Abstract: Understanding and predicting dynamical systems is a central challenge across science and engineering, with critical applications in fields like biomedicine. Traditional modeling approaches offer interpretability and theoretical rigor, while machine learning excels in its flexibility and ability to capture un-discovered patterns. My research bridges these paradigms, developing hybrid frameworks that integrate the strengths of both to achieve scalable, interpretable, and high-fidelity models. In this talk, I will present key methodological contributions toward this vision, followed by applications in biomedicine that demonstrate actionable insights. The method development will focus on 1) a Bayesian framework for learning nonlinear dynamical systems from noisy, partial, and irregular time-series data (with a publicly available JAX package derived from Scott Linderman and Kevin Murphy’s Dynamax), 2) data-free parameter reduction techniques to address un-identifiability within the framework of (1), and 3) continuum attention mechanisms that give rise to Transformer Neural Operators, which learn function-to-function mappings arising in operator-learning and data-assimilation problems. I will then discuss recent applications, including 1) prediction of blood glucose dynamics in people with diabetes that leverages novel hybridizations of expert knowledge and data-driven insights, and 2) characterization of under-explored biological computations performed by reaction kinetics of dimerization networks. Together, these methodological advances and scientific applications help establish a path towards next-generation modeling techniques with transformative potential across disciplines.

Bio: Matthew Levine is a postdoctoral fellow in the Eric and Wendy Schmidt Center at the Broad Institute and an affiliate postdoc with the MIT Uncertainty Quantification (UQ) Group, led by Youssef Marzouk. He earned his PhD in Computing and Mathematical Sciences at Caltech under the supervision of Andrew Stuart, with partial support from an NSF Graduate Research Fellowship, and has a B.A. in Biophysics from Columbia University. His research lies at the intersection of machine learning, dynamical systems, and biomedicine. Matt aims to combine the power of black-box, data-driven learning with the interpretability and transferability of principled physics-based models to drive next-generation advancements in the modeling and prediction of complex systems. For more info: https://mattlevine.netlify.app/