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

EAGER：使用概率数字逻辑研究动态系统的新方法

• 批准号: 1450798
• 负责人: Kia Bazargan
• 金额: $ 7.78万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-01-15 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1450798&HistoricalAwards=false
• 关键词: EAGER; New; Methodology; Studying; Dynamical

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.

动态系统理论和模拟在理解复杂物理现象的行为（例如天气及其预测，移动的车辆和飞机，洋流以及建筑物内温暖和冷空气的流动产生的湍流）中起着重要作用。尽管已经研究了数十年的动态系统，但研究人员仍在准确地表征其行为。大规模硬件和软件仿真通常用于此目的。这项研究将研究一种非常规的硬件设计方法，该方法使用概率代表与动态系统行为相关的参数值。这导致动态系统模拟的硬件成本和运行时大大降低。该方法还可能导致固有的优质设计方法，这些方法可以更快，更准确地表征动态系统，对改善天气预测，汽车和平面燃料效率以及具有有效加热和冷却的绿色建筑物具有很大的影响。 探索性研究（急切）的早期授予的目的是使用一种固有的概率计算方法来处理动态系统中的复杂性，称为随机计算 - 一种非传统计算方式，将值编码为概率而不是确定性的二进制数字。随机计算并没有扰动确定性动力学系统，例如带有噪声的逻辑映射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中。这种固有的随机方法可以指向大型动力学系统中计算的新且有效的途径，并可以使用传统硬件和软件解决方案所需的一小部分资源来使用非常简单的电路来执行非平凡的计算。但是，对于成功地应用随机计算到动态系统模拟中，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。从系统输出到输入的动态系统中的反馈路径不可避免地会在输入的概率表示之间产生较强的相关性，除非使用特定技术来减少此类相关性。 PIS计划通过添加不会大幅提高硬件成本的硬件资源来调查此类方法。