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Physics-informed neural network for material identification via distortion-robust polychromatic x-ray attenuation correction in photon-counting detectors |
| Xin Yan(闫欣)1,2, Jie Zhang(张杰)2,†, Kai He(何凯)2,‡, Yiheng Liu(刘毅恒)2, Yuetong Zhao(赵悦彤)2, Gang Wang(王刚)2, Xinlong Chang(常新龙)1, and Youwei Zhang(张有为)3 |
1 Rocket Force University of Engineering, Xi'an 710025, China;
2 State Key Laboratory of Ultrafast Optical Science and Technology, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China;
3 National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract Spectral distortions in photon-counting detectors (PCDs) fundamentally limit the quantitative accuracy of material identification. While machine learning is used for compensation, current data-driven methods often lack physical constraints, limiting their interpretability and reliability across varying conditions. To address this issue, we propose a physics-informed neural network (PINN) framework that explicitly embeds the Beer-Lambert law into the learning architecture. By integrating an explicit differential layer to extract high-order curvature features from distorted spectra, the model enables direct inference of the effective atomic number and areal density. This approach effectively leverages the $Z$-dependent non-linear profile of the photoelectric effect, even when explicit absorption edges are outside the primary detection window. Simulation results establish a high-precision benchmark for $Z_{\rm{eff}}$ estimation in the target low-$Z$ range (613), with an RMSE of 0.2111. Experimental validation on a CdZnTe-PCD further demonstrates that this accuracy improvement is preserved under realistic pulse pile-up and noise conditions, achieving an RMSE of 0.2457 and an $R^{{2}}$ of 0.9670. Compared with conventional physical correction methods (typically $\pm 0.5$ error margin), the proposed framework provides improved precision, with 92.86 % of $Z_{\rm{eff}}$ estimation errors falling within $\pm 0.4$, corresponding to an approximately 20 % tighter error bound. These results confirm that the proposed framework effectively mitigates spectral distortion, providing a robust, calibration-free solution for precise material identification of low-$Z$ materials in industrial non-destructive testing.
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Received: 12 February 2026
Revised: 24 March 2026
Accepted manuscript online: 01 April 2026
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PACS:
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07.85.Fv
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(X- and γ-ray sources, mirrors, gratings, and detectors)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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81.70.-q
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(Methods of materials testing and analysis)
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87.59.-e
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(X-ray imaging)
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| Fund: Project supported by the Natural Science Basic Research Program — General Program (Grant No. 2025JC-YBMS-712). |
Corresponding Authors:
Jie Zhang,E-mail:zhangjie@opt.ac.cn;Kai He,E-mail:hekai@opt.ac.cn
E-mail: zhangjie@opt.ac.cn;hekai@opt.ac.cn
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Cite this article:
Xin Yan(闫欣), Jie Zhang(张杰), Kai He(何凯), Yiheng Liu(刘毅恒), Yuetong Zhao(赵悦彤), Gang Wang(王刚), Xinlong Chang(常新龙), and Youwei Zhang(张有为) Physics-informed neural network for material identification via distortion-robust polychromatic x-ray attenuation correction in photon-counting detectors 2026 Chin. Phys. B 35 050702
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