  In this paper, we propose a new neural network architecture based on the H2
matrix. Even though networks with H2-inspired architecture already exist, and
our approach is designed to reduce memory costs and improve performance by
taking into account the sparsity template of the H2 matrix. In numerical
comparison with alternative neural networks, including the known H2-based ones,
our architecture showed itself as beneficial in terms of performance, memory,
and scalability.
