Many industrial processes belong to distributed parameter systems (DPS) that have strong
spatial–temporal dynamics. Modeling of DPS is difficult but essential to simulation, control …

In this paper we derive a posteriori error estimates for space-time finite element
discretizations of parabolic optimization problems. The provided error estimates assess the …

There is tremendous potential in using neural networks to optimize numerical methods. In
this paper, we introduce and analyze a framework for the neural optimization of discrete …

We present an approach for efficient numerical solution of optimization problems governed
by parabolic partial differential equations. The main ingredients are: space-time finite …

The least-squares support vector machine (LS-SVM) has been successfully used to model
nonlinear time dynamics; however, it does not have the capability to handle space …

PDE-constrained optimization refers to the optimization of systems governed by PDEs. The
simulation problem is to solve the PDEs for the state variables (eg, displacement, velocity …

We consider the calibration of parameters in physical models described by partial differential
equations. This task is formulated as a constrained optimization problem with a cost …

The Green function of the Poisson equation in two dimensions is not contained in the
Sobolev space H^1(Ω) such that finite element error estimates for the discretization of a …

We develop a priori error analysis for the finite element Galerkin discretization of elliptic
Dirichlet optimal control problems. The state equation is given by an elliptic partial …

In this paper we consider a problem of initial data identification from the final time
observation for homogeneous parabolic problems. It is well-known that such problems are …