Research programme
Research
Computational and applied mathematics for inverse problems, imaging, and scientific machine learning.
Programme
Recovering information that cannot be measured directly
I work on inverse problems: mathematical problems where indirect measurements are used to reconstruct the quantity that produced them. These problems arise in medical imaging, non-destructive testing, and geophysics. They are usually ill-posed, so small measurement errors can produce large reconstruction errors without suitable regularization.
My approach combines variational methods and regularization theory with numerical optimization and scientific machine learning. My doctoral work developed inversion frameworks for electrical impedance tomography with partial boundary data. My current research extends these ideas to linear and nonlinear inverse problems in medical and subsurface imaging.
Inverse problems and regularization
Variational inversion frameworks, adaptive primal-dual algorithms, and parameter identification for ill-posed and nonlinear problems.
Applications and relevance
Applications: Seismic exploration, anomaly detection in medical imaging, non-destructive testing, and parameter recovery in fluid and heat-flow models.
Industry connection: The same mathematical structure appears in velocity-model building, medical image reconstruction, and engineering model calibration.
Computational imaging and tomography
Reconstruction methods for linear modalities such as CT and MRI, and nonlinear modalities such as EIT, ultrasound tomography, and full waveform inversion.
Applications and relevance
Applications: EIT lung monitoring, sparse-view CT, undersampled MRI, ultrasound tomography, and subsurface velocity recovery.
Industry connection: These reconstruction methods form the computational basis of medical imaging systems and seismic processing workflows.
Scientific machine learning
Physics-informed neural networks, learned regularizers, and GPU-accelerated methods for inverse problems and differential equations.
Applications and relevance
Applications: Accelerating PDE-constrained simulation, learning reconstruction priors from data, and reducing the cost of iterative inversion.
Industry connection: Physics-informed methods and neural operators are studied for computational fluid dynamics, seismic processing, and digital-twin models.
Numerical methods
Finite element methods, iterative solvers, collocation methods, and constrained optimization for differential equations and large-scale computation.
Applications and relevance
Applications: Forward simulation in imaging, fluid dynamics, heat transfer, and the numerical models required for inversion.
Industry connection: Finite element solvers and iterative linear algebra underpin reservoir simulation, structural analysis, and climate models.
Publications
Selected publications
A complete and current citation record is available on Google Scholar.
Approximate numerical solutions of second-order delay differential equations using artificial neural networks
In Neural Networks: Theory, Algorithms, Simulation, and Applications, Springer Nature Switzerland, pp. 91–112
An artificial neural network method for second-order delay differential equations that incorporates the history function directly into the network structure.
DOIA new spectral conjugate gradient method for convex constrained monotone nonlinear equations with application to image restoration
Japan Journal of Industrial and Applied Mathematics, Vol. 43, No. 2
A spectral conjugate gradient algorithm for constrained nonlinear equation systems, tested on image deblurring and compressed signal recovery.
DOIAccelerated double step-length method for solving monotone nonlinear equations with convex-constraint and application
AIMS Mathematics, Vol. 11, No. 4, pp. 10908–10935
An accelerated step-length strategy with convergence analysis and numerical tests for signal reconstruction and machine learning problems.
DOICombined effects of anisotropic permeability, chemical reaction, and dual stratifications on unsteady free convection around a vertical circular cylinder
International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol. 12, No. 1, pp. 104–128
An adaptive collocation study of unsteady free convection in an anisotropic porous medium, including global parameter-sensitivity analysis.
DOINumerical solution of first and higher order IVPs via a single continuous block method
Scientific Journal of Mehmet Akif Ersoy University, Vol. 8, No. 1, pp. 16–34
A seventh-order continuous collocation scheme for solving first and higher order ordinary differential equations.
ArticlePhysics-informed neural networks in iterative form of nonlinear equations for numerical algorithms and simulations of delay differential equations
Physica A: Statistical Mechanics and its Applications
Physics-informed methods for differential equations with time-delay terms, with examples from population dynamics, control, and epidemic modelling.
DOINumerical simulation of time-dependent non-Newtonian compressible fluid flow in porous media: finite element method and time integration approach
International Communications in Heat and Mass Transfer
Finite element simulation of compressible non-Newtonian flow through porous media, with relevance to reservoir simulation and industrial filtration.
DOINumerical assessment of some semi-analytical techniques for solving a fractional-order leptospirosis model
Malaysian Journal of Science
A comparison of semi-analytical methods for a fractional-order epidemiological model of leptospirosis.
DOIPresentations
Selected talks and academic events
Harnessing AI for Innovative and Ethical Use in Academia
ANSHK Research Forum 2025
Industrial and Applied Mathematics
HK-SIAM Conference 2025
Harnessing AI for Innovative Teaching and Ethical Research in Academia
Academic Discourse with MLA, Nigeria
SIAM Student Chapter Workshop
The Chinese University of Hong Kong
Software
Open research software
Implementations and computational experiments connected to my research programme. Development history and current releases are available on GitHub.
EIT Reconstruction Toolkit
Classical and learned reconstruction methods for Electrical Impedance Tomography, including Tikhonov regularization, total variation, and primal-dual algorithms.
Seismic Inversion ML
Physics-informed and data-driven methods for recovering subsurface velocity models from seismic measurements.
Medical Imaging
Compressed sensing and sparse recovery algorithms for accelerated MRI and low-dose CT reconstruction.
Groundwater Detection
Electrical resistivity inversion for identifying water-bearing zones from surface measurements.
Collaborate
Research and technical collaboration
I welcome research collaborations with academic groups, industry teams, and public institutions working on inverse problems, scientific machine learning, computational imaging, or PDE-constrained models.
If your problem involves indirect measurements, large-scale simulation, data-sparse inversion, or the integration of physical models with data, I would be glad to discuss the mathematical and computational requirements.