Ozan Tuğluk
Assistant Professor
Institute of Applied Mathematics, METU
Home
Research
Publications
Software
Talks
Teaching
Supervision
Contact
📣 Fall 2026: I am teaching IAM 774 Scientific Machine Learning and IAM 574 Mathematical Foundations for Data Analysis. See Teaching.
About
I am an assistant professor at the Institute of Applied Mathematics (IAM) of Middle East Technical University (METU), Ankara.
My research is about certified error bounds for scientific computing: guarantees that tell you how far a computed quantity can be from the true one. I work on error-bounded lossy compression of scientific data with multilevel (multigrid) methods, on machine-checked proofs of these guarantees in Lean 4, on quantum algorithms for computational fluid dynamics, and on direct numerical simulation of turbulence and drag reduction.
Background:
- Now @ METU: Assistant Professor, Institute of Applied Mathematics
- @ Brown University: co-developer of MGARD, the multilevel compression framework, with Mark Ainsworth, and Ben Whitney. Division of Applied Math.
- @ METU: doctoral research in the Department of Engineering Sciences with Hakan I. Tarman on spectral DNS of turbulent pipe flow and drag reduction
- Bunch of other places and roles in other lives, mostly forgotten 🙂
Research
Error-bounded compression of scientific data
Multilevel (multigrid-based) methods for reducing large scientific datasets while keeping the reconstruction error, and the error in derived quantities of interest, under user-specified bounds. This includes the MGARD framework and its use on modern HPC and GPU systems.
Formal verification of numerical methods
Machine-checked proofs, in Lean 4 and Mathlib, of the error guarantees that numerical software relies on, including the effects of floating-point arithmetic.
Quantum algorithms for fluid dynamics
Quantum and hybrid algorithms for linear and nonlinear PDEs arising in fluid flow, with an emphasis on extracting engineering quantities of interest from a quantum state and on honest comparison with classical methods.
Turbulence and drag reduction
Spectral direct numerical simulation of turbulent pipe flow and mechanisms of turbulent drag reduction.
High-order CFD and scientific machine learning
High-order flux-reconstruction solvers on heterogeneous hardware, high-temperature gas thermodynamics, and machine-learning methods for scientific computing.
Selected Publications
Journal articles
- Multilevel Techniques for Compression and Reduction of Scientific Data—The Unstructured Case
M. Ainsworth, O. Tuğluk, B. Whitney, S. Klasky. SIAM Journal on Scientific Computing 42(2), A1402–A1427, 2020. - Multilevel Techniques for Compression and Reduction of Scientific Data—Quantitative Control of Accuracy in Derived Quantities
M. Ainsworth, O. Tuğluk, B. Whitney, S. Klasky. SIAM Journal on Scientific Computing 41(4), A2146–A2171, 2019. - Multilevel Techniques for Compression and Reduction of Scientific Data—The Multivariate Case
M. Ainsworth, O. Tuğluk, B. Whitney, S. Klasky. SIAM Journal on Scientific Computing 41(2), A1278–A1303, 2019. - Multilevel Techniques for Compression and Reduction of Scientific Data—The Univariate Case
M. Ainsworth, O. Tuğluk, B. Whitney, S. Klasky. Computing and Visualization in Science 19, 65–76, 2018.
Conference contributions
- Drag Reduction via Phase Randomization in Turbulent Pipe Flow
O. Tuğluk, H. I. Tarman. ENUMATH 2015, European Conference on Numerical Mathematics and Advanced Applications, Ankara, 2015. - POD Analysis of Drag Reduction in Turbulent Pipe Flow
O. Tuğluk, H. I. Tarman. ECCOMAS 2012, European Congress on Computational Methods in Applied Sciences and Engineering, 2012.
Software
- MGARD: error-bounded multilevel lossy compression and refactoring for scientific data, with CPU and GPU backends, progressive retrieval and quantity-of-interest preservation.
Talks
Reading Engineering Answers Off a Quantum Fluid Solve
- QTADE 2026: Quantum Techniques and Algorithms for Differential Equations, Bilbao, 21–25 September 2026
Drag Reduction via Phase Randomization in Turbulent Pipe Flow
- ENUMATH 2015, Ankara, 2015
POD Analysis of Drag Reduction in Turbulent Pipe Flow
- ECCOMAS 2012
Teaching
Fall 2026, METU Institute of Applied Mathematics
- IAM 774 Scientific Machine Learning: deep-learning foundations, physics-informed neural networks, neural ODEs and operator learning, taught in PyTorch. Reading and correcting AI-generated SciML code is a graded skill.
- IAM 574 Mathematical Foundations for Data Analysis: linear algebra up to the spectral theorem, matrix decompositions, least squares, SVD and PCA, vector calculus and automatic differentiation, continuous optimization, probability and maximum likelihood.
- IAM 590 / 690 Scientific Presentation Seminar: MS and PhD students give two talks each and peer-review every classmate against a shared rubric.
Supervision
I supervise MS theses at the Institute of Applied Mathematics and serve on thesis committees in Scientific Computing and Data and Decision Sciences.
I welcome prospective MS and PhD students interested in compression with guarantees, formal verification of numerical methods, scientific machine learning or quantum algorithms for PDEs. Please get in touch by email.
Contact
Email: tugluk@metu.edu.tr
Address: Institute of Applied Mathematics, Middle East Technical University, 06800 Çankaya, Ankara, Türkiye
GitHub: github.com/tugluk