CBE Doctoral Dissertation Defense: “Scientific Machine Learning for Data‑Limited Biological Dynamics” (Mitchell Daneker)

Abstract: 

Many biological models relevant to clinical and biochemical applications are governed by ordinary and partial differential equations. Traditional numerical methods are well suited for forward simulations of these models; however, patient and system‑specific inference often requires invasive measurements or data that is experimentally inaccessible. As a result, inference tasks involving the reconstruction of state variables and parameters become ill‑posed, rendering traditional numerical approaches impractical. This dissertation addresses how inference and surrogate modeling in these data-limited biological systems should be approached in varying levels of available physical knowledge. Scientific machine learning methods are developed across three modeling regimes defined by whether governing physics is fully known, partially known, or unavailable.
When the governing equations are known but essential measurements are missing, physics‑informed neural networks are used to enforce physical structure while working with limited data. Our warm‑start pretraining strategy improves optimization stability and convergence for accurate reconstruction of hemodynamic flows in the evolving false lumen of aortic dissections. Transfer learning further reduces computational cost and data requirements across changing aneurysm geometries. When governing equations are available but unknown parameters or physics must be inferred, the primary challenge becomes identifiability rather than forward simulation. The Ultradian endocrine model for glucose–insulin interaction is used as a case study to combine systems‑biology‑informed neural networks with structural and practical identifiability analyses for parameter inference and forecasting. This includes cases with non‑constant parameters or partially unknown physics. Finally, when governing equations are unknown, neural operators are used as data‑driven surrogates to represent families of differential equations. We develop a self‑predictive uncertainty quantification framework for operator networks to assess model reliability in downstream Bayesian optimization and active learning tasks. This approach is validated against ensemble and Monte Carlo-based approaches in a time‑dependent 2D advection–diffusion problem, achieving similar performance to these baselines. Its computational advantages are further demonstrated on a wave‑equation example, where traditional uncertainty quantification methods are prohibitively expensive. In this work, we find that physics can be enforced when known, learned when incomplete, and replaced with uncertainty‑aware surrogates when unavailable.

Zoom Meeting ID: 254 427 7959