Hardware ODE solvers using stochastic circuits

A novel ordinary differential equation (ODE) solver is proposed by using a stochastic integrator to implement the accumulative function of the Euler method. We show that a stochastic integrator is an unbiased estimator for a Euler numerical solution. Unlike in conventional stochastic circuits, in which long stochastic bit streams are required to produce a result with a high accuracy, the proposed stochastic ODE solver provides an estimate of the solution for every bit in the stochastic bit stream, thus significantly reducing the latency and energy consumption of the circuit. Complex ODE solvers are constructed for solving nonhomogeneous ODEs, systems of ODEs and higher-order ODEs. Experimental results show that the stochastic ODE solvers provide very accurate solutions compared to their binary counterparts, with on average an energy saving of 46% (up to 74%), 8× throughput per area (up to nearly 12×) and a runtime reduction of 72% (up to 82%).