Data-Enabled Acceleration of Stochastic Computational Experiments

该项目将借助异构数据（例如，经验观察、多保真度模拟和专家知识）提高加速随机计算实验的能力。这项工作的动机是科学和工程中计算实验的趋势。这些实验越来越依赖概率模型来表示认知的不确定性（例如那些基于物理的模型规范）和偶然性的不确定性（实验和观测数据中的噪声）。迄今为止，粗糙的蒙特卡罗模拟主要是由于它的简单性而在这种随机计算实验中占主导地位。加速实验的努力通常是临时的，并且只适用于特定的科学或工程问题。该项目将为领域科学家和工程师提供方法和工具，有可能加快甚至实现基于随机计算实验的突破。这些方法将有助于克服与调查对国家经济、安全和健康至关重要的异常事件（例如，核泄漏、级联停电和流行病爆发）相关的计算挑战。为了最大限度地接触到领域的科学家和工程师，该项目将设计和实现一个开源软件包的方法。将设计并开展一个在线讲习班，以演示该软件并培训研究人员和实践者。为了培养下一代研究人员和实践者的能力，项目团队将通过与大学的多样性增强项目合作，招募大学生和高中生，特别是那些来自代表性不足背景的学生，并与他们进行接触。研究生将直接参与设计和执行研究，而本科生将参与软件开发和测试，作为数据支持的计算研究人员接受指导和培训。尽管在科学或工程研究中全面考虑不确定性是值得赞扬的，但对粗糙的蒙特卡罗模拟进行无指导的计算投资往往会导致时间和资源的巨大浪费。此外，为了获得所需的概率分析精度，相关的计算负担可能成为科学和工程发现的主要瓶颈甚至障碍，特别是当感兴趣的事件是极端的、罕见的或特殊的。为了应对这一挑战，该项目将创新一个统一的方法框架，利用异构数据来加速随机计算实验，同时不影响概率分析的准确性。该框架将包括识别和利用高维模拟输入空间的低维流形（自然出现在科学和工程中）的方法，通过解决维度诅咒来加速随机计算实验。对于加速概率分析，将构造渐近有效的置信区间以保证期望的分析精度。该框架将规定如何自适应地分配计算资源，以探索模拟输入空间，同时利用重要的输入流形，以最大限度地减少计算支出，同时保持所需的分析准确性。该项目将基于两个工程模拟案例研究，即风力涡轮机的结构可靠性评估和电网的级联故障分析，验证这些方法并验证为更广泛影响而开发的开源软件。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will advance the ability to accelerate stochastic computational experiments with the aid of heterogeneous data (for example, empirical observations, multi-fidelity simulations, and expert knowledge). This work is motivated by the trend of computational experiments in science and engineering. These experiments increasingly rely on probabilistic models to represent epistemic uncertainties (such as those in physics-based model specification) and aleatory uncertainties (noise in experiments and observational data). To date crude Monte Carlo simulation dominates such stochastic computational experiments mainly due to its simplicity. Efforts to accelerate the experiments have generally been ad-hoc and narrowly applicable to a particular science or engineering problem. This project will produce methods and tools for domain scientists and engineers with a potential to expedite or even enable breakthroughs based on stochastic computational experiments. These methods will help overcome the computational challenge associated with investigating unusual strings of events (for example, nuclear meltdown, cascading blackout, and epidemic outbreak) that are critical to the nation's economy, security, and health. To maximally reach out to domain scientists and engineers, this project will design and implement an open-source software package of the methods. An online workshop will be designed and conducted to demonstrate the software and train researchers and practitioners. To build the capacity of the next generation of researchers and practitioners, the project team will recruit and engage with college and high-school students, especially those from underrepresented backgrounds, through a partnership with diversity enhancement programs in the university. Graduate students will be directly involved in designing and executing research, while undergraduate students will participate in software development and testing, being mentored and trained as data-enabled computational researchers.Even though comprehensive consideration of uncertainties in a scientific or engineering study is commendable, an unguided computational investment on crude Monte Carlo simulation often results in an enormous waste of time and resources. Furthermore, to attain a required accuracy of probabilistic analysis, the associated computational burden can be a major bottleneck or even a barrier to scientific and engineering discovery, especially when the event of interest is extreme, rare, or peculiar. To address this challenge, this project will innovate a unified methodological framework that leverages heterogeneous data for speeding up stochastic computational experiments without compromising the accuracy of probabilistic analysis. The framework will include methods for identifying and exploiting a low-dimensional manifold (naturally appearing in science and engineering) of high-dimensional simulation input space to speed up stochastic computational experiments by addressing the curse of dimensionality. For the accelerated probabilistic analysis, asymptotically valid confidence bounds will be constructed to ensure the desired analysis accuracy. The framework will prescribe how to adaptively allocate computational resources for exploring the simulation input space while exploiting the important input manifold to minimize the computational expenditure while maintaining the desired analysis accuracy. The project will validate the methods and verify the open-source software developed for broader impacts, based on two engineering simulation case studies, namely, structural reliability evaluation of a wind turbine and cascading failure analysis of a power grid.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.