People
PDELab brings together researchers across numerical methods, scientific machine learning, quantum computing, and high-performance computing, all working towards developing simulation tools applicable to real-world problems.
Principal Investigator
Prof. David Del Rey Fernández
Associate Professor, Department of Applied Mathematics, University of Waterloo
Pratt & Whitney Canada Chair in Industrial Artificial Intelligence
David C. Del Rey Fernández is an Associate Professor in the Department of Applied Mathematics at the University of Waterloo, the Pratt & Whitney Canada Research Chair in Industrial Artificial Intelligence, an Associate Director of the Waterloo Institute for Sustainable Aeronautics, and a Research Cluster Lead (Modelling) for the Future Cities Institute. He is also the Graduate Officer of the Computational Mathematics Program and serves on the Advisory Committee for Women in Mathematics at the University of Waterloo and the Canvassing Committee for the Association for Women in Mathematics.
He obtained his PhD from the University of Toronto Institute for Aerospace Studies in 2015 and was a postdoctoral fellow and then research scientist at NASA Langley Research Center through the National Institute of Aerospace from 2016 to 2021. He is a recipient of the CAIMS/PIMS Early Career Award in Applied Mathematics (2024), the Faculty of Mathematics Golden Jubilee Research Excellence Award (2025), and the Ontario Early Researcher Award (2026).
Prof. Del Rey Fernández develops efficient and robust numerical methods and algorithms for a broad class of time-dependent partial differential equations (PDEs), with mathematical guarantees and applicability to high-performance computing systems. His research focuses on mathematically rigorous numerical frameworks, with an emphasis on numerical methods with mathematical guarantees; mesh adaptation; geometric complexity and moving meshes; machine-learning-accelerated numerical methods; machine learning for automation and increased efficiency; and quantum computing algorithms.
His projects involve industry partners such as Pratt & Whitney Canada, Bombardier, NVIDIA and Ansys as well as partnerships with various Canadian municipalities; collaborators in government labs, including NRC, NASA, INRIA, Sandia National Laboratories, and Argonne National Laboratory; and various academic partners.

Postdoctoral Researchers
2
PhD Students
6
Master's Students
11

Alumni
Former members of PDELab and where they are now. Select a year to view its graduates.
20262 graduates
| Name | Degree | Thesis | First Destination |
|---|---|---|---|
| Adam Vieno | MMath in Applied Mathematics | A Reduced-Order Modeling Approach to Shape Optimization Via Time-Dependent Bases | |
| Joshua Joseph George | MMath in Applied Mathematics | A Hamiltonian Systems Approach to Neural Network Optimization | PhD @ University of Michigan |
20251 graduate
| Name | Degree | Thesis | First Destination |
|---|---|---|---|
| Vyom Patel | MMath in Applied Mathematics (Quantum Information) | Quantum Algorithms for PDEs via Summation-by-Parts Discretisations | Research Scientist @ BEIT |
















