Applied Mathematics, AI, and High-Performance Scientific Computing for Complex Multiscale Systems
I develop advanced mathematical models, high-performance numerical simulation, and AI-driven inverse methods for computational medicine, biomedical systems, fluid mechanics, porous media transport, and industrial-multiscale computational engineering—bridging theory, computation, and real-world impact.
Priority Research Interests
Computational Medicine & Biomedical Simulation. I develop advanced mathematical models, high-performance simulation, and AI-driven inverse methods to analyze physiological systems, medical imaging, and disease mechanisms—supporting next-generation healthcare technologies and precision medicine.
- Biomedical modeling & simulation for cardiovascular systems, tissue transport, and medical imaging
- Computational physiology and multiscale biological transport
- Medical imaging & inverse modeling (regularized reconstruction, wavelets, meshless discretization)
- Computational biomedicine integrating mechanistic models with data-driven inference
Professional Overview
I am an Applied Mathematician, Engineering Scientist, and Civil Engineer with extensive experience in applied mathematics and mathematical modeling, scientific computing and numerical methods, and computational engineering. My research is best summarized as the development of novel numerical methods— combined with classical tools of applied mathematics—to solve physical and biomedical problems of current interest, including fluid mechanics, porous media, inverse problems, and computational medicine.
I earned my Ph.D. in Mathematics from Virginia Polytechnic Institute and State University (Virginia Tech), one of the premier institutions in applied and computational mathematics. My academic and research appointments have included Brown University and the University of Maryland (Research Associate Scientist), and faculty positions at Prince Sultan University, Marquette University, and the University of Wisconsin–Milwaukee. Across these roles, I have led and contributed to interdisciplinary efforts spanning modeling, simulation, and data-driven scientific computing.
Research Expertise
Modeling, Physics, and Engineering
- Applied Mathematics and Mathematical Modeling
- Differential Equations and Computational Physics
- Fluid Dynamics and Multiphase Flow Simulation
- Porous Media Transport and Multiscale Systems
- Computational Engineering and Industrial Modeling
- Computational Medicine & Biomedical Simulation
Computation, Data, and AI
- Scientific Computing and Numerical Methods
- High-Performance Computing and Parallel Simulation
- Parallel scientific computing & high-performance numerical simulation
- Machine Learning for Scientific and Engineering Applications
- Machine Learning (Deep Learning) for Scientific Computing (physics-informed + data-driven)
- Data Science, visualization, and inverse modeling
Research at a Glance
Medical Imaging & Inverse Modeling
Wavelet-based, meshless reconstruction algorithms (e.g., MIT), including regularized inversion for high-resolution conductivity imaging and uncertainty-aware reconstruction.
Porous Media & Multiscale Transport
Volume-averaged, Richards-type macroscopic models capturing unsaturated flow, inter-layer mass exchange, and deformation in multilayered thin swelling porous structures.
CFD, Multiphase Flow & Stability
Hydrodynamic stability, turbulence modeling, interfacial modes, thin-film dynamics, and microchannel flows with rigorous spectral and eigenvalue-based analysis.
Signature Contributions
Wavelet Meshless MIT Imaging (Inverse Problem)
Developing wavelet-based discretization of MIT convolution integrals to reduce reliance on precisely known target boundaries, enabling adaptive spatial resolution. Integrates SVD-based inversion, regularized least squares, and error-aware reconstruction.
- Meshless wavelet discretization of kernels and conductivity fields
- Regularization for underdetermined inversion with limited sensor data
- Applied linear algebra, optimization, and scalable computational workflows
Industrial-Grade Porous Media Modeling (Thin Swelling Layers)
Rigorous volume-averaging upscaling frameworks reducing micro-scale transport to efficient macroscopic models, with closure relations for inter-layer exchange and deformation—supporting fast, reliable simulation for design decisions.
- Unsaturated flow + deformation modeling in multilayer porous structures
- Validated FEM-based simulation pipelines for product-performance prediction
- Extensions to energy systems and other thin porous media applications
Multiphase Microgap Flow: Instabilities & Thin Films
Stability analysis of viscous two-layer flows in microchannels/microgaps using modified Orr–Sommerfeld formulations solved via Chebyshev collocation and QZ eigenvalue methods to predict interfacial instability and thin-film rupture.
- Full eigenspectrum computation; asymptotics matched with numerics
- Mode competition (shear vs interfacial), growth-rate maxima, nonlinear evolution
- Predictive tools relevant to microfluidics, coatings, and thermal systems
Shear-Flow Stability in Complex Fluids
Viscoelastic shear-flow stability (upper-convected Maxwell model), emphasizing inertia–elasticity coupling in transition mechanisms, supported by efficient spectral solvers and validation against asymptotic regimes.
- Spectral/eigenvalue solvers for stability of Poiseuille/Couette/shear layers/jets
- Free-surface and short-wave instability mechanisms in complex fluids
- Rigorous mathematical analysis with high-fidelity computational validation
Computational & Numerical Methods
PDE Solvers and Discretizations
- Finite Difference Methods
- Finite Element Methods (FEM)
- Discontinuous Galerkin Methods (DG)
- Finite Volume Methods (FVM)
- Spectral / pseudospectral methods
- Boundary Element Methods (BEM)
- ENO/WENO high-order methods
- ALE (moving-mesh) formulations
Scientific Computing, HPC, and AI
- Parallel scientific computing and high-performance numerical simulation
- Applied linear algebra: SVD, QZ, regularization, ill-posed inversion
- Optimization, inverse problems, and uncertainty/error-aware modeling
- Machine Learning for Scientific Computing (physics-informed + data-driven)
- Machine Learning for Scientific and Engineering Applications
- Data science and visualization for interpretable computational modeling
Teaching, Mentorship, and Inclusive Excellence
My teaching emphasizes rigor, clarity, and real-world relevance. I integrate computation (MATLAB, Python, and modern simulation tools) with mathematical foundations in Calculus, differential equations, linear algebra, numerical analysis, and modeling. I am committed to accessible STEM pathways and high-impact mentorship—preparing students for graduate study, research careers, and advanced technical roles.
Collaboration and Hiring Interests
I welcome collaborations and professional opportunities in applied mathematics, computational science, biomedical simulation, scientific computing, and engineering modeling. I am particularly interested in roles that value rigorous mathematical modeling, advanced numerical methods, high-performance simulation, and interdisciplinary impact—across academia, national laboratories, healthcare technology, and industry.