John Nardini, Department of Applied Mathematics, University of Colorado Boulder
Data-driven modeling for noisy biological data and agent-based Models
I will consider the problem of inferring the dynamics underlying biological data using two case studies in equation learning and topological data analysis. The math biology field presents several exciting challenges for these methods. I will first investigate the performance of equation learning methods in the presence of noisy and sparsely sampled data with application to glioblastoma multiforme, a harmful cancer of the brain. We will use our results to propose suitable times to collect data for informative datasets. In the second case study, I will demonstrate how topology can accurately summarize the time-varying persistent homology of swarming data over multiple scales. This topological approach can outperform more traditional swarm summaries in supervised machine learning tasks.