CAREER: Scalable Algorithms for Nonlinear, Large-Scale Inverse Problems Governed by Dynamical Systems

职业：动态系统控制的非线性、大规模反问题的可扩展算法

• 批准号: 2145845
• 负责人: Andreas Mang
• 金额: $ 50万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2027-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2145845&HistoricalAwards=false
• 关键词: CAREER; Scalable; Algorithms; Nonlinear; Large

Large-scale inverse problems governed by dynamical systems are of paramount importance in numerous scientific disciplines. Examples include geoscience, medicine, climate science, manufacturing, national security, and economics. Inversion is an indispensable tool to infer knowledge from data in a consistent and predictable way, enabling scientific discovery, decision-making, and ultimately dependable model- and data-informed predictions. However, the practical use of inversion remains limited unless uncertainties can be quantified as they propagate through models and algorithms, Uncertainty quantification adds significant mathematical complications and massive computational costs to an already challenging problem. This project will develop a generic mathematical framework for large-scale, statistical inverse problems alongside software infrastructure with algorithms that scale on modern and future computing architectures. It blends mathematical methods and theory with data-intensive applications and good algorithmic practices to advance the frontiers of computational and data-enabled sciences, with the ultimate aspiration to promote data-driven scientific discovery and model-based prediction and by that, science in general. Alongside research activities, an educational and dissemination program is developed to communicate the results under this work to STEM students and researchers, and a broad audience of computational scientists and application specialists. The project will train students in areas that have seen exceptionally high industry demand in the US in recent years, such as optimization, statistical inference, data-enabled science, performance evaluation, and workload characterization. Educational activities include hands-on research experiences for graduate and undergraduate students, explicitly encouraging participation by minorities and underrepresented groups. Public domain software modules will be made available to a broad STEM audience and practitioners. Applications of this work include medicine, imaging, and geosciences.Fundamental mathematical and computational aspects of optimization under uncertainty, statistical inference, and the solution of large-scale inverse problems will be investigated in this project to promote the progress of scientific discovery and data exploration. The overarching aim is the design of fast computational kernels and scalable, black-box algorithms that rigorously follow mathematical and physical principles, have a sound theoretical basis, and provably converge to an optimal solution independent of the problem dimension. This includes the development of adaptive, hierarchical numerical schemes and mixed-precision algorithms, enabling high-accuracy computations if desired, and low-accuracy approximations when possible, targeting high data-throughput applications. The project explores (i) foundational mathematical aspects and the deployment of fast (scalable) algorithms for transport-based variational inference, (ii) the design of problem-informed regularization schemes for nonlinear inverse problems, and (iii) the integration of randomized algorithms and learning for the construction of low-order surrogate models for optimization, inference, sampling, and preconditioning. Effective numerical techniques and computational kernels for a fast evaluation of gradient and curvature information and their approximation are of paramount importance for the designed methodology. The performance will be assessed for parabolic (diffusion-dominated) and hyperbolic (advection-dominated) dynamical systems of varying complexity with applications in computational medicine, climate science, and geoscience.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.

由动力系统控制的大规模反问题在许多科学学科中至关重要。例子包括地球科学、医学、气候科学、制造业、国家安全和经济学。反演是以一致且可预测的方式从数据中推断知识的不可或缺的工具，从而实现科学发现、决策以及最终可靠的基于模型和数据的预测。然而，除非不确定性在通过模型和算法传播时能够被量化，否则反演的实际应用仍然有限。不确定性量化给本已具有挑战性的问题增加了显着的数学复杂性和大量的计算成本。该项目将为大规模统计逆问题开发通用数学框架，以及软件基础设施和可在现代和未来计算架构上扩展的算法。它将数学方法和理论与数据密集型应用和良好的算法实践相结合，以推进计算和数据驱动科学的前沿，最终愿望是促进数据驱动的科学发现和基于模型的预测，从而促进整个科学的发展。除了研究活动之外，还制定了一项教育和传播计划，以便向 STEM 学生和研究人员以及广大计算科学家和应用专家传达这项工作的结果。该项目将在美国近年来行业需求异常高的领域对学生进行培训，例如优化、统计推理、数据支持的科学、绩效评估和工作负载表征。教育活动包括为研究生和本科生提供实践研究经验，明确鼓励少数群体和代表性不足的群体参与。公共领域软件模块将提供给广大 STEM 受众和从业者。这项工作的应用包括医学、成像和地球科学。该项目将研究不确定性下的优化、统计推断和大规模反问题的解决的基础数学和计算方面，以促进科学发现和数据探索的进步。总体目标是设计快速计算内核和可扩展的黑盒算法，这些算法严格遵循数学和物理原理，具有良好的理论基础，并可证明收敛到独立于问题维度的最优解决方案。这包括开发自适应的分层数值方案和混合精度算法，在需要时实现高精度计算，并在可能的情况下实现低精度近似，针对高数据吞吐量应用。该项目探索（i）基础数学方面和基于传输的变分推理的快速（可扩展）算法的部署，（ii）非线性逆问题的问题知情正则化方案的设计，以及（iii）随机算法的集成学习构建用于优化、推理、采样和预处理的低阶代理模型。用于快速评估梯度和曲率信息及其近似的有效数值技术和计算内核对于设计方法至关重要。 该奖项将针对不同复杂性的抛物线（扩散主导）和双曲（平流主导）动力系统及其在计算医学、气候科学和地球科学中的应用进行评估。该奖项反映了 NSF 的法定使命，并被认为值得通过以下方式获得支持：使用基金会的智力价值和更广泛的影响审查标准进行评估。

项目成果

An operator-splitting approach for variational optimal control formulations for diffeomorphic shape matching

微分同胚形状匹配变分最优控制公式的算子分割方法

• DOI: 10.1016/j.jcp.2023.112463
• 发表时间: 2023-11
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Mang, Andreas;He, Jiwen;Azencott, Robert
• 通讯作者: Azencott, Robert

CLAIRE—Parallelized Diffeomorphic Image Registration for Large-Scale Biomedical Imaging Applications

CLAIRE – 用于大规模生物医学成像应用的并行微分同胚图像配准

• DOI: 10.3390/jimaging8090251
• 发表时间: 2022-09-16
• 期刊: Journal of Imaging
• 影响因子: 3.2
• 作者: Himthani, Naveen;Brunn, Malte;Kim, Jae-Youn;Schulte, Miriam;Mang, Andreas;Biros, George
• 通讯作者: Biros, George