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Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…

Dynamical Systems · Mathematics 2026-01-05 Yevgeniya Filanova , Igor Pontes Duff , Pawan Goyal , Peter Benner

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…

Machine Learning · Computer Science 2023-10-09 Teeratorn Kadeethum , Daniel O'Malley , Youngsoo Choi , Hari S. Viswanathan , Hongkyu Yoon

We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…

Numerical Analysis · Mathematics 2024-03-19 Fernando Henríquez , José Pinto

In this paper, we propose a reduced order approach for 3D variational data assimilation governed by parametrized partial differential equations. In contrast to the classical 3D-VAR formulation that penalizes the measurement error directly,…

Numerical Analysis · Mathematics 2019-05-16 Nicole Aretz-Nellesen , Martin A. Grepl , Karen Veroy

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and…

Numerical Analysis · Mathematics 2014-05-16 Fabien Casenave

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

Numerical Analysis · Mathematics 2023-08-30 Gianluigi Rozza , Martin Hess , Giovanni Stabile , Marco Tezzele , Francesco Ballarin

Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning methods to construct simulators for such systems is a…

Numerical Analysis · Mathematics 2025-01-03 Xili Wang , Kejun Tang , Jiayu Zhai , Xiaoliang Wan , Chao Yang

In the framework of reduced basis methods, we recently introduced a new certified hierarchical and adaptive surrogate model, which can be used for efficient approximation of input-output maps that are governed by parametrized partial…

Numerical Analysis · Mathematics 2023-03-01 Tizian Wenzel , Bernard Haasdonk , Hendrik Kleikamp , Mario Ohlberger , Felix Schindler

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…

Optimization and Control · Mathematics 2021-11-18 Joseph E. Gaudio , Anuradha M. Annaswamy , Eugene Lavretsky , Michael A. Bolender

Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process…

Machine Learning · Computer Science 2025-10-24 Felix Kronenwett , Georg Maier , Thomas Längle

Stochastic inverse problems are generally solved by some form of finite sampling of a space of uncertain parameters. For computationally expensive models, surrogate response surfaces are often employed to increase the number of samples used…

Numerical Analysis · Mathematics 2018-07-04 Steven Mattis , Barbara Wohlmuth

One of the main obstacles to broad application of reinforