Collaborative Research: Cost-Efficient and Confident Sampling for Modern Scientific Discovery

现在有了新的高质量数据来源，可以解决一系列迫切需要解决的科学和工程问题，以提高我们的生活质量。然而，这种高保真度的数据往往来自昂贵的模拟，限制了可用数据。因此，开发具有成本效益的采样方法，并结合严格的、数据驱动的误差测量结果模型是至关重要的。这个项目结合了计算数学和统计学的思想来发现这些成本效益和自信的抽样方法。参与该项目的学生将被教育成为下一代以科学为基础的计算研究人员，他们可以熟练地在不同和多学科的科学团队中工作，推动科学知识的前沿。该项目开发了一个框架，其特点是方法（包括支持理论和算法），将经典的低差异（即高度分层）采样技术扩展到现代科学问题中遇到的各种具有挑战性的场景，包括经济高效的贝叶斯推断、大规模数据的高效子采样、多保真度建模和密度估计。这些方法包括昂贵的后验贝叶斯抽样、自适应多保真算法、大数据子抽样以及分布、密度和分位数估计。主要的重点是证明这些方法在加速科学发现方面的有效性，特别是对于pi正在进行的重离子碰撞和无人飞行器实时发动机控制研究的合作，以及将在项目中发展的新合作。这种合作将通过我们的开源Python QMC库QMCPy进一步加强。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。

There are now novel sources of high-quality data for tackling a broad array of pressing scientific and engineering problems that need to be solved to improve our quality of life. However, such high-fidelity data often comes from costly simulations, limiting the available data. Thus, developing cost-efficient sampling methods combined with rigorous, data-driven error measures for the resulting models is critically important. This project combines ideas from computational mathematics and statistics to discover these cost-efficient and confident sampling methods. Students involved in this project will be educated to become the next generation of science-based computational researchers who can adeptly work in diverse and multi-disciplinary scientific teams pushing forward the frontiers of scientific knowledge. This project develops a framework featuring methodologies (with supporting theory and algorithms) that extend classical low discrepancy (i.e., highly stratified) sampling techniques for a broad range of challenging scenarios encountered in modern scientific problems, including cost-efficient Bayesian inference, efficient subsampling of massive data, multi-fidelity modeling, and density estimation. These methodologies include Bayesian sampling for expensive posteriors, adaptive multifidelity algorithms, big data subsampling, and distribution, density, and quantile estimation. The major emphasis is to demonstrate the effectiveness of these methods for accelerating scientific discoveries, especially for the PIs’ ongoing collaborations on the study of heavy-ion collisions and real-time engine control of unmanned aircraft vehicles, but also for new collaborations that will be developed over the project. Such collaborations will be further strengthened via our open-source Python QMC library QMCPy.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.