Mathematical and numerical modelling of the cardiovascular system is a research topic that
has attracted remarkable interest from the mathematical community because of its intrinsic …

This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …

A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …

In this survey, we describe controlled interacting particle systems (CIPS) to approximate the
solution of the optimal filtering and the optimal control problems. Part I of the survey is …

Solving inverse problems without the use of derivatives or adjoints of the forward model is
highly desirable in many applications arising in science and engineering. In this paper we …

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in
partially, noisily observed dynamical systems and for parameter estimation in inverse …

Mathematical and numerical modelling of the human cardiovascular system has attracted
remarkable research interest due to its intrinsic mathematical difficulty and the increasing …

This paper provides a unifying mean field based framework for the derivation and analysis of
ensemble Kalman methods. Both state estimation and parameter estimation problems are …

Parameters in climate models are usually calibrated manually, exploiting only small subsets
of the available data. This precludes both optimal calibration and quantification of …

Ensemble Kalman inversion is a parallelizable methodology for solving inverse or
parameter estimation problems. Although it is based on ideas from Kalman filtering, it may …