ArticleNature communications2025
Deep empirical neural network for optical phase retrieval over a scattering medium.
Article in Nature communications, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
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Who cites it
3 citing papers in PubMed.
- Deciphering optical coupled resonant systems with physics-data co-driven deep neural networks.Light, science & applications · 2026Article
- An end-to-end hybrid deep-learning approach for single-shot wavefront sensing and correction.Nature communications · 2026Article
- Monocular complex amplitude imaging via a polarization-multiplexed liquid-crystal-lens-informed Fourier neural network.National science review · 2026Article
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Authors and funding
11 authors.
Funding
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.
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Registered trials
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