BiLO: Bilevel Local Operator Learning for PDE inverse problems

no code implementations • 27 Apr 2024 • Ray Zirui Zhang, Xiaohui Xie, John Lowengrub

At the lower level, we train a neural network 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.

Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans

no code implementations • 28 Nov 2023 • Ray Zirui Zhang, Ivan Ezhov, Michal Balcerak, Andy Zhu, Benedikt Wiestler, Bjoern Menze, John Lowengrub

This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion PDE model of GBM growth from a single 3D structural MRI snapshot.