Efficient Memristive Stochastic Differential Equation Solver

Abstract

Herein, an efficient numerical solver for stochastic differential equations based on memristors is presented. The solver utilizes the stochastic switching effect in memristive devices to simulate the generation of a Brownian path and employs iterative Euler method computations within memristive crossbars. The correctness of the solution paths generated by the system is examined by solving the Black–Scholes equations and comparing the paths to analytical solutions. It is found that the absolute error of a 128‐step path is limited to an order of 10 − 2 . The tolerance of the system to crossbar nonidealities is also assessed by comparing the numerical and analytical paths' variation in error. The numerical solver is sensitive to the variation in operating conditions, with the error increasing by 1.17 × , 38.7 × , and 1222 × as the ambient temperature, wire resistance, and stuck probability of the memristor increase to extreme conditions. The solver is tested on a variety of problems to show its utility for different calculations. And, the resource consumption of the proposed structure built with existing technology is estimated and it is compared with similar iterative solvers. The solver generates a solution with the same level of accuracy from 4 × to 10 × faster than similar digital or mixed‐signal designs.

Keywords

• Black–Scholes equation
• Brownian path
• memristor crossbar
• stochastic differential equation
• vector–matrix multiplication