Related papers: Cross-Gramian-Based Model Reduction: A Comparison

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

We analyze a family of Runge-Kutta based quadrature algorithms for the approximation of the gramians of linear time invariant dynamical systems. The approximated gramians are used to obtain an approximate balancing transformation similar to…

This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to…

We consider a compression method for boundary element matrices arising in the context of the computation of electrostatic fields. Green cross approximation combines an analytic approximation of the kernel function based on Green's…

We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…

We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…

Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…

We consider two approaches to balanced truncation of stochastic linear systems, which follow from different generalizations of the reachability Gramian of deterministic systems. Both preserve mean-square asymptotic stability, but only the…

The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for…

This work presents a technique to estimate on-line the inertia of a power system based on ambient measurements. The proposed technique utilizes the covariance matrix of these measurements and solves an optimization problem that fits such…

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…

Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model…

This paper is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly-symmetric stationary…

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Cross-validation is one of the most popular model selection methods in statistics and machine learning. Despite its wide applicability, traditional cross validation methods tend to select overfitting models, due to the ignorance of the…

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…

In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on…

We complement our earlier position-space exploration of a recently proposed S-matrix for transplanckian scattering by a momentum-space analysis. As in the previous paper, we restrict ourselves to the case of axisymmetric collisions of…

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…