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，移动车辆和飞机产生的湍流，洋流以及建筑物内的冷暖空气流动。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态系统行为相关的参数值。这将导致显着减少的硬件成本和运行时间的动态系统仿真。该方法还可能导致固有的上级设计方法，更快，更准确地表征动力系统，具有深远的影响，改善天气预报，汽车和飞机的燃油效率，以及绿色建筑物的高效加热和冷却。 EARLY探索性研究资助（EAGER）的目标是使用称为随机计算的固有概率计算方法来接近动力系统的复杂性-这是一种非传统的计算方式，将值编码为概率，而不是确定性的二进制数。而不是扰动一个确定性的动力系统，如逻辑斯蒂映射x|-- u x（1-x）对于噪声，随机计算将变量本身编码为随机变量，从而将噪声嵌入编码本身中。这种固有的随机方法可以为大型动态系统中的计算指出一种新的有效途径，并使非常简单的电路能够使用传统硬件和软件解决方案所需的一小部分资源来执行非平凡的计算。然而，一个基本的问题必须解决的成功应用随机计算的动力系统仿真：随机计算要求的概率输入是不相关的随机变量。动态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计划通过添加不会显著增加硬件成本的硬件资源来研究此类方法。

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.