Learning-Based Acceleration of Classical Numerical Algorithms: An Adaptive Framework for High-Performance Scientific Computing

It is considered in this research paper to use adaptive methods via machine learning techniques in order to increase the speed of classical algorithms in the field of high-performance computing (HPC). Indeed, it is known that classical iterative methods such as CG, GMRES, and BICGSTAB were quite costly during the process of computations and ineffective since they could not quickly find convergence. In order to solve this issue, a hybrid method was introduced using machine learning techniques with classical algorithms, wherein the former predicts the optimal values of parameters in the latter at each stage of computation. The effectiveness of this new approach is measured through the application of the Suite Sparse Matrix Collection with scientific data sets. It can be stated, according to the results, that this new method can ensure convergence within 15 iterations instead of 20 iterations that were needed by classical methods to ensure convergence with a residual of 0.001. As for the computational efficiency problem, the presented algorithm enabled decreasing computational time down to 1.25 seconds, thereby leading to the improvement in performance by 40-45%. In addition to this, the efficiency of the new method is expressed by the high degree of accuracy because of the low level of mean squared error (0.0011) and fast convergence rate (98.9%). In such a manner, the presented algorithm demonstrated higher performance when compared to both traditional methods and machine learning-based algorithms. As one can see, the combination of numerical algorithms and machine learning has led to acceleration of convergence process, decreased computational complexity, and increased numerical accuracy. The proposed technique can be the basis for improving computational efficiency in scientific problems.