A Neural Hierarchical-Matrix Preconditioner for Real-Time GPU Solves
Interactive simulation solves Ax=b for a sparse SPD A that changes every frame, inside an 8-16 ms budget. At a few thousand unknowns, the setup of algebraic multigrid alone exceeds that budget, while Jacobi and other local preconditioners have no setup but cannot move error across the domain. We learn a preconditioner for this gap: a graph-and-attention network predicts an SPD approximate inverse in H^2-matrix format. On a spatially ordered 3D mesh, blocks of the true inverse lose rank as the clusters they couple move apart; the nested bases of the format follow that decay, so inference and apply are dominated by leaf-block work linear in N, where a dense inverse costs N^2. Our main findi...
| Authors | Carl Osborne, Minghao Guo, Crystal Owens et al. |
|---|---|
| Primary category | cs.GR |
| Published | 13 May 2026 |
| Last updated at source | 24 September 2026 |
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