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 …

This work proposes a space--time least-squares Petrov--Galerkin (ST-LSPG) projection
method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear …

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 …

The generalized empirical interpolation method (GEIM) can be used to estimate the physical
field by combining observation data acquired from the physical system itself and a reduced …

Although design optimization has shown its great power of automatizing the whole design
process and providing an optimal design, using sophisticated computational models, its …

Solving the linear system is often the major computational burden when a forward-backward
evolutionary equation must be solved in a problem, where is the so-called all-at-once matrix …

Matrices or operators in two-by-two block form with square blocks arise in numerous
important applications, such as in optimal control problems for PDEs. The problems are …

Hessian preconditioners are the key to efficient numerical solution of large-scale distributed
parameter PDE-constrained inverse problems with highly informative data. Such inverse …

Current state-of-the-art preconditioners for the reduced Hessian and the Karush--Kuhn--
Tucker (KKT) operator for large-scale inverse problems are typically based on …

Optimal control problems for PDEs arise in many important applications. A main step in the
solution process is the solution of the arising linear system, where the crucial point is usually …