Mixed-Precision Partial Differential Equation Solver Design Based on Nonvolatile Memory

In this study, a nonvolatile memory (NVM)-based mixed-precision partial differential equation (PDE) solver is developed to achieve both high computational accuracy and high energy efficiency in a non-Von Neumann manner. The mixed-precision architecture consists of an outer solver utilizing CPU/GPU for a small amount of high-precision computing and an inner solver using NVM array for a large number of approximate iterations by in-memory computing. The impacts of inner iteration number and inner precision on time and energy cost are analyzed to configure the optimum algorithm. Based on this, we investigate the impacts of device reliability properties on the performance of mixed-precision computing system, including device variation, read noise, ON/OFF ratio, and read disturb. The results indicate that the computational accuracy is highly tolerant to the device variation. However, the time and energy cost are increased due to the device reliability, especially the ON/OFF ratio. To suppress the impact of ON/OFF ratio, we present a circuit compensation method, which subtracts the current of reference string with all devices OFF before quantization. To improve the hardware utilization and reduce the number of iterations, a matrix slicing method combined with hybrid layer update is proposed. By employing the two optimization methods, a $57.3\times $ reduction at energy cost with the matrix size of $1600\times1600$ is achieved.