Matrix Diagonalization as a Board Game: Teaching an Eigensolver the Fastest Path to Solution

• URL: http://arxiv.org/abs/2306.10075v2
• Date: Wed, 21 Jun 2023 05:05:42 GMT
• Title: Matrix Diagonalization as a Board Game: Teaching an Eigensolver the Fastest Path to Solution
• Authors: Phil Romero, Manish Bhattarai, Christian F. A. Negre, Anders M. N. Niklasson, Adetokunbo Adedoyin
• Abstract summary: Matrix diagonalization is at the cornerstone of numerous fields of scientific computing. We show how reinforcement learning, using the AlphaZero framework, can accelerate Jacobi matrix diagonalizations. Our findings highlight the opportunity to use machine learning as a promising tool to improve the performance of numerical linear algebra.
• Score: 2.239917051803692
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Matrix diagonalization is at the cornerstone of numerous fields of scientific computing. Diagonalizing a matrix to solve an eigenvalue problem requires a sequential path of iterations that eventually reaches a sufficiently converged and accurate solution for all the eigenvalues and eigenvectors. This typically translates into a high computational cost. Here we demonstrate how reinforcement learning, using the AlphaZero framework, can accelerate Jacobi matrix diagonalizations by viewing the selection of the fastest path to solution as a board game. To demonstrate the viability of our approach we apply the Jacobi diagonalization algorithm to symmetric Hamiltonian matrices that appear in quantum chemistry calculations. We find that a significant acceleration can often be achieved. Our findings highlight the opportunity to use machine learning as a promising tool to improve the performance of numerical linear algebra.

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