Related papers: Certification of projection-based reduced order mo…

The known a posteriori error analysis of hybrid high-order methods (HHO) treats the stabilization contribution as part of the error and as part of the error estimator for an efficient and reliable error control. This paper circumvents the…

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper…

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

The paper deals with the accuracy of guaranteed error bounds on outputs of interest computed from approximate methods such as the finite element method. A considerable improvement is introduced for linear problems thanks to new bounding…

Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…

Even with the most advanced computational capabilities, high-fidelity (e.g., large-eddy) simulations of large-scale rocket engines remain far out of reach. In the current work, we develop and establish a component-based reduced-order…

Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive…

To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…

In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…

A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…

In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

Complex engineering models are typically computationally demanding and defined by a high-dimensional parameter space challenging the comprehensive exploration of parameter effects and design optimization. To overcome this curse of…

Predictions from machine learning algorithms can vary across random seeds, inducing instability in downstream debiased machine learning estimators. We formalize random seed stability via a concentration condition and prove that subbagging…

Solving high-dimensional dynamical systems in multi-query or real-time applications requires efficient surrogate modelling techniques, as e.g., achieved via model order reduction (MOR). If these systems are Hamiltonian systems their…

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires…