CAREER: Goal-Oriented Variable Transformations for Efficient Reduced-Order and Data-Driven Modeling

职业：面向目标的变量转换，用于高效的降阶和数据驱动建模

• 批准号: 2144023
• 负责人: Boris Kramer
• 金额: $ 61.44万
• 依托单位: University of California-San Diego
• 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: 2022-05-01 至 2027-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2144023&HistoricalAwards=false
• 关键词: CAREER; Goal; Oriented; Variable; Transformations

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). This Faculty Early Career Development Program (CAREER) grant will fund research that enables efficient data-driven modeling of complex natural and engineering processes, including climate dynamics and rocket combustion, thereby promoting the progress of science, and advancing the national prosperity and welfare. Fast and accurate computer simulation of such processes is required for real-time prediction, control intervention, or engineering design. Current techniques for developing simulation models from measurements rely on approximations that may complicate analysis and certification, without a reduction in computational cost or guarantees that underlying physical laws are respected. This project overcomes these challenges by developing a new theoretical approach for systematically uncovering optimal formulations of the system dynamics that are computationally tractable and rigorously certifiable, and that preserve key properties of the physical processes. Such formulations may enable computationally efficient and reliable modeling of chemical and thermal processes or be used to predict long-term ocean flow dynamics that can then be integrated with coupled climate models. In collaboration with industry, this research will advance the design and control of air-conditioning systems by allowing them to use more accurate and faster models of air flow in buildings. Through close integration of research and education, this project will support and engage with first-generation and low-income students from local high schools, community colleges, and universities through outreach, mentoring, and undergraduate research. Free educational material aimed at an undergraduate audience will be disseminated widely to promote training of new generations of engineers with strong computational skills.This research aims to develop the foundations of a new theoretical and computational paradigm that leverages variable transformations to uncover low-dimensional structures in nonlinear dynamical systems and achieve efficient and accurate model reduction that may be certified with respect to stability and structure-preservation. It accomplishes this aim in model- and data-driven settings by exploiting symbolic computing algorithms for systematically identifying transformations and subsequent order-reduction projections that result in optimal quadratic or polynomial models that also preserve symplectic structure for Hamiltonian systems. In the data-driven case, transformations are sought that lead to long-term predictive reduced-order models that are physically interpretable and have favorable numerical properties. Through this effort, new low-dimensional models of the physics of medium-scale applications of chemical reaction dynamics and additive manufacturing will be discovered. The methodological contributions will be assessed on large-scale models of reactive flows and ocean dynamics.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.

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。该学院早期职业发展计划（CAREER）拨款将资助研究，使复杂的自然和工程过程的有效数据驱动建模，包括气候动力学和火箭燃烧，从而促进科学进步，促进国家繁荣和福利。实时预测、控制干预或工程设计都需要对这些过程进行快速准确的计算机模拟。目前用于从测量结果开发仿真模型的技术依赖于近似，这可能使分析和认证复杂化，而没有降低计算成本或保证遵守基本的物理定律。该项目通过开发一种新的理论方法来克服这些挑战，该方法用于系统地揭示系统动力学的最佳配方，这些配方在计算上易于处理，并且可以严格验证，并且保留物理过程的关键特性。这种公式可以使化学和热过程的计算效率和可靠的建模，或用于预测长期的海洋流动动态，然后可以与耦合的气候模型集成。通过与工业界的合作，这项研究将推动空调系统的设计和控制，使他们能够在建筑物中使用更准确、更快速的空气流动模型。通过研究和教育的紧密结合，该项目将通过推广，指导和本科生研究，支持和参与当地高中，社区学院和大学的第一代和低收入学生。针对本科生的免费教育材料将广泛传播，以促进培养具有强大计算能力的新一代工程师。这项研究旨在发展一种新的理论和计算范式的基础，该范式利用变量变换来揭示低成本的计算能力。非线性动力系统中的三维结构，并实现有效和准确的模型简化，可以证明关于稳定性和结构保护。它通过利用符号计算算法系统地识别变换和随后的降阶投影来实现模型和数据驱动设置中的这一目标，这些变换和降阶投影导致最佳的二次或多项式模型，这些模型也保留了Hamilton系统的辛结构。在数据驱动的情况下，寻求转换，导致长期预测的降阶模型，物理上可解释的，并具有良好的数值属性。通过这一努力，将发现化学反应动力学和增材制造的中等规模应用的新的低维物理模型。该奖项反映了NSF的法定使命，并被认为值得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。

项目成果

Learning state variables for physical systems

学习物理系统的状态变量

• DOI: 10.1038/s43588-022-00283-4
• 发表时间: 2022
• 期刊: Nature Computational Science
• 作者: Kramer, Boris