Deep-learning application to the separation of variables method for light scattering by spheroids: optimal number of expansion terms and improved prolate radial spheroidal function calculation

The spheroid model provides a first-order approximation to account for the effect of particle nonsphericity on light scattering. The separation of variables method (SVM) in the spheroidal coordinate system was recently employed to accurately compute the optical properties of spheroids with small-to-large size parameters. To balance numerical robustness and computational cost and to correct computational errors that arise for large-size parameters (greater than 300) and small aspect ratios (less than 0.5), we integrate two deep-learning models into the SVM computational program. These models include a deep neural network (DNN) for predicting the optimal truncation number of the vector spheroidal wave function expansions, and a mixture-of-experts (MoE) model for selecting the optimal value of hyperbolic angle <i>η</i> that is critical to calculating second-kind prolate radial spheroidal functions. The present results demonstrate the advantage of using deep-learning models to improve the efficiency and accuracy of SVM under extreme aspect ratio and size parameter conditions.