Related papers: Inverse Boundary Value and Optimal Control Problem…
A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
We consider the inverse problem of finding matrix valued edge or nodal quantities in a graph from measurements made at a few boundary nodes. This is a generalization of the problem of finding resistors in a resistor network from voltage and…
The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…
We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative…
This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
We formulate the immersed-boundary method (IBM) as an inverse problem. A control variable is introduced on the boundary of a larger domain that encompasses the target domain. The optimal control is the one that minimizes the mismatch…
Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear…
Anomaly detection in complex domains poses significant challenges due to the need for extensive labeled data and the inherently imbalanced nature of anomalous versus benign samples. Graph-based machine learning models have emerged as a…
Uncertainty principles present an important theoretical tool in signal processing, as they provide limits on the time-frequency concentration of a signal. In many real-world applications the signal domain has a complicated irregular…
In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…
This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee…
We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…