6 papers
Identifiability Limits of Physics-Informed Inference for Spatial Stochastic Dynamics from Static Snapshots
Rujie Gu, Ray Zirui Zhang, Christopher E. Miles
Despite increasing scale and resolution, many biological measurements remain destructive, revealing only spatial information rather than the dynamics it encodes. By combining flexi…
Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie +1
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while prese…
BiLO: Bilevel Local Operator Learning for PDE Inverse Problems
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie +1
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization…
Individualizing Glioma Radiotherapy Planning by Optimization of Data and Physics-Informed Discrete Loss
Michal Balcerak, Jonas Weidner, Petr Karnakov +8
Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-s…
Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans
Ray Zirui Zhang, Ivan Ezhov, Michal Balcerak +4
Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.…
A Compact Coupling Interface Method with Accurate Gradient Approximation for Elliptic Interface Problems
Ray Zirui Zhang, Li-Tien Cheng
We propose the Compact Coupling Interface Method (CCIM), a finite difference method capable of obtaining second-order accurate approximations of not only solution values but their…