Related papers: Error Estimation and Stopping Criteria for Krylov-…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we…
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…
Many optimization problems require hyperparameters, i.e., parameters that must be pre-specified in advance, such as regularization parameters and parametric regularizers in variational regularization methods for inverse problems, and…
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using…
A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear naturally, as hundreds or more optimization steps are needed with…
Modern safety-critical systems are heterogeneous, complex, and highly dynamic. They require reliability evaluation methods that go beyond the classical static methods such as fault trees, event trees, or reliability block diagrams.…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
One of the challenges in computational acoustics is the identification of models that can simulate and predict the physical behavior of a system generating an acoustic signal. Whenever such models are used for commercial applications an…
We propose an adaptive randomized truncation estimator for Krylov subspace methods that optimizes the trade-off between the solution variance and the computational cost, while remaining unbiased. The estimator solves a constrained…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
The rapid growth of circuit complexity has rendered Model Order Reduction (MOR) a key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and…
The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair…