A fast direct solver based neural network for solving PDEs
The matrices arising from large scale $N$-body problems can be efficiently represented using hierarchical matrices, whose key idea is that the admissible off-diagonal sub-matrices can be well approximated by low-rank matrices across a hierarchy of matrix partitions. HODLR (Hierarchical Off-Diagonal Low-Rank) matrices are a subclass of hierarchical matrices in which all off-diagonal submatrices at every level of a recursive binary partition are low-rank. In this article, we present a neural network that learns the inverse operation of HODLR matrices based on the fast direct solver for HODLR matrices developed by Ambikasaran and Darve (2013). We further extend the architecture to learn nonl...
| Authors | Jashwanth Reddy Kadaru, Vaishnavi Gujjula |
|---|---|
| Primary category | math.NA |
| Published | 18 June 2026 |
| Last updated at source | 18 June 2026 |
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