CAREER: Integrating Physical Models into Data-Driven Inference

对高维时空系统--例如活体人体生理系统--的个性化评估越来越多地得益于两个领域的并行进步：支持对这些系统的动态行为和机制进行定量理解的计算机建模，以及不断提高可用于分析的测量数据的数量和质量的现代传感器技术。然而，在这两个领域之间存在着一个在许多应用领域中普遍存在的差距：计算机建模的当前状态通常与单个系统的特定测量分离，而个性化的数据驱动分析通常难以适应现实的领域上下文。该项目旨在通过研究和开发新的方法、算法和软件来弥合这一差距，这些方法、算法和软件将使复杂的领域知识--通过计算机模拟领域物理模型产生--集成到数据驱动的推理过程中。这项研究的首要主题是灵活性和稳健性。具体地说，它解决了以下三个挑战：1)允许即插即用地包括迎合不同效率和精度需求的域物理模型；2)通过利用高维系统中的低维结构来进一步克服域物理模型中缺乏测量和潜在误差；以及3)使得能够健壮地适应潜在存在于域物理模型中的时变误差。该项目的主要应用是使用非侵入性生物医学和生理数据对体内心血管系统进行个性化建模，以改进心脏病的预防、诊断和治疗。该项目的成果将在理论上、算法上和计算上为统计推断的基础做出贡献，并扩展到广泛的应用，如肿瘤建模、气候建模、系统生物学和金融。此外，该项目将提供公开可用的多核/图形处理器软件，该软件将封装所开发的最有效的算法。这些工具包将有助于国家对非侵入性医学和医疗保健的努力，同时支持涉及数据驱动建模和推理的众多科学应用程序。该项目还包括一个综合教育和推广计划，以促进跨学科研究培训，并增加STEM学科中代表性不足的群体的参与。它包括：1)在研究生和本科教育中发展和评价“边做边学”的概念；2)对从研究生到高中的学生进行研究性培训，重点是在早期阶段让妇女和代表性不足的学生参与；以及3)向K-12学生和辅助医疗界开展更广泛的外联活动。通过PI与RIT、当地学区和社区大学提供的不同项目之间的持续伙伴关系，加强了代表不足的妇女、K-12和辅助医疗团体的参与。

Individualized assessment of high-dimensional spatiotemporal systems - such as in-vivo human physiological systems - has been increasingly enabled by paralleled advances in two fields: computer modeling that supports quantitative understanding of the dynamic behavior and mechanism of these systems, and modern sensor technologies that continuously improve the quantity and quality of measurement data available for analysis. There is, however, a gap between the two fields that is ubiquitous in many application domains: the current state of computer modeling is generally decoupled from specific measurements of an individual system, while individualized data-driven analysis often struggles for realistic domain contexts. This project aims to bridge this gap by investigating and developing new methodologies, algorithms, and software that will enable the integration of complex domain knowledge - yielded by computer simulation of domain physical models - into the process of data-driven inference. The overarching theme of this research is flexibility and robustness. Specifically, it addresses the following three challenges: 1) to enable a plug-and-play inclusion of domain physical models catering to different efficiency vs. accuracy needs; 2) to further overcome the lack of measurements and potential errors in domain physical models by exploiting the low-dimensional structure in high-dimensional systems; and 3) to enable a robust adaptation of the time-varying error that potentially exists in domain physical models. The driving application of this project is individualized modeling of in-vivo cardiovascular systems - using noninvasive biomedical and physiological data - for improved prevention, diagnosis, and treatment of heart diseases. The outcome of this project will contribute theoretically, algorithmically, and computationally to the foundations of statistical inference, and extend to a wide range of applications such as tumor modeling, climate modeling, systems biology, and finance. In addition, this project will deliver publicly-available multicore/GPU software that will encapsulate the most effective algorithms developed. These toolkits will contribute to the national effort toward noninvasive medicine and healthcare, while supporting numerous scientific applications involving data-driven modeling and inference. This project also includes an integrated educational and outreach program to foster interdisciplinary research training and to increase participation of underrepresented groups in STEM disciplines. It includes: 1) development and evaluation of "learning-by-doing" concept in graduate and undergraduate education; 2) research training for students from graduate to high-school levels, with a focus on engaging women and underrepresented students at an early stage; and 3) broader outreach activities to area K-12 students and Paramedic communities. The participation of women, underrepresented, K-12, and Paramedic groups are reinforced through continued partnerships between the PI and different programs offered in RIT, local school district, and community college.