Related papers: Empirical least-squares fitting of parametrized dy…
Within the context of recursive least squares (RLS) parameter estimation, the goal of the present paper is to study the effect of regularization-induced bias on the transient and asymptotic accuracy of the parameter estimates. We consider…
We develop a Levenberg-Marquardt method for minimizing the sum of a smooth nonlinear least-squar es term $f(x) = \tfrac{1}{2} \|F(x)\|_2^2$ and a nonsmooth term $h$. Both $f$ and $h$ may be nonconvex. Steps are computed by minimizing the…
Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…
We develop an efficient numerical method for the probabilistic quantification of the response statistics of nonlinear multi-degree-of-freedom structural systems under extreme forcing events, emphasizing accurate heavy-tail statistics. The…
We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…
Parallel transmission has been a very promising candidate technology to mitigate the inevitable radio-frequency field inhomogeneity in magnetic resonance imaging (MRI) at ultra-high field (UHF). For the first few years, pulse design…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…
Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously…
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…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits…
We propose an SDP-based framework to address the stabilization of input delay systems while taking into account dissipative constraints. A key to our approach is the introduction of the concept of parameterized linear dynamical state…
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental…