Research Areas & Expertise
Computational Mathematics: The Foundation of Modern AI
My expertise in computational mathematics forms the mathematical foundation that powers modern artificial intelligence and machine learning systems. The algorithms, numerical methods, and mathematical frameworks I work with are fundamental to AI development, from neural network optimization to large language models (LLMs) and scientific computing applications.
- Computational and Applied Mathematics
- Computer Science, Distributed Computing, AI and Machine Learning
- Numerical Analysis and Scientific Computing
- Partial Differential Equations
- Numerical Solutions to Partial Differential Equations
- Numerical Linear Algebra and Matrices
- Shock Waves, Supersonic Flows, and Aerodynamics
- Wave Propagation and Propagation of Discontinuities
- Computational Fluid Dynamics (CFD)
- Multiscale and Multiphase Systems
- Continuum Mechanics and Elasticity
- Electromagnetics and Semiconductor Physics
- Mathematical Physics and Differential Equations
- Mathematical Biology
- Financial Mathematics and Quantitative Analytics
- Data Analytics and Statistical Modeling
- AI and Machine Learning (Neural Networks, LLMs)
- Large Scale Distributed Computing
- Software Engineering and Reliable System Design
- Semiconductor Research and Nanotechnology
Graduate Research: Numerical Modeling of Shock-Induced Cavity Collapse
My doctoral research focused on advanced computational modeling of shock wave interactions with gaseous cavities in solid matrices, a phenomenon known as cavity collapse in supersonic regimes.
- Cavity Collapse Dynamics: Developed sophisticated mathematical models and computational algorithms for simulating the interaction between strong shock waves and gaseous cavities within solid matrices. Extended computational fluid dynamics (CFD) software frameworks to handle multi-material configurations with robust interface tracking capabilities.
- Discovery of Tall-Cavity Collapse Mechanism: Identified and characterized a novel collapse mechanism resulting from geometric interface variations. This discovery revealed the generation of extremely high pressure and temperature concentrations, sufficient to trigger deflagration-to-detonation transitions and other high-energy phenomena such as Inertial Confinement Fusion (ICF).
Simulation Videos
Publications
Indexed work and citation metrics: Google Scholar, Semantic Scholar.
- Ozlem, M., Schwendeman, D.W., Kapila, A.K., Henshaw, W.D. (2012). "A Numerical Study of Shock-Induced Cavity Collapse." Shock Waves, Springer.
- Ozlem, M. (2007). "Maximizing Minimum Pressure in Fluid Dynamic Bearings of Hard Disk Drives." 23rd Annual Workshop on Mathematical Problems in Industry, University of Delaware.
- Ozlem, M. (2007). "My Air Conditioner? You're Standing on it!" Graduate Student Mathematical Modeling Camp, Rensselaer Polytechnic Institute.
- Patent: "Method and system for template pattern optimization for dsa patterning using graphoepitaxy" (14/723570, Disclosure # YOR820130312, Docket # YOR920150102US1)
Invited Presentations
- "Shock Induced Single Cavity Collapse." Applied Math Days, Rensselaer Polytechnic Institute, March 2010.
- "Numerical Multi-Material Flow and Shock Wave-Cavity Interactions: Effects of Hydrodynamic Void Collapse on Ignition Process." Applied Math Days, Rensselaer Polytechnic Institute, November 2008.
- "Numerical Modeling of Void Collapse: Shock Wave and Gas Cavity Interaction." SIAM Gators Conference, University of Florida, March 2009.
Education
- Ph.D. in Mathematics (GPA: 3.95/4.0)
- M.S. in Applied Mathematics (GPA: 4.0/4.0)
- B.A. in Mathematics and Computer Science (GPA: 3.98/4.0)
AI Science Research
I founded AI Science Research, an independent institute for machine learning theory and practical AI tools.
Current work includes mathematical theory for deep networks and backpropagation, scaling symmetry in deep networks, and exact differentiable extraction of multi-material interfaces, alongside shipped GenAI tools.
Current focus:
- Deep Network Theory: Mathematical analysis of backpropagation and scaling behavior in deep networks, with empirical checks on CNN, MLP, ResNet, and ViT.
- Differentiable Geometry: Exact differentiable extraction of multi-material interfaces.
- Applied Tools: Customer-facing GenAI systems and model-serving frameworks on self-hosted GPUs.
Professional Experience
- Adjunct Professor
- Teaching Assistant
- Research Assistant
- Mathematical Modeling
- Software Engineering and Reliable System Design