Neural incomplete factorization: learning preconditioners for the conjugate gradient method

Finding suitable preconditioners to accelerate iterative solution methods, such as the conjugate gradient method, is an active area of research. In this paper, we develop a computationally efficient data-driven approach to replace the typically hand-engineered algorithms with neural networks. Optimizing the condition number of the linear system directly is computationally infeasible. Instead, our method generates an incomplete factorization of the matrix and is, therefore, referred to as neural incomplete factorization (NeuralIF). For efficient training, we utilize a stochastic approximation of …

algorithms cs.lg cs.na data data-driven factorization gradient iterative linear math.na math.oc networks neural networks paper research solution stat.ml