Related papers: An inverse problem in estimating the time dependen…
This paper investigates using the conjugate gradient iterative solver for ill-posed problems. We show that preconditioner and Tikhonov-regularization work in conjunction. In particular when they employ the same symmetric positive…
In this contribution we show sufficient conditions for simultaneous unique identification of unknown spacewise coefficients and heat source in a parabolic partial differential equation given additional final time measurements. Our approach…
The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different…
Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models,…
This paper presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal norm control problems and optimal time control problems. Controlled systems in this study…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
Here we define and study the properties of retrodictive inference. We derive equations relating retrodiction entropy and thermodynamic entropy, and as a special case, show that under equilibrium conditions, the two are identical. We…
In this work, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
Considering high-temperature heating, the equations of transient heat conduction model require an adaptation, i.e. the dependence of thermophysical parameters of the model on the temperature is to be identified for each specific material to…
Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…
Further development of the method of computational experiments for solving ill-posed problems is given. The effective (unoverstated) estimate for solution error of the first-kind equation is obtained using the truncating singular numbers…
A parametric instability of an incompressible, viscous, and Boussinesq fluid layer bounded between two parallel planes is investigated numerically. The layer is assumed to be inclined at an angle with horizontal. The planes bounding the…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…
Urbanization is the key contributor for climate change. Increasing urbanization rate causes an urban heat island (UHI) effect, which strongly depends on the short- and long-wave radiation balance heat flux between the surfaces. In order to…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…
We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…