Generalized Lorentz-Mie Theory (GLMT) provides analytical far-field solutions to electromagnetic (EM) scattering of an aggregate of spheres in a fixed orientation. One of the computational codes that implements the GLMT calculation is that provided by Xu, dubbed GMM which returns EM responses such as the extinction cross section, σext, given the information of incident wavelength, particle arrangement, the common radius, and reflective indices of the aggregate. We have attempted to represent the GMM code in the form a neural network dubbed NNGMM. The NNGMM obtained was stress tested and systematically quantified for its accuracy by comparing the σext predicted against that produced by the original GMM code. The σext produced by the NNGMM for arbitrary aggregates at random wavelength yielded a good fidelity with respect to that calculated by the GMM calculator up to an R-squared value of above 99% level and mean squared error of ≈5.0. The realization of NNGMM proves the feasibility of representing the GMM code by a neural network. The optimally-performing NNGMM obtained in this work can serve as an alternative computational tool for calculating σext in place of the original GMM code at a much cheaper cost, albeit with a slight penalty in terms of absolute accuracy.
Ying Li Thong,
Tiem Leong Yoon,
"A Neural Network Representation of Generalized Multiparticle Mie-Solution," Progress In Electromagnetics Research M,
Vol. 112, 15-28, 2022. doi:10.2528/PIERM22050504
3. Berdnik, V. V., K. Gilev, A. Shvalov, V. Maltsev, and V. A. Loiko, "Characterization of spherical particles using high-order neural networks and scanning ow cytometry," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 102, No. 1, 62-72, 2006, doi: https://doi.org/10.1016/j.jqsrt.2006.03.002. doi:10.1016/j.jqsrt.2006.03.002
4. Gugliotta, L. M., G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, "A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements," Particle & Particle Systems Characterization, Vol. 26, No. 1-2, 41-52, 2009, doi: https://doi.org/10.1002/ppsc.200800010. doi:10.1002/ppsc.200800010
5. Atsushi, Y., S. Tomonobu, A. Y. Saber, F. Toshihisa, S. Hideomi, and C. Kim, "Application of neural network to 24-hour-ahead generating power forecasting for PV system," 2008 IEEE Power and Energy Society General Meeting --- Conversion and Delivery of Electrical Energy in the 21st Century, Jul. 20-24, 2008.
6. Draine, B. T. and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," Journal of the Optical Society of America A, Vol. 11, No. 4, 1491-1499, 1994, doi: 10.1364/JOSAA.11.001491. doi:10.1364/JOSAA.11.001491
7. Moon, C. Y., "Particle sensing in gas turbine inlets using optical measurements and machine learning,", Doctoral Dissertations, Blacksburg, Virginia, 2020, http://hdl.handle.net/10919/101969.
8. Stegmayer, G. S., O. A. Chiotti, L. M. Gugliotta, and J. R. Vega, "Particle size distribution from combined light scattering measurements. A neural network approach for solving the inverse problem," 2006 IEEE International Conference on Computational Intelligence for Measurement Systems and Applications, Jul. 12-14, 2006.
9. Guerrero, J. A., F. M. Santoyo, D. Moreno, M. Funes-Gallanzi, and S. Fernandez-Orozco, "Particle positioning from CCD images: Experiments and comparison with the generalized Lorenz-Mie theory," Measurement Science and Technology, Vol. 11, No. 5, 568-575, 2000, doi: 10.1088/0957-0233/11/5/318. doi:10.1088/0957-0233/11/5/318
10. Wang, H. and X. Xu, "Determination of spread constant in RBF neural network bygenetic algorithm," Int. J. Adv. Comput. Technol. (IJACT), Vol. 5, No. 9, 719-726, 2013.
11. Akashi, N., M. Toma, and K. Kajikawa, "Design of metamaterials using neural networks," SPIE, Vol. 11194, 2019.
12. Mamun, M. M. and D. Müller, "Retrieval of intensive aerosol microphysical parameters from multiwavelength Raman/HSRL lidar: Feasibility study with artificial neural networks," Atmos. Meas. Tech. Discuss., 1-46, 2016, doi: 10.5194/amt-2016-7.
