CAREER: Scalable Approaches for Large-Scale Data-driven Bayesian Inverse Problems in High Dimensional Parameter Spaces

逆问题是网络基础设施和数学研究中的当代工具，特别是在从观测和实验数据以及模拟和模型推断知识方面。它们在复杂的、自然的、工程的和社会系统的科学发现和决策中无处不在，因此在包括工程数学和物理科学在内的许多学科中都是至关重要的。对于作为设计、控制、发现和决策基础的逆问题，其解必须具有一定程度的置信度。尽管在过去的几十年里，反问题的理论和计算算法都取得了进展，但量化反问题解决方案中的不确定性仍然是一个挑战，也是计算科学和工程界面临的一个开放问题。测量和数据量的急剧增加为数据驱动的科学发现带来了希望。然而，许多数据仍然未被使用，因为反演-一种从数据推断知识的系统工具-无法扩展到生成的数据量。本提案发展了计算和数据可扩展的策略，以解决大规模数据驱动的统计逆问题的挑战，以继续科学发现的步伐，促进科学的进步，与NSF的使命保持一致。拟议的综合研究和教育计划为未来STEM劳动力的现代教育和培训提供不确定性量化（UQ）技能；提供可扩展的逆/UQ数学算法/软件，潜在地推进计算科学和工程的前沿；提供逆向/UQ前沿算法/软件，可以潜在地改善石油/天然气的发现，以满足不断增长的能源需求；构成PI？为培养美国科学家、工程师和创新者做出持续贡献，以保持美国在科技领域的全球领导地位；并为大数据/昆士兰大学的研究社区提供更多的领导者/专家。该项目开发了一个综合教育和跨学科研究计划，解决高维参数空间中大数据驱动的大规模不确定性量化（UQ）问题。该项目严格开发了一种随机错配方法，利用极端计算系统有效地减少不断增长的观测数据量。它开发了一种全面的集成转换方法，该方法有可能使用当前和未来的NSF计算基础设施以可扩展的方式解决大规模统计贝叶斯逆问题。提出的跨学科方法的新颖之处在于将随机规划，概率论，并行计算和计算机视觉的进展结合起来，为逆/UQ问题提供了一种新的严格的数据约简方法；大规模贝叶斯反问题的合理有效抽样方法以及实现这些方法的开源软件。这些产品可以使基于传感学科的数学家、科学家和工程师解决具有挑战性的逆/UQ问题，从而带来新的科学发现。选择逆地震波传播作为开发要求高的试验台。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。

Inverse problems are contemporary tools in cyberinfrastructure and mathematical research, especially in inferring knowledge from observational and experimental data together with simulations and models. They are pervasive in scientific discovery and decision-making for complex, natural, engineered, and societal systems, and thus are of paramount importance across many disciplines including engineering mathematical and physical sciences. For inverse problems that serve as a basis for design, control, discovery, and decision-making, their solutions must be equipped with certain degree of confidence. Though the past decades have seen advances in both theories and computational algorithms for inverse problems, quantifying the uncertainty in their solution remains challenging and an open problem facing the computational science and engineering community. The drastic increase in the quantity of measurements and data holds promise for data-driven scientific discoveries. However, much data remains unused as inversion - a systematic tool to infer knowledge from data - is unable to scale up to the quantity of data being generated. This proposal develops computational and data scalable strategies to tackle the challenge of large-scale data-driven statistical inverse problems in order to continue the pace of scientific discoveries and to promote the progress of science, aligned with NSF's mission. The proposed integrated research and education program contributes uncertainty quantification (UQ) skills to modern education and training of future STEM workforce; provides scalable inverse/UQ mathematical algorithms/software that potentially advance the frontiers of computational science and engineering; provides inverse/UQ cutting-edge algorithms/software that can potentially improve oil/gas discovery in order to meet the ever-increasing demand in energy; constitutes the PI?s ongoing contribution to the pipeline of US scientists, engineers, and innovators to maintain the US global leadership in technology and sciences; and educates and supplies additional leaders/experts from underrepresented minorities to Big-Data/UQ research communities.This project develops an integrated education and cross-disciplinary research program that tackles big-data-driven large-scale uncertainty quantification (UQ) problems in high dimensional parameter spaces. The project rigorously develops a randomized misfit approach that exploits extreme computing systems to efficiently reduce the amount of ever-growing observational data. It develops a comprehensive ensemble transform approach that has potential to solves large-scale statistical Bayesian inverse problems in a scalable manner using current and future NSF computing infrastructures. The novelty of the proposed interdisciplinary approach is to bring together advances from stochastic programming, probability theory, parallel computing, and computer vision to produce a new and rigorous data reduction method for inverse/UQ problems; justifiable efficient sampling approaches for large-scale Bayesian inverse problems; and open-source software implementing these approaches. These products can enable mathematicians, scientists, and engineers in sensing-based disciplines to address challenging inverse/UQ problems that can lead to new scientific discoveries. Inverse seismic wave propagation is chosen as the demanding testbed for the developments.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.