Publications

1. Ata O., Aygun A., Warburton T. Karakus A. (2026). Implicit large eddy simulation of nearly incompressible flows with a discontinuous Galerkin-Boltzmann formulation. Physics of Fluids 38 (5), 055134 (Publisher) (arXiv)
2. Aygun A., Karakus A. (2024). Physics-Informed Neural Networks for Weakly Compressible Flows Using Galerkin-Boltzmann Formulation. Physics of Fluids 36 (11), 117125. (Publisher) (arXiv)
3. Aygun A., Maulik R., Karakus A. (2023). Physics-Informed Neural Networks for Mesh Deformation Problems with Exact Boundary Enforcement. Engineering Applications of Artificial Intelligence, 125, 106660. (Publisher), (arXiv)
4. Aygun A., Karakus A. (2022). Physics-Informed Neural Networks for Two Dimensional Incompressible Thermal Convection Problems. Journal of Thermal Science and Technology, 42(2), 221-232. (Publisher), (arXiv)

Preprints

1. Kaya F., Koc B., Aygun A., Ata O. Karakus A. (2026). Hybrid ROM-PINN Framework for Closure Modeling in Convection-Dominated Systems. arXiv:2603.01998

Conference Proceedings and Talks

1. Aygun A., Ata. O. and Karakus A., 2026, GPU Accelerated Discontinuous Galerkin Solutions of Galerkin-Boltzmann Formulations for Nearly Incompressible Flows on Moving Meshes. SIAM Conference on Parallel Processing for Scientific Computing (PP26), Berlin, Germany.
2. Aygun A., Ata. O. and Karakus A., 2025, Physics-Informed Neural Networks for Heat Transfer and Fluid Flow problems. 15th International Conference on Computational Heat and Mass Transfer, Antalya, Turkey.
3. Aygun A. and Karakus A., 2025, Discontinuous Galerkin Solutions of Moving Boundary Problems Using Arbitrary Lagrangian-Eulerian Method on GPUs. SIAM CSE25, Fort Worth, Texas, USA.
4. Tasdelen A.S., Aygun A. and Karakus A., 2023, Remin: A Physics-Informed Neural Network framework and its Application to Thermal Convection Problems. 24th Congress on Thermal Science and Technology, Ankara, Turkey.
5. Aygun A. and Karakus A., 2023, Physics-Informed Neural Networks for Mesh Deformation Problems with Exact Boundary Enforcement. SIAM CSE23, Amsterdam, The Netherlands.
6. Aygun A. and Karakus A., 2022, Physics-Informed Neural Networks to Solve 1D Euler Equations, National Conference of Aerospace, Izmir, Turkey (Virtual).

Thesis

1. 2023 MSc Thesis: Physics-Informed Neural Networks for Computational Fluid Dynamics