arXiv:2605.26854v1 Announce Type: new Abstract: The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis. While algebraic multigrid (AMG) offers optimal linear scaling, its performance is severely constrained by the trade-off between the sparsity and convergence quality of coarse-grid operators. Classical AMG heuristics struggle to balance these objectives, often sacrificing stability or performance for sparsity. We propose RAPNet, a graph neural network (GNN) framework that resolves this trade-off by learning to generate sparse, robust co
The increasing complexity of scientific computing and AI models necessitates highly efficient numerical solvers, pushing researchers to integrate machine learning with traditional algorithms.
Improving the efficiency of large sparse linear system solutions directly impacts the scalability and speed of complex simulations, graph analyses, and AI training, which are foundational to scientific and technological progress.
The trade-off between sparsity and convergence quality in algebraic multigrid methods can now be potentially optimized through learnable GNN frameworks, leading to faster and more stable solvers.
- · High-performance computing sector
- · Scientific research institutions
- · AI/ML developers
- · Industries relying on complex simulations
- · Developers of less efficient numerical solvers
- · Applications bottlenecked by current computational limits
Faster and more accurate solutions to large-scale computational problems across various domains.
Reduced computational costs and time for scientific discovery and engineering design, accelerating product development cycles.
Enhanced capabilities for AI model training and deployment, particularly in scientific AI and large-scale graph analysis applications.
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Read at arXiv cs.LG