TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: John Lowengrub, University of California, Irvine

ABSTRACT: Predicting brain tumor infiltration from MRI scans is crucial for understanding tumor progression and optimizing personalized treatment. While mathematical models of tumor growth provide valuable insights, estimating patient specific parameters from clinical data remains a challenging inverse problem due to sparse and noisy data. We first developed a physics-informed neural network (PINN) approach to estimate model parameters from a single time point using multimodal medical scans. However, we observe soft constraints in PINNs lead to a trade-off between enforcing physical laws and fitting noisy data. To address this limitation, we introduce Bilevel Local Operator Learning (BiLO) for PDE inverse problems. BiLo formulates the inverse problem as a bilevel optimization problem. At the upper level, the data loss is minimized with respect to the PDE parameters. At the lower level, a neural network is trained to locally approximate the PDE solution operator in the neighborhood of a given set of PDE parameters, which enables an accurate approximation of the descent direction for the upper level optimization problem. This eliminates the need to balance fitting data and solving PDEs and improves robustness to sparse and noisy data. Furthermore, by leveraging transfer learning techniques, we extend BiLO to enable efficient sampling and uncertainty quantification within a Bayesian framework. Beyond tumor modeling, many scientific challenges—from modeling stochastic gene expression snapshots to understanding the accumulation of misfolded proteins in Alzheimer’s disease—require fitting increasingly complex mathematical models to ever evolving data. We discuss how our approach can be extended to build an adaptable digital twin framework that adjusts to new data and new models, accelerating scientific discovery. 

HOST: Christopher Curtis