Related papers: Adjoint System in the Shooting Method to Solve Bou…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
Shot boundary detection in video is one of the key stages of video data processing. A new method for shot boundary detection based on several video features, such as color histograms and object boundaries, has been proposed. The developed…
A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are discussed and used to determine the periodic, compressible,…
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by…
In this paper, we propose a numerical method to solve the classic $L^2$-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continuation procedure, to solve the boundary value problem…
In design of optical systems based on LED (Light emitting diode) technology, a crucial task is to handle the unstructured data describing properties of optical elements in standard formats. This leads to the problem of data fitting within…
Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total…
Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or differential-algebraic equations. In this paper, we explore the geometric properties and develop methods…
The classical shooting-method is about finding a suitable initial shooting positions to shoot to the desired target. The new approach formulated here, with the introduction and the analysis of the `target map' as its core, naturally…
In this paper, we present a variational integrator that is based on an approximation of the Euler--Lagrange boundary-value problem via Taylor's method. This can viewed as a special case of the shooting-based variational integrator. The…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used in the equation, which permits to evaluate the wave-function normalization after the…
This paper investigates the randomized version of the Kaczmarz method to solve linear systems in the case where the adjoint of the system matrix is not exact---a situation we refer to as "mismatched adjoint". We show that the method may…
In this work we give an efficient method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of two-point boundary value problems.
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ…
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…