Related papers: Reduced basis approximation and a~posteriori error…
This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…
This work presents a method to adaptively refine reduced-order models \emph{a posteriori} without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive $h$-refinement: it enriches the reduced-basis space…
In this study we propose a-posteriori error estimation results to approximate the precision loss in quantities of interests computed using reduced order models. To generate the surrogate models we employ Proper Orthogonal Decomposition and…
We propose a method for variable selection and basis learning for high-dimensional classification with ordinal responses. The proposed method extends sparse multiclass linear discriminant analysis, with the aim of identifying not only the…
In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several…
Accurate estimation of error covariances (both background and observation) is crucial for efficient observation compression approaches in data assimilation of large-scale dynamical problems. We propose a new combination of a covariance…
Data Assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state. This…
Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…
This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…
In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints and bilateral parameter constraints. The approach employs successively enriched Reduced…
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator…
We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…