Related papers: Online adaptive basis construction for nonlinear m…
In this contribution we consider localized, robust and efficient a-posteriori error estimation of the localized reduced basis multi-scale (LRBMS) method for parametric elliptic problems with possibly heterogeneous diffusion coefficient. The…
A comprehensive approach for real-time computations using a database of parameterized linear reduced-order models (ROMs) is proposed. The method proceeds by sampling offline ROMs for specific values of the parameters and interpolating…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
Cardio-mechanical models can be used to support clinical decision-making. Unfortunately, the substantial computational effort involved in many cardiac models hinders their application in the clinic, despite the fact that they may provide…
We study online boosting, the task of converting any weak online learner into a strong online learner. Based on a novel and natural definition of weak online learnability, we develop two online boosting algorithms. The first algorithm is an…
The onerous task of repeatedly resolving certain parametrized partial differential equations (pPDEs) in, e.g. the optimization context, makes it imperative to design vastly more efficient numerical solvers without sacrificing any accuracy.…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
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…
We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted…
Nonlinear and nonaffine terms in parametric partial differential equations can potentially lead to a computational cost of a reduced order model (ROM) that is comparable to the cost of the original full order model (FOM). To address this,…
This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
In aircraft design, structural optimization and uncertainty quantification concerning transonic aeroelastic issues are computationally impractical, because the iterative process requires great number of aeroelastic analysis. Emerging…
Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the…
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally,…
Reduced-order models (ROM) are popular in online motion planning due to their simplicity. A good ROM for control captures critical task-relevant aspects of the full dynamics while remaining low dimensional. However, planning within the…
The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…
The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} portion of the algorithm is a greedy algorithm, requiring…
The goal of a learner, in standard online learning, is to have the cumulative loss not much larger compared with the best-performing function from some fixed class. Numerous algorithms were shown to have this gap arbitrarily close to zero,…
Online Feedback Optimization leverages properties of optimization algorithms to develop controllers for systems with limited model availability, which is often the case in process control. The interplay between the parameters of the chosen…