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的科学和工程问题，这些问题需要解决，以提高我们的生活质量。然而，这种高保真数据通常来自昂贵的模拟，限制了可用的数据。因此，开发具有成本效益的抽样方法，并结合严格的数据驱动的误差措施，对所产生的模型至关重要。 该项目结合了计算数学和统计学的思想，以发现这些具有成本效益和自信的抽样方法。 参与该项目的学生将接受教育，成为下一代以科学为基础的计算研究人员，他们可以熟练地在多元化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，其特征在于方法（具有支持理论和算法），扩展了经典的低差异（即，高度分层的）采样技术，用于现代科学问题中遇到的各种具有挑战性的场景，包括具有成本效益的贝叶斯推理，大规模数据的有效子采样，多保真度建模和密度估计。这些方法包括昂贵后验的贝叶斯采样，自适应多保真度算法，大数据子采样以及分布，密度和分位数估计。主要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研究和无人驾驶航空器实时发动机控制的合作，以及将在该项目上开发的新合作。这种合作将通过我们的开源Python QMC库QMCPy得到进一步加强。该奖项反映了NSF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而被认为值得支持。

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.