A memristive neural network based matrix equation solver with high versatility and high energy efficiency

As the main topic in modern scientific computing and machine learning tasks, matrix equation solving is suffering high computational latency and tremendous power consumption due to the frequent data movement in traditional von Neumann computers. Although the in-memory computing paradigms have shown the potential to accelerate the execution of solving matrix equations, the existing memristive matrix equation solvers are still limited by the low system versatility and low computation precision of the memristor arrays. In this work, we demonstrate a hybrid architecture for accurate, as well as efficient, matrix equation solving problems, where the memristive crossbar arrays are used for the parallel vector-matrix multiplication and the digital computer for accuracy. The linear neural-network solving (NNS) method is adopted here and its versatility for various types of matrix equations is proved. The weight-slice computation method is developed to perform the analog matrix multiplication with high efficiency and high robustness in the array. The solution results confirmed that typical matrix equations can be solved by this memristive matrix equation solver with high accuracy. Further performance benchmarking demonstrates that the generalized memristive matrix equation solver has low solving time-complexity while outperforming the state-of-the-art CMOS and in-memory processors.