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

人们发现计算机模型在许多应用中都是有效的，例如气候模拟、人体器官模拟和核物理问题。人们越来越感兴趣的是如何将计算机输出与本地可用的数据相结合，以便快速推断无数的不确定性来源。除了相关的软件开发外，该项目还将开发新的计算技术和灵活的模型构建。由于核物理学、计算机建模和统计理论的跨学科研究，该项目将对科学和社会产生影响。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实践者。快速和可扩展的计算将增强计算机模型在现实世界问题解决中的应用。该项目开发了统计上有效的技术，这些技术在计算上既便宜又实用，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。该方法扩展为一种健壮的建模方法，用于在覆盖大型研究领域时可能发生的模型失败。特别是，研究人员开发了基于高斯过程的模拟器，该模拟器既可以模拟稀疏观察到的计算机模型，也可以模拟解释模型与现实之间差距的未知差异。该方法是贝叶斯，它提供了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）的标准实践。虽然变分贝叶斯在机器学习文献中很流行，但该技术在统计学中并不像基于MCMC的采样技术那样流行。对VB框架的缓慢接受似乎是由于它给建模增加了额外的复杂性和相对未知的理论属性。本项目将发展一种创新的VB算法，以解决目前在计算机模型校准方面的问题，目的是在稳健的建模方法中提高计算可扩展性和可扩展性。研究人员计划为转化研究构建软件，以达到最大影响所需的应用程序。该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。

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 will develop 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 investigators 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 will develop 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. The investigators 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.