Collaborative Research: Variational Inference Approach to Computer Model Calibration, Uncertainty Quantification, Scalability, and Robustness

计算机模型被发现在气候模拟、人体器官模拟和核物理问题等许多应用中都是有效的。人们越来越感兴趣的是，如何将计算机输出与当地可用数据结合起来，进行快速推断，这是无数不确定来源的原因。该项目专注于开发新的计算技术和灵活的模型构建，以及相关的软件开发。该项目将影响科学和社会，因为核物理、计算机建模和统计理论之间的跨学科研究。这项研究将揭示统计特性和计算技术，以改变下一代计算科学家和从业者。快速和可扩展的计算将提高计算机模型在现实世界问题解决中的使用。该项目开发了统计上有效的技术，既计算成本低，又实用，以促进计算机模型输出与本地数据会计模型和参数不确定性的使用。该方法扩展到在覆盖大研究领域时可能发生的模型故障的情况下的健壮建模方法。特别是，研究小组将开发基于高斯过程的仿真器，对稀少观察的计算机模型和解释模型与现实之间差距的未知差异进行建模。这种方法是贝叶斯方法，它提供了对不确定性的自然量化。统计推断的关键工具是用变分贝叶斯(VB)推理的新用法取代马尔可夫链蒙特卡罗(MCMC)的标准做法。虽然变分贝叶斯在机器学习文献中很受欢迎，但该技术在统计学中并不像基于MCMC的抽样技术那样受欢迎。VB框架理解缓慢似乎是因为它增加了建模的复杂性，以及相对未知的理论属性。本项目开发了一种创新的VB算法，以解决目前计算机模型校准中存在的问题，目的是提高健壮建模方法中的计算可伸缩性和可扩展性。我们计划为翻译研究构建软件，以达到所需的应用程序的最大影响。这项研究将提供影响统计计算、贝叶斯统计、计算机建模和校准以及相关应用的变革性研究。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。

Computer models are found to be effective in many applications such as climate modeling, human organ modeling, and nuclear physics problems. There is an increasing interest how the computer output could be coupled with locally available data for quick inference that accounts for the myriad of uncertainty sources. This project focuses on developing new computational techniques and flexible model building in addition to associated software development. The project will impact science and society because of the interdisciplinary research between nuclear physics, computer modeling, and statistical theory. This research will uncover statistical properties and computational techniques to transform the next generation computational scientists and practitioners. The fast and scalable computation will enhance the use of computer models in real world problem solving.This project develops statistically valid techniques that are both computationally inexpensive and practical to facilitate the use of computer model outputs together with local data accounting model and parameter uncertainty. The approach extends to a robust modeling approach in case of model failures that can occur when covering a large study domain. In particular, the research team will develop Gaussian process-based emulator that models both the sparsely observed computer model and the unknown discrepancy that explains the gap between the model and reality. The approach is Bayesian which provides for the natural quantification of uncertainties. The key tool for statistical inference is to replace the standard practice of Markov Chain Monte Carlo (MCMC) with a novel usage of variational Bayes (VB) inference. While the variational Bayes is popular in machine learning literature, the technique is not as popular in statistics as MCMC based sampling techniques. The slow uptake the VB framework seems to be due to the additional complexities it adds to modeling and the relatively uncharted theoretical properties. This project develops an innovative VB algorithm to resolve the present issues in computer model calibration with the aim of improving the computation scalability and extendibility in a robust modeling approach. We plan to build software for translational research to reach the desired applications for maximum impact. The research will provide transformative research that impacts statistical computation, Bayesian statistics, computer modeling and calibration, and related applications.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.