Advances in manufacturing process technology are key ensembles for the production of
integrated circuits in the sub-micrometer region. It is of paramount importance to assess the …

Physics-informed neural network architectures have emerged as a powerful tool for
developing flexible PDE solvers that easily assimilate data. When applied to problems in …

In this paper we present a quasi-optimal sample set for ordinary least squares (OLS)
regression. The quasi-optimal set is designed in such a way that, for a given number of …

In many areas of science and engineering, computer simulations are widely used as proxies
for physical experiments, which can be infeasible or unethical. Such simulations are often …

In this paper, a new non-intrusive method for the propagation of uncertainty and sensitivity
analysis is presented. The method is based on the cut-HDMR approach, which is here …

Gaussian processes are commonly used for modeling the output of deterministic computer
models. We consider the behavior of maximum likelihood estimators (MLEs) of parameters …

In this work, we discuss the problem of approximating a multivariate function by discrete
least-squares projection onto a polynomial space using a specially designed deterministic …

Well-known tools developed for satellite and debris re-entry perform break-up and trajectory
simulations in a deterministic sense and do not perform any uncertainty treatment. The …

The accuracy of metamodelling is determined by both the sampling and approximation. This
article proposes a new sampling method based on the zeros of Chebyshev polynomials to …

A unified framework for surrogate model training point selection and error estimation is
proposed. Building auxiliary local surrogate models over subdomains of the global …