13. Xu, Y.-L., "Electromagnetic scattering by an aggregate of spheres: Errata," Applied Optics, Vol. 37, No. 27, 6494-6494, 1998, doi: 10.1364/AO.37.006494. doi:10.1364/AO.37.006494
14. Xu, Y.-L., "Electromagnetic scattering by an aggregate of spheres: Far field," Applied Optics, Vol. 36, No. 36, 9496-9508, 1997, doi: 10.1364/AO.36.009496. doi:10.1364/AO.36.009496
15. Xu, Y.-L., "Electromagnetic scattering by an aggregate of spheres: Asymmetry parameter," Physics Letters A, Vol. 249, No. 1, 30-36, 1998, doi: https://doi.org/10.1016/S0375-9601(98)00708-. doi:10.1016/S0375-9601(98)00708-7
16. Xu, Y.-L. and R. T. Wang, "Electromagnetic scattering by an aggregate of spheres: Theoretical and experimental study of the amplitude scattering matrix," Physical Review E, Vol. 58, No. 3, 3931-3948, 1998, doi: 10.1103/PhysRevE.58.3931. doi:10.1103/PhysRevE.58.3931
17. Xu, Y.-L., B. A. S. Gustafson, F. Giovane, J. Blum, and S. Tehranian, "Calculation of the heat- source function in photophoresis of aggregated spheres," Physical Review E, Vol. 60, No. 2, 2347-2365, 1999, doi: 10.1103/PhysRevE.60.2347. doi:10.1103/PhysRevE.60.2347
18. Xu, Y.-L. and R. T. Wang, "Electromagnetic scattering by an aggregate of spheres: Theoretical and experimental study of the amplitude scattering matrix," Physical Review E, Vol. 58, No. 3, 3931-3948, 1998, doi: 10.1103/PhysRevE.58.3931. doi:10.1103/PhysRevE.58.3931
19. Guerrero, J. A., F. M. Santoyo, D. Moreno, M. Funes-Gallanzi, and S. Fernandez-Orozco, "Particle positioning from CCD images: Experiments and comparison with the generalized Lorenz-Mie theory," Measurement Science and Technology, Vol. 11, No. 5, 568-575, 2000, doi: 10.1088/0957-0233/11/5/318. doi:10.1088/0957-0233/11/5/318
20. Lock, J. A. and G. Gouesbet, "Generalized Lorenz-Mie theory and applications," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 110, No. 11, 800-807, Jul. 2009. doi:10.1016/j.jqsrt.2008.11.013
21. Ren, K. F., G. Gréhan, and G. Gouesbet, "Prediction of reverse radiation pressure by generalized Lorenz-Mie theory," Applied Optics, Vol. 35, No. 15, 2702-2710, 1996, doi: 10.1364/AO.35.002702. doi:10.1364/AO.35.002702
22. Pellegrini, G., G. Mattei, V. Bello, and P. Mazzoldi, "Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems," Materials Science and Engineering: C, Vol. 27, 1347-1350, 2007, doi: 10.1016/j.msec.2006.07.025. doi:10.1016/j.msec.2006.07.025
23. Xu, F., K. Ren, G. Gouesbet, G. Gréhan, and X. Cai, "Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid," Journal of the Optical Society of America A, Vol. 24, No. 1, 119-131, 2007. doi:10.1364/JOSAA.24.000119
24. Lock, J. A. and G. Gouesbet, "Generalized Lorenz-Mie theory and applications," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 110, No. 11, 800-807, 2009, doi: https://doi.org/10.1016/j.jqsrt.2008.11.013. doi:10.1016/j.jqsrt.2008.11.013
25. Jia, X., J. Shen, and H. Yu, "Calculation of generalized Lorenz-Mie theory based on the localized beam models," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 195, 44-54, 2017, doi: https://doi.org/10.1016/j.jqsrt.2016.10.021. doi:10.1016/j.jqsrt.2016.10.021
26. Xu, Y.-L. and B. S. Gustafson, "A generalized multiparticle Mie-solution: Further experimental verification," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 70, No. 4, 395-419, 2001, doi: https://doi.org/10.1016/S0022-4073(01)00019-X. doi:10.1016/S0022-4073(01)00019-X
27. Xu, Y.-L., "Efficient evaluation of vector translation coefficients in multiparticle light-scattering theories," Journal of Computational Physics, Vol. 139, 137-165, 1998. doi:10.1006/jcph.1997.5867
28. Xu, Y.-L., "Fortran source codes for calculation of radiative scattering by aggregated particles in both fixed and random orientations for homogeneous spheres, core-mantle and for ensembles of variously shaped (meaning rotationally symmetric) particles," GMM --- Generalized Multiparticle Mie-Solution [Fortran Source Code], Oct. 2, 2013, https://scattport.org/index.php/light-scattering-software/multiple-particle-scattering/135-gmm-generalized-multiparticle-mie-solution.
