EAGER: A New Methodology for Studying Dynamical Systems Using Probabilistic Digital Logic

动力系统理论和模拟在理解复杂物理现象的行为方面发挥着重要作用，例如天气及其预报，由移动车辆和飞机产生的湍流，洋流以及建筑物内冷暖空气的流动。尽管动力系统已经被研究了几十年，研究人员仍然在努力准确地描述它们的行为。为此，通常采用大规模的硬件和软件模拟。本研究将探讨一种非传统的硬件设计方法，该方法使用概率来表示与动力系统行为相关的参数值。这大大降低了动态系统仿真的硬件成本和运行时间。该方法还可能产生内在优越的设计方法，更快、更准确地表征动力系统，对改善天气预报、汽车和飞机燃油效率以及具有高效供暖和制冷的绿色建筑具有深远的影响。这个探索性研究早期拨款（EAGER）的目标是使用一种称为随机计算的固有概率计算方法来处理动态系统中的复杂性。随机计算是一种非传统的计算方式，它将值编码为概率，而不是确定性二进制数。随机计算不是用噪声干扰确定性动力系统，如逻辑映射x |—u x(1-x)，而是将变量本身编码为随机变量，从而将噪声嵌入编码本身。这种固有的随机方法可以为大型动态系统的计算指明一条新的有效途径，并且可以使用传统硬件和软件解决方案所需资源的一小部分，使用极其简单的电路来执行非平凡的计算。然而，为了成功地将随机计算应用于动力系统模拟，必须解决一个基本问题：随机计算要求概率输入是不相关的随机变量。动力系统中从系统输出到输入的反馈路径不可避免地在输入的概率表示之间产生强相关性，除非使用特定的技术来减少这种相关性。pi计划通过增加硬件资源来研究这些方法，而不会显著增加硬件成本。

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.