu: Guangdong University of Technology
Haotian Liu: Guangdong University of Technology
Tuqiang Pan: Guangdong University of Technology
Wuping Xie: Guangdong University of Technology
Zihao Ma: Guangdong University of Technology
Fan Zhang: Guangdong University of Technology
Pengbai Xu: Guangdong University of Technology
Leiming Wu: Guangdong University of Technology
Ou Xu: Guangdong University of Technology
Yi Xu: Guangdong University of Technology
Yuwen Qin: Guangdong University of Technology

Nature Communications, 2025, vol. 16, issue 1, 1-9

Abstract: Abstract Supervised learning, a popular tool in modern science and technology, thrives on huge amounts of labeled data. Physics-enhanced deep neural networks offer an effective solution to alleviate the data burden by incorporating an analytical model that interprets the underlying physical processes. However, it completely fails in tackling systems without analytical solution, where wave scattering systems with multiple input multiple output are typical examples. Herein, we propose a concept of deep empirical neural network (DENN) that is a hybridization of a deep neural network and an empirical model, which enables seeing through an opaque scattering medium in an untrained manner. The DENN does not rely on labeled data, all while delivering as high as 58% improvement in fidelity compared with the supervised learning using 30000 data pairs for achieving the same goal of optical phase retrieval. The DENN might shed new light on the applications of deep learning in physics, information science, biology, chemistry and beyond.

Date: 2025
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DOI: 10.1038/s41467-025-56522-5

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