Ray Zirui Zhang

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I am an Assistant Professor in the Department of Mathematical Sciences at Worcester Polytechnic Institute (WPI).

Before this role, I was a Visiting Assistant Professor in the Department of Mathematics at the University of California, Irvine, mentored by John Lowengrub. I obtained my Ph.D. at UC San Diego, advised by Li-Tien Cheng, co-advised by Bo Li. Prior to my doctoral studies, I obtained my Bachelor of Engineering degree from the University of Hong Kong.

My research interests lie in scientific machine learning and numerical analysis, with applications in biophysics and cancer research.

Selected Publication

Bilevel Local Operator Learning for PDE Inverse Problems

Bilevel Local Operator Learning for PDE Inverse Problems

Many scientific models contain unknown parameters that must be inferred from data. We develop a neural-network-based method that identifies the best parameters while respecting the underlying model, using a two-level optimization scheme. Try the interactive Physics-Informed Machine Learning Playground to explore PINNs and BiLO on simple ODEs.

Zhang, R.Z., Miles, C.E., Xie, X., Lowengrub, J.S., 2026. BiLO: Bilevel Local Operator Learning for PDE Inverse Problems. Journal of Computational Physics.

Personalized Predictions of Glioblastoma Infiltration

Brain tumors, such as glioblastomas, often grow invisibly beyond what standard MRI scans can show. While this hidden infiltration can’t be fully measured, it follows physical laws of growth and diffusion that can be modeled using partial differential equations (PDEs). By combining these mathematical models with machine learning, we aim to make personalized predictions of tumor spread, paving the way for highly targeted and effective treatment planning.

Zhang, R.Z., Ezhov, I., Balcerak, M., Zhu, A., Wiestler, B., Menze, B., Lowengrub, J.S., 2025. Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans. Medical Image Analysis.

Binary Level Set Method

Binary Level Set Method

Mathematically, a surface is simply a boundary that separates the “inside” from the “outside.” By intelligently flipping grid points between these two states (hence, “binary”), we can efficiently compute optimal surfaces. We use this algorithm to study the interface between water and a protein, which affect the binding process

Zhang, R.Z., Cheng, L.-T., 2023. Binary Level Set Method for Variational Implicit Solvation Model. SIAM J. Sci. Comput.