Related papers: Adaptive Interpolatory MOR by Learning the Error E…

This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…

Derivative-Free optimization (DFO) focuses on designing methods to solve optimization problems without the analytical knowledge of gradients of the objective function. There are two main families of DFO methods: model-based methods and…

Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…

In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in [9] for adaptive interpolation by radial basis functions (RBFs). More precisely, we introduce in the context of sub-sampling methods a maximum profile…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most of the…

Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…

Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…

Frequency domain sweeps of array antennas are well-known to be time-intensive, and different surrogate models have been used to improve the performance. Data-driven model order reduction algorithms, such as the Loewner framework and vector…

A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…

Rule ensembles are designed to provide a useful trade-off between predictive accuracy and model interpretability. However, the myopic and random search components of current rule ensemble methods can compromise this goal: they often need…

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

Conventional time-series forecasting methods typically aim to minimize overall prediction error, without accounting for the varying importance of different forecast ranges in downstream applications. We propose a training methodology that…

First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…

The quality of datasets is a critical issue in big data mining. More interesting things could be mined from datasets with higher quality. The existence of missing values in geographical data would worsen the quality of big datasets. To…

Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…

Transformer-based Large Language Models (LLMs) struggle with inputs exceeding their training context window due to positional out-of-distribution (O.O.D.) issues that disrupt attention. Existing solutions, including fine-tuning and…

Decomposition has become an increasingly popular technique for evolutionary multi-objective optimization (EMO). A decomposition-based EMO algorithm is usually designed to approximate a whole Pareto-optimal front (PF). However, in practice,…

We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is…