Related papers: Optimal control for parameter estimation in partia…
Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…
In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in…
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…
We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…
We present a parameter estimation method for nonlinear mixed effect models based on ordinary differential equations (NLME-ODEs). The method presented here aims at regularizing the estimation problem in presence of model misspecifications,…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…
A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…
In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to…
Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics in…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
This paper is devoted to an optimal control problem of fully coupled forward-backward stochastic differential equations driven by sub-diffusion, whose solutions are not Markov processes. The stochastic maximum principle is obtained, where…
There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include…
This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by partial differential equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
In this paper we consider some optimal control problems governed by elliptic partial differential equations. The solution is the state variable, while the control variable is, depending on the case, the coefficient of the PDE, the…