Dr. Wenyuan Liao

My research focuses on developing mathematical and computational methods for inverse problems arising in geophysical imaging, fluid dynamics, and emerging biomedical imaging technologies. These methods enable the recovery of unknown physical parameters from indirect measurements and support improved predictive modelling in complex systems.

Wave equation-based inversion and applications

I have long been dedicated to applying full waveform inversion to seismic imaging, and I have recently begun extending this approach to the inversion of medical data to provide high-resolution images for medical diagnosis.

High performance computing and scientific computation

Many inverse problems and PDE-constrained optimization problems require large-scale computation and a large number of iterations . My research develops efficient and scalable numerical algorithms that leverage modern high-performance computing environments to enable accurate and practical solutions for large scientific and engineering problems in high dimension with large number of unknown parameters.

Numerical methods for PDEs

Partial differential equations (PDEs play a fundamental role in modeling physical processes across science and engineering, yet analytical solutions are often unavailable due to complex parameters and boundary conditions. My research focuses on the development and analysis of higher-order compact numerical schemes for PDEs, including fractional-order models, with an emphasis on adjoint-based methods and PDE-constrained inverse problems.

Numerical methods and applications to geophysics

Deep Neural Networks Method for PDEs and Inverse Problems

Deep neural networks provide a universally adaptive function approximation framework. I am interested in integrating them with full waveform inversion and, based on various convenient development platforms (such as TensorFlow, PyTorch, etc.), developing and researching fast, efficient, and stable parameter estimation and imaging algorithms as well as software packages.

Participation in university strategic initiatives

Energy Innovations for Today and Tomorrow (2013-2021)

Transdisciplinary Research

Energy Futures

Courses

Course number	Course title	Semester
MATH 277	Multivariable Calculus for Engineers and Scientists	Winter 2026
MATH 661.05	Numerical Solution of Differential Equations	Fall 2025

Awards

CAIMS-Fields Industrial Mathematics Prize, Canadian Applied and Industrial Mathematics Society, Fields Institute. 2025
Plenary Speaker, The Third Joint SIAM/CAIMS Annual Meetings, SIAM/CAIMS. 2025
Fellow of IMA - Institute of Mathematics and its Applications, Institute of Mathematics and its Applications, UK. 2026

Publications

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