The Monge–Ampère equation is a full y nonlinear partial differential (PDE) of fundamental importance in analysis, geometry and the applied sciences. In this paper we solve Dirichlet problem associated with using neural networks show that an ansatz deep input convex can be used to find unique solution. As part our analysis study effect singularities, discontinuities noise source function, consid...

Corresponding Author: Shomanov Aday Department of Computer Science, al-Farabi Kazakh National University, Almaty, Kazakhstan Email: [email protected] Abstract: Parallel computations are essential tool in solving large-scale computationally demanding problems. Due to large diversity and heterogeneity of the currently available parallel processing techniques and paradigms it is usually diff...

Dirichlet processes have been very popular in recent years, particularly as prior distributions over unknown probability distributions. The purpose of this review is to provide both an intuition into and a mathematical understanding of Dirichlet processes. We will begin by discussing mixture models as a motivating problem. We will find that our model forces us to make some strong assumptions ab...

Actual performance of sequential decision-making problems can be extremely sensitive to errors in the models, and this research addressed the role of robustness in coping with this uncertainty. The first part of this thesis presents a computationally efficient sampling methodology, Dirichlet Sigma Points, for solving robust Markov Decision Processes with transition probability uncertainty. A Di...

in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to reduction of operator equation pair right hand side function and unknown second normal derivative be sought, design an iterative method at both continuous discrete levels numerical solution problem. Some examples demonstrate that is fourth order convergence. When does not depend on its deri...

This paper introduces a high-order time stepping technique for solving the incompressible Navier–Stokes equations which, unlike coupled techniques, does not require solving a saddle point problem at each time step and, unlike projection methods, does not produce splitting errors and spurious boundary layers. The technique is a generalization of the artificial compressibility method; it is uncon...

Let Ω be an open, simply connected, and bounded region in R, d ≥ 2, and assume its boundary ∂Ω is smooth. Consider solving the eigenvalue problem Lu = λu for an elliptic partial differential operator L over Ω with zero values for either Dirichlet or Neumann boundary conditions. We propose, analyze, and illustrate a ‘spectral method’ for solving numerically such an eigenvalue problem. This is an...