ReLOPE: Resistive RAM-Based Linear First-Order Partial Differential Equation Solver

Data movement between memory and processing units poses an energy barrier to Von-Neumann-based architectures. In-memory computing (IMC) eliminates this barrier. RRAM-based IMC has been explored for data-intensive applications, such as artificial neural networks and matrix-vector multiplications that are considered as ``soft'' tasks where performance is a more important factor than accuracy. In ``hard'' tasks such as partial differential equations (PDEs), accuracy is a determining factor. In this brief, we propose ReLOPE, a fully RRAM crossbar-based IMC to solve PDEs using the Runge-Kutta numerical method with 97% accuracy. ReLOPE expands the operating range of solution by exploiting shifters to shift input data and output data. ReLOPE range of operation and accuracy can be expanded by using fine-grained step sizes by programming other RRAMs on the BL. Compared to software-based PDE solvers, ReLOPE gains 31.4x energy reduction at only 3% accuracy loss.