CAREER: Integrating Physical Models into Data-Driven Inference

个体化评估高维时空系统-如在体内人体生理系统-已越来越多地使两个领域的快速发展：计算机建模，支持定量了解这些系统的动态行为和机制，和现代传感器技术，不断提高的数量和质量的测量数据可用于分析。然而，在许多应用领域中普遍存在的两个领域之间的差距：计算机建模的当前状态通常与单个系统的特定测量解耦，而个性化的数据驱动分析通常难以实现现实的领域上下文。该项目旨在通过调查和开发新的方法，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（由领域物理模型的计算机模拟产生）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鲁棒性。具体而言，它解决了以下三个挑战：1）使域物理模型能够满足不同的效率与精度需求的即插即用包括; 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错误;以及3）实现对域物理模型中潜在存在的时变误差的鲁棒自适应。该项目的驱动应用是体内心血管系统的个性化建模-使用非侵入性生物医学和生理数据-以改善心脏病的预防，诊断和治疗。该项目的成果将在理论、算法和计算方面为统计推断的基础做出贡献，并扩展到肿瘤建模、气候建模、系统生物学和金融等广泛的应用。此外，该项目将提供公开的多核/GPU软件，该软件将封装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。该项目还包括一个综合的教育和推广计划，以促进跨学科研究培训，并增加代表性不足的群体在STEM学科的参与。它包括：1）研究生和本科教育中“边做边学”概念的发展和评估; 2）为从研究生到高中的学生提供研究培训，重点是让女性和代表性不足的学生在早期阶段参与;和3）对K-12地区学生和护理人员社区进行更广泛的外展活动。妇女、代表性不足、K-12和护理人员群体的参与通过PI与RIT、当地学区和社区学院提供的不同方案之间的持续伙伴关系得到加强。

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.