XTRIPODS: Advances and novel applications of closed-loop data assimilation, and educational improvements to data science courses

To adequately warn citizens of impending natural disasters and other events, one needs accurate predictions of weather, but also of wildfire spread, the melting of ice sheets, and even economic growth. Incorporating observable data into a model that is based on physical (or economical) principles is referred to as data assimilation. Unlike some artificial intelligence (AI) algorithms popularized today that are built exclusively from data, data assimilation uses data and scientific knowledge about how the underlying phenomena behaves, resulting in predictions that are interpretable. This grant will support students and faculty researching two data assimilation methods to generate comparisons between the two approaches, and to see what physical circumstances are best modeled by each. Specifically, the investigators are interested in testing these data assimilation methods in the modeling of wildfires. In carrying out this research, the team will involve students, which will help prepare them for careers involving high performance computing and scientific modeling. This funding will also support the creation of two graduate level courses in data assimilation and the mathematical foundations of deep learning. These courses will help students understand the theoretical foundations of data science and to prepare for interdisciplinary careers in which they harness the data revolution. The investigators are developing these courses in collaboration with faculty at the Institute for Foundations of Data Science (IDFS), an NSF-TRIPODS institute which will greatly enhance the experience of the students at Brigham Young University. The primary contribution of the project is an in-depth comparison between the continuous data assimilation (CDA) method developed for partial differential equations, and the conditionally Gaussian Kalman filtering (CGKF) approach. Anecdotally these two methods are applicable on exactly the same physical phenomena, but at the same time fail for the same set of models as well. Using recently developed insights into CDA which tie CDA into an optimization framework reminiscent of a machine learning context, the research team will provide a rigorous comparison between these two methods and identify how the CGKF approach makes use of noise in the system and the observations. These scientific questions will directly complement the development of the courses mentioned above, which will focus on a survey of data assimilation methods, and the optimization routines that determine the identification of deep neural networks that generalize well. The funds will support graduate students who will both work on the active research questions in optimization and data assimilation, and who will assist in the development of the curriculum for both courses. 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.