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Dec.  2022

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# Application of a Neural Network to Store and Compute the Optical Properties of Non-Spherical Particles

• Radiative transfer simulations and remote sensing studies fundamentally require accurate and efficient computation of the optical properties of non-spherical particles. This paper proposes a deep learning (DL) scheme in conjunction with an optical property database to achieve this goal. Deep neural network (DNN) architectures were obtained from a dataset of the optical properties of super-spheroids with extensive shape parameters, size parameters, and refractive indices. The dataset was computed through the invariant imbedding T-matrix method. Four separate DNN architectures were created to compute the extinction efficiency factor, single-scattering albedo, asymmetry factor, and phase matrix. The criterion for designing these neural networks was the achievement of the highest prediction accuracy with minimal DNN parameters. The numerical results demonstrate that the determination coefficients are greater than 0.999 between the prediction values from the neural networks and the truth values from the database, which indicates that the DNN can reproduce the optical properties in the dataset with high accuracy. In addition, the DNN model can robustly predict the optical properties of particles with high accuracy for shape parameters or refractive indices that are unavailable in the database. Importantly, the ratio of the database size (~127 GB) to that of the DNN parameters (~20 MB) is approximately 6810, implying that the DNN model can be treated as a highly compressed database that can be used as an alternative to the original database for real-time computing of the optical properties of non-spherical particles in radiative transfer and atmospheric models.
摘要: 辐射传输模拟和遥感反演需要准确和快速地计算非球形粒子的光学特性。传统上一般采用查找表方法来解决电磁散射计算效率低的问题。但随着粒子参数增加，查找表数据体量变大，不便于模式使用。本文提出了一种深度学习方法用于存储和计算非球形粒子光学特性。我们将基于不变嵌入T-矩阵方法计算的超椭球粒子光学特性作为训练数据库，选取长宽比、圆滑度、粒径和复折射指数作为训练参数，设计了四种最优的神经网络架构分别计算或预测消光效率因子、单次散射消光比、不对称因子以及相矩阵元素。结果表明：神经网络预测值与数据库真值之间的决定系数大于0.999，可以准确再现数据库的光学特性信息。另外，神经网络模型还能够可靠预测出未知参数（尺寸和折射指数）的粒子光学特性值。通过将大型数据库近乎无损压缩为四个神经网络后，可将小巧的网络模型代替原始查找表接入辐射传输算法中，从而实现非球形粒子光学特性的高效计算。
• Figure 1.  Twenty-five representative super-spheroid shapes including oblate ($a/c > 1.0$), prolate ($a/c < 1.0$), concave ($n > 2.0$), and convex particles ($n < 2.0$).

Figure 3.  Deep Neural Network (DNN) architectures for ${Q_{{\text{ext}}}}$, SSA, g, and ${P_{ij}}$. The number of layers is 5, 5, 6, and 7 for ${Q_{{\text{ext}}}}$, SSA, g, and ${P_{ij}}$, respectively. The number of neuron nodes in the layer is included in the parentheses. For example, $\left( {{Q_{{\text{ext}}}},{\text{ }}128} \right)$ indicates 128 neuron nodes in a layer for the prediction of ${Q_{{\text{ext}}}}$.

Figure 2.  Scatter plot of RMSE (orange dots) and the coefficient of determination ${R^2}$ (green dots) from several established DNN models for (a) ${Q_{{\text{ext}}}}$, (b) SSA, (c) g, and (d) ${P_{11}}$. In each subfigure, the left y-axis represents the RMSE, and the right y-axis represents ${R^2}$. As the network parameters increase, the DNN models have an upper limit of the prediction accuracy for each optical property.

Figure 4.  Scatter plot of (a) ${Q_{{\text{ext}}}}$, (b) SSA, (c) g, (d) ${P_{11}}$, and (e) – (i) ${P_{ij}}/{P_{11}}$ by DNN predictions against the true values.

