This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …

A normalizing flow is an invertible mapping between an arbitrary probability distribution and
a standard normal distribution; it can be used for density estimation and statistical inference …

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

Variational iteration method has been extensively employed to deal with linear and
nonlinear differential equations of integer and fractional order. The key property of the …

This book provides an introduction to some modern computational techniques for
optimization problems governed by partial differential equations (PDEs). The optimization …

In current study, the modified variational iteration algorithm-I is investigated in the form of the
analytical and numerical treatment of different types of nonlinear partial differential …

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 …

The discretisation of the Oseen problem by finite element methods may suffer in general
from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated …

This paper is the second part of our work on a priori error analysis for finite element
discretizations of parabolic optimal control problems. In the first part [SIAM J. Control Optim …

In this article, we motivate, derive, and test effective preconditioners to be used with the
Minres algorithm for solving a number of saddle point systems which arise in PDE …