Collaborative Research: Gaussian Process Frameworks for Modeling and Control of Stochastic Systems

在不确定情况下进行决策的定量模型继续吸引着自然科学和工程学领域的巨大努力。随着越来越复杂的模型在应用中的出现，计算需求继续超过可行的，有效的数值方法的溢价仍然很高。研究人员将探索最新的机器学习技术和控制范例之间的协同效应，这些范例出现在金融、能源储存和安全等各种应用中，以及传染病的流行病学建模。开发的“智能”算法将提供性能升级，这对于在处理大规模/复杂环境中使用模拟至关重要。该项目还将促进本科生、研究生和博士后在数学科学方面的跨学科培训。研究人员将研究用于非线性动态随机系统建模、分析和控制的统计学习技术。通过开发复杂随机模拟器的算法和统计模型，以及自主获取数据的主动学习策略，该项目将在动态随机现象的数学分析方面实现更高的能力和效率。该方法的关键是使用高保真近似高斯过程代理自适应地分配计算资源，以最大化用于建模目标的输入输出关系或用于动态规划的输入控制映射的学习率。通过将随机模拟与机器学习和非参数统计相结合，并与计算实施相结合，该项目将增强大规模模拟和优化环境中的知识发现。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantitative models for decision making under uncertainty continue to attract intense effort across natural sciences and engineering. With the advent of ever more sophisticated models in applications, computational demands continue to outpace what is feasible and the premium on efficient numerical approaches remains high. The investigators will explore synergies between the latest machine learning techniques and control paradigms, arising in applications as diverse as finance, energy storage and security, and the epidemiological modeling of infectious diseases. The developed "smart" algorithms will deliver performance upgrades essential for using simulations in tackling large-scale/complex settings. The project will also contribute to inter-disciplinary training in mathematical sciences across undergraduate, graduate and post-doctoral levels. The investigators will investigate statistical learning techniques for modeling, analysis and control of nonlinear dynamic stochastic systems. Through developing algorithms and statistical models for complex stochastic simulators, and active learning strategies for autonomous data acquisition, the project will achieve enhanced capabilities and efficiency in mathematical analysis of dynamic random phenomena. The approach hinges on the use of high fidelity approximate Gaussian Process surrogates to adaptively allocate computing resources in order to maximize the learning rate of the input-output relationship for modeling objectives or of the input-control map for dynamic programming. By connecting stochastic simulation with machine learning and non-parametric statistics, and integrating with the computational implementation, the project will enhance knowledge discovery in large-scale simulation and optimization settings.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.