arXiv subjects

Ömür Uğur

Publications and source records attributed to Ömür Uğur.

3 recordsLinked to original sources

arXiv2026

A physics-informed SUPG-stabilized finite element framework with shock-capturing for simulating inviscid high-speed flows around a cylinder

This study presents a hybrid computational framework for simulating non-reacting inviscid high-speed flows of nitrogen gas (N$_2$) around a circular cylinder. Owing to the strongly convection-dominated nature of the compressible Euler equations, the compressible-flow streamline-upwind/Petrov--Galerkin (SUPG) formulation is combined with the YZ$β$ shock-capturing technique to stabilize the finite element discretization in the presence of strong discontinuities. Building upon the stabilized solution, a physics-informed neural network (PINN) is employed as a post-processing correction stage (\underline{P}INN-\underline{A}ugmented \underline{S}UPG with \underline{S}hock-\underline{C}apturing---PASSC). The network is anchored to the finite element solution through a shock-weighted data-consistency loss, while the governing equations are enforced in a conservative space--time control-volume form supplemented by macroscopic conservation windows, an entropy-admissibility penalty, and the boundary conditions of the underlying problem. Two-dimensional simulations are performed for free-stream Mach numbers ranging from $2.0$ to $12.0$, and the results are assessed against analytical normal-shock and stagnation relations, the semi-empirical Billig correlation, and reference solutions from the literature. The correction is designed to improve the numerical representation of shocks by reducing localized discretization-induced oscillations and mesh-scale serrations while preserving the agreement of the stabilized solution with the analytical and semi-empirical reference quantities.

physics.flu-dyn↗

arXiv2026

Physics-informed post-processing of stabilized finite element solutions for transient convection-dominated problems

The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often generate spurious oscillations, requiring advanced stabilization techniques. However, even stabilized finite element methods may require additional regularization to accurately resolve localized steep layers. On the other hand, standalone physics-informed neural networks (PINNs) struggle to capture sharp solution structures in convection-dominated regimes and typically require a large number of training epochs. This work presents a hybrid computational framework that extends the PINN-Augmented SUPG with Shock-Capturing (PASSC) methodology from steady to unsteady problems. The approach combines a semi-discrete stabilized finite element method with a PINN-based correction strategy for transient convection-diffusion-reaction equations. Stabilization is achieved using the Streamline-Upwind Petrov-Galerkin (SUPG) formulation augmented with a YZbeta shock-capturing operator. Rather than training over the entire space-time domain, the neural network is applied selectively near the terminal time, enhancing the finite element solution using the last K_s temporal snapshots while enforcing residual constraints from the governing equations and boundary conditions. The network incorporates residual blocks with random Fourier features and employs progressive training with adaptive loss weighting. Numerical experiments on five benchmark problems, including boundary and interior layers, traveling waves, and nonlinear Burgers dynamics, demonstrate significant accuracy improvements at the terminal time compared to standalone stabilized finite element solutions.

math.NA↗

arXiv2023

The QLBS Model within the presence of feedback loops through the impacts of a large trader

We extend the QLBS model by reformulating via considering a large trader whose transactions leave a permanent impact on the evolution of the exchange rate process and therefore affect the price of contingent claims on such processes. Through a hypothetical limit order book we quantify the exchange rate altered by such transactions. We therefore define the quoted exchange rate process, for which we assume the existence of a postulated hedging strategy. Given the quoted exchange rate and postulated hedging strategy, we find an optimal hedging strategy through batch-mode reinforcement learning given the trader alters the course of the exchange rate process. We assume that the trader has its own concept of fair price and we define our problem as finding the hedging strategy with much lower transaction costs yet delivering a price that well converges to the fair price of the trader. We show our contribution results in an optimal hedging strategy with much lower transaction costs and convergence to the fair price is obtained assuming sensible parameters.

q-fin.MF↗