A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity

Date

2023-04-01

Author

Toraman, Sıtkı Can
Yücel, Hamdullah

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

225
views

0
downloads

In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum term to minimize the objective functional containing random terms. A full error analysis including Monte Carlo, finite element, and stochastic momentum gradient iteration errors is done. Numerical examples are presented to illustrate the performance of the proposed stochastic approximations in the PDE-constrained optimization setting.

Subject Keywords

Monte Carlo, PDE-constrained optimization, Stochastic momentum, Uncertainty quantification

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142122266&origin=inward
https://hdl.handle.net/11511/101662

Journal

Journal of Computational and Applied Mathematics

DOI

https://doi.org/10.1016/j.cam.2022.114919

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

A SUPG Formulation for Solving a Class of Singularly Perturbed Steady Problems in 2D Cengizci, Süleyman; Uğur, Ömür; Srinivasan, Natesan (2020-09-02) In this presentation, approximate solutions of singularly perturbed partial differential equations are examined. It is a well-known fact that the standard Galerkin finite element method (GFEM) experiences some instability problems in obtaining accurate approximations to the solution of convection-dominated equations. Therefore, in this work, the Streamline-Upwind/Petrov-Galerkin (SUPG) method is employed to overcome the instability issues for the numerical solution of these kinds of problems. Furthermore,...
A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind Kaya, Ruşen; Taşeli, Hasan (2022-01-01) A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are co...
A quadtree-based adaptively-refined cartesian-grid algorithm for solution of the euler equations Bulkök, Murat; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2005) A Cartesian method for solution of the steady two-dimensional Euler equations is produced. Dynamic data structures are used and both geometric and solution-based adaptations are applied. Solution adaptation is achieved through solution-based gradient information. The finite volume method is used with cell-centered approach. The solution is converged to a steady state by means of an approximate Riemann solver. Local time step is used for convergence acceleration. A multistage time stepping scheme is used to ...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
A DRBEM Approach for the STOKES Eigenvalue Problem Tezer, Münevver; Türk, Önder (2016-07-04) In this study, we propose a novel approach based on the dual reciprocity boundary element method (DRBEM) to approximate the solutions of various Steklov eigenvalue problems. The method consists in weighting the governing differential equation with the fundamental solutions of the Laplace equation where the definition of interior nodes is not necessary for the solution on the boundary. DRBEM constitutes a promising tool to characterize such problems due to the fact that the boundary conditions on part or all...

Citation Formats

S. C. Toraman and H. Yücel, “A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity,” Journal of Computational and Applied Mathematics, vol. 422, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142122266&origin=inward.