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The irregular particulate surfaces of asteroids lead to complex light-scattering processes affected by multiple surface properties, such as particle size, shape, refractive index, and spatial distribution. When modelling the scattering processes, the single scatterers can be described with the scattering matrix, a 4x4 Mueller matrix [1]. However, inverse modelling of the surface properties remains an open problem due to the complexity of the underlying scattering processes.
Muinonen and Leppälä [2] precented recently a parametrized version of scattering matrix guaranteed to fulfil all symmetry relations for a physically valid Mueller matrix. Furthermore, a decomposition of such matrices into so-called pure Mueller matrices was developed, making it possible to incorporate such matrices in geometric optics code with correct coherent backscattering treatment [3]. However, finding an optimal parametrized scattering matrix to represent laboratory measurements of particle scattering properties is not straightforward.
Machine learning has emerged as an aid in complex modelling and simulation of physical processes and in recent years development of methods, such as physics-informed neural networks (PINN) [4], brings new ways of incorporating known physical constraints into data-driven machine learning. We study if a neural network model can be developed to find optimal parametrized scattering matrix. The target is to train a transformer-based PINN to independently find the best fitting empirical parameters for an experimentally measured sample scattering phase matrix. Neural networks have been recently used in studies in a similar field [5], showing the method to have potential.
[1] Bohren, C. F., & Huffman, D. R. (1998). Absorption and scattering of light by small particles (1st ed.). Wiley. https://doi.org/10.1002/9783527618156
[2] Muinonen, K., & Leppälä, A. S. (2025). Scattering of light by cosmic dust: Parameterized Mueller matrix. Astronomy & Astrophysics, 704, A106 https://doi.org/10.1051/0004-6361/202555555
[3] Muinonen, K., & Penttilä, A. (2024). Scattering matrices of particle ensembles analytically decomposed into pure Mueller matrices. Journal of Quantitative Spectroscopy and Radiative Transfer, 324, https://doi.org/10.1016/j.jqsrt.2024.109058
[4] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045
[5] Tang, Y., Jiang, Y., Feng, Y., Zhang, X., & Jiang, X. (2025). Transformer-based Approach for Accurate Asteroid Spectra Taxonomy and Albedo Estimation. The Astronomical Journal, 169(4), 201. https://doi.org/10.3847/1538-3881/adb710