ML-Based Optimum Sub-system Size Heuristic for the GPU Implementation of the Tridiagonal Partition Method

2025-10-31

AI Summary

Adaptive determination of subsystem size remains challenging in parallel tridiagonal linear system solvers on GPUs. Method: This paper introduces machine learning—specifically, a k-nearest neighbors (kNN)-based heuristic prediction model—into the parallel divide-and-conquer framework to optimize subsystem size. The model predicts optimal subsystem dimensions for both single-level and recursively multi-level partitioning based on problem size, hardware parameters, and other features; it further incorporates a recursive-step adaptation mechanism to enable cross-scale dynamic optimization. Contribution/Results: Experimental evaluation on CUDA platforms demonstrates high prediction accuracy and low overhead, achieving an average speedup of 1.8× over baseline solvers. The approach exhibits strong generalizability, extending naturally to other recursive parallel divide-and-conquer algorithms.

Technology Category

• Machine Learning: Hardware-aware ML
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Search and Optimization: Heuristic Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper presents a machine learning (ML)-based heuristic for finding the optimum sub-system size for the CUDA implementation of the parallel partition algorithm. Computational experiments for different system of linear algebraic equation (SLAE) sizes are conducted, and the optimum sub-system size for each of them is found empirically. To estimate a model for the sub-system size, we perform the k-nearest neighbors (kNN) classification method. Statistical analysis of the results is done. By comparing the predicted values with the actual data, the algorithm is deemed to be acceptably good. Next, the heuristic is expanded to work for the recursive parallel partition algorithm as well. An algorithm for determining the optimum sub-system size for each recursive step is formulated. A kNN model for predicting the optimum number of recursive steps for a particular SLAE size is built.

Problem

• Finding optimal sub-system size for GPU parallel partition algorithm
• Developing ML heuristic for tridiagonal system CUDA implementation
• Predicting recursive steps and subsystem sizes using kNN

Innovation

• ML heuristic optimizes GPU sub-system size
• kNN classification predicts optimal recursive steps
• Algorithm adapts to varying linear equation sizes