Dynamical systems theory and simulation play an important role in the understanding of the behavior of complex physical phenomena such as weather and its forecast, turbulence generated by moving vehicles and planes, ocean currents and flow of warm and cold air inside buildings. Even though dynamical systems have been studied for decades, researchers still struggle with the accurate characterization of their behavior. Large-scale hardware and software simulations are usually employed to that end. This research will investigate an unconventional hardware design methodology that uses probabilities to represent values of parameters associated with the behavior of dynamical systems. This results in significant reductions of the hardware cost and runtime of dynamical systems simulations. The approach also potentially results in inherently superior design methods that characterize dynamical systems faster and more accurately, with far reaching implications for improved weather forecasting, car and plane fuel efficiency, and green buildings with efficient heating and cooling.
The goal of this EArly-Grant for Exploratory Research (EAGER) is to approach the complexity in dynamical systems using an inherently probabilistic computational methodology called stochastic computing - a non-traditional way of computing that encodes values as probabilities, instead of deterministic binary numbers. Instead of perturbing a deterministic dynamical system such as the logistic map x |--> u x(1-x) with noise, stochastic computing encodes a variable itself as a random variable, thus embedding the noise in the encoding itself. Such an inherently stochastic approach could point to a new and effective avenue for computations in large dynamical systems, and enables extremely simple circuits to be used to perform non-trivial computations using a fraction of the resources required by traditional hardware and software solutions. However, a fundamental issue has to be addressed for the successful application of stochastic computing to dynamical system simulation: stochastic computing requires the probabilistic inputs to be uncorrelated random variables. The feedback path in dynamical systems from system outputs to the inputs inevitably creates strong correlations between probabilistic representations of the inputs unless specific techniques are used to reduce such correlations. The PIs plan to investigate such methods by adding hardware resources that do not increase hardware costs significantly.