Figure 5.  Absolute errors of ${Q_{{\text{ext}}}}$ predicted by the DNNs and the true values from the database.

Figure 6.  Absolute errors of SSA predicted by the DNNs and the true values from the database.

Figure 7.  Absolute errors of g predicted by the DNNs and the true values from the database.

Figure 8.  Comparison of ${Q_{{\text{ext}}}}$, SSA, and g predicted by the DNNs against the true values in the database. The upper row (a–c) in the figure shows the results for parameters in light-colored areas, and the lower row (d–f) shows the results for parameters in dark-colored areas (Figs. 5–7). The mean absolute errors (MAEs) are also included in each subplot.

Figure 9.  Comparison of (a) ${P_{11}}$, (b) ${P_{12}}/{P_{11}}$, (c) ${P_{22}}/{P_{11}}$, (d) ${P_{33}}/{P_{11}}$, (e) ${P_{43}}/{P_{11}}$, and (f) ${P_{44}}/{P_{11}}$ predicted by the DNNs against the true values. The size parameter xsize is unavailable in the database.

Figure 10.  Comparison of (a) ${P_{11}}$, (b) ${P_{12}}/{P_{11}}$, (c) ${P_{22}}/{P_{11}}$, (d) ${P_{33}}/{P_{11}}$, (e) ${P_{43}}/{P_{11}}$, and (f) ${P_{44}}/{P_{11}}$ predicted from the DNNs against the true values. The refractive index is unavailable in the database.

Figure 11.  Comparison of (a) ${P_{11}}$, (b) ${P_{12}}/{P_{11}}$, (c) ${P_{22}}/{P_{11}}$, (d) ${P_{33}}/{P_{11}}$, (e) ${P_{43}}/{P_{11}}$, and (f) ${P_{44}}/{P_{11}}$ predicted from the DNNs against the true values. Both the size parameter xsize and refractive index are unavailable in the database.

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## Manuscript History

Manuscript revised: 17 November 2021
Manuscript accepted: 23 November 2021
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## Application of a Neural Network to Store and Compute the Optical Properties of Non-Spherical Particles

###### Corresponding author: Wei HAN, hanwei@cma.gov.cn;
• 1. Key Laboratory of Geoscience Big Data and Deep Resource of Zhejiang Province, School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
• 2. Center for Earth System Modeling and Prediction, China Meteorological Administration, Beijing 100081, China
• 3. Numerical Weather Prediction Center, China Meteorological Administration, Beijing 100081, China
• 4. Key Laboratory of Atmospheric Chemistry of China Meteorological Administration, Institute of Atmospheric Composition, Chinese Academy of Meteorological Sciences, Beijing 100081, China

Abstract: Radiative transfer simulations and remote sensing studies fundamentally require accurate and efficient computation of the optical properties of non-spherical particles. This paper proposes a deep learning (DL) scheme in conjunction with an optical property database to achieve this goal. Deep neural network (DNN) architectures were obtained from a dataset of the optical properties of super-spheroids with extensive shape parameters, size parameters, and refractive indices. The dataset was computed through the invariant imbedding T-matrix method. Four separate DNN architectures were created to compute the extinction efficiency factor, single-scattering albedo, asymmetry factor, and phase matrix. The criterion for designing these neural networks was the achievement of the highest prediction accuracy with minimal DNN parameters. The numerical results demonstrate that the determination coefficients are greater than 0.999 between the prediction values from the neural networks and the truth values from the database, which indicates that the DNN can reproduce the optical properties in the dataset with high accuracy. In addition, the DNN model can robustly predict the optical properties of particles with high accuracy for shape parameters or refractive indices that are unavailable in the database. Importantly, the ratio of the database size (~127 GB) to that of the DNN parameters (~20 MB) is approximately 6810, implying that the DNN model can be treated as a highly compressed database that can be used as an alternative to the original database for real-time computing of the optical properties of non-spherical particles in radiative transfer and atmospheric models.

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