Machine Learning-Assisted Matrix Compression for Electromagnetic Scattering Analysis

In this paper a Machine Learning algorithm is used to assist randomized techniques to compress the Method of Moments linear system matrix when analyzing electromagnetic scattering problems modeled with integral equations. Our main focus is the pivot selection procedure, which is a key aspect of the overall compression of the impedance matrix in CUR-like algorithms. We propose the utilization of a random forest model to automatically determine an appropriate dimension for the CUR matrices, thereby ensuring a reasonable compression error without the need of prior information. The random forest methodology seeks to establish links between the key geometric parameters of the electromagnetic interaction under analysis and the optimal number of compression pivots required to achieve the desired compression error. We compare the results obtained using this methodology with those obtained using Adaptive Cross Approximation (ACA), a well-established and reliable compression algorithm widely utilized in practice. Our findings reveal that the CUR with random forest approach achieves faster compression times than ACA, a crucial factor in reducing the computational resources needed for solving scattering problems. Furthermore, the compression error remains adequate and similar in both cases, suggesting the potential benefits of implementing this random forest approach in multilevel algorithms currently employing a CUR-like compression formulation.