Models meet Data

Computational and data-enabled science has become the third pillar of science, completing theory and experimentation. One simplified way to organize the vast number of approaches in this area is by the specificity of the model and the amounts of data required. This idea is often used to categorize approaches as model-based and data-driven approaches. Model-based approaches calibrate unknown parameters in integral or differential equations derived from first principles using measurement data; a process known as data assimilation. Advances in theory and computation have impacted many applications, e.g., numerical weather prediction, medical applications, and storm surge modeling. Due to the high specificity of the modeling, one often needs only a few measurements to predict reliably. By contrast, data-driven approaches use a fairly generic model (e.g., a neural network) that is trained with larger amounts of data. Their use has been successful in applications in which the relevant first principles are ill-defined, or a consistent model is mathematically and computationally intractable for real problems. Despite achieving impressive results, with some notable exceptions, these models are data greedy and often lack understanding and interpretability. In our projects, the teams will apply, compare, and combine data-driven and model-based approaches to solve real problems.


Models Meet Data

Shallow vs. Deep Brain Network Models for Mental Disorder Analysis
Human brains are complex organs with structures, functions, and mechanisms that are still largely unknown to us. Modern neuroscience research aims to help us better understand them. Some recent studies have agreed that interactions among brain regions are related to neural development and mental disorders, and modeling these interactions is a way to gain further insight into how brain regions, neural activity, and disease interact with each other. It is unclear what kind of mathematical models will be most useful for the task of modeling neural activity, so mathematicians with interests in this field are building and testing mathematical models that could progress neuroscience research further. In this project, we explore and analyze different approaches for modeling brain networks, ranging from traditional shallow graph models to modern deep graph neural networks. The goal of these models is to aid in the analysis of mental disorders and diseases such as post-traumatic stress disorder (PTSD), bipolar disorder, depression, and human immunodeficiency virus (HIV). We aim to harness modern computational methods to improve the accuracy of pre-existing models, especially ones that aim to predict whether a patient is diseased or healthy based on brain scan data. We adapt different graph mining techniques for brain networks, statistically and visually analyze the results, and evaluate each model’s classification performance.