29., , https://scattport.org/files/xu/codes.htm, assessed on 15 Dec. 2021.
30. LeCun, Y., Y. Bengio, and G. Hinton, "Deep learning," Nature, Vol. 521, No. 7553, 436-444, 2015. doi:10.1038/nature14539
31. Chen, X., Z. Wei, M. Li, and P. Rocca, "A review of deep learning approaches for inverse scattering problems (invited review)," Progress In Electromagnetics Research, Vol. 167, 67-81, 2020. doi:10.2528/PIER20030705
32. Thomée, V., "From finite differences to finite elements: A short history of numerical analysis of partial differential equations," Numerical Analysis: Historical Developments in the 20th Century, 361-414, Elsevier, 2001.
33. Yee, K. S. and J. S. Chen, "The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell's equations," IEEE Transactions o Antennas and Propagation, Vol. 45, No. 3, 354-363, 1997. doi:10.1109/8.558651
34. Jin, J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons, 2015.
35. Banerjee, P. K., P. K. Banerjee, and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw-Hill, UK, 1981.
37. Chew, W. C., E. Michielssen, J. M. Song, and J. M. Jin, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Inc., 2001.
38. Ren, Q., Y. Wang, Y. Li, and S. Qi, Sophisticated Electromagnetic forward Scattering Solver via Deep Learning, Springer Singapore Pte. Limited, 2021.
39. Jia, R., X. Zhang, F. Cui, G. Chen, H. Li, H. Peng, and S. Pei, "Machine-learning-based computationally efficient particle size distribution retrieval from bulk optical properties," Applied Optics, Vol. 59, No. 24, 7284-7291, 2020. doi:10.1364/AO.398364
40. Giannakis, I., A. Giannopoulos, and C. Warren, "A machine learning-based fast-forward solver for ground penetrating radar with application to full-waveform inversion," IEEE Transactions on Geoscience and Remote Sensing, Vol. 57, No. 7, 4417-4426, 2019. doi:10.1109/TGRS.2019.2891206
41. Tang, W., T. Shan, X. Dang, M. Li, F. Yang, S. Xu, and J. Wu, "Study on a Poisson's equation solver based on deep learning technique," 2017 IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS), 1-3, IEEE, Dec. 2017.
42. Wu, H., Y. Zhang, W. Fu, C. Zhang, and S. Niu, "A novel pre-processing method for neural network-based magnetic field approximation," IEEE Transactions on Magnetics, Vol. 57, No. 10, 1-9, 2021.
43. Ma, Z., K. Xu, R. Song, C. F. Wang, and X. Chen, "Learning-based fast electromagnetic scattering solver through generative adversarial network," IEEE Transactions on Antennas and Propagati, Vol. 69, No. 4, 2194-2208, 2020.
44. Abadi, M., A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, and X. Zheng, "TensorFlow: Large-scale machine learning on heterogeneous distributed systems,", [Application software], 2015, https://www.tensorflow.org.
45. Abadi, M., P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, and X. Zheng, "TensorFlow: A system for large-scale machine learning," Proceedings of the 12th USENIX Conference on Operating Systems Design and Implementation, Savannah, GA, USA, 2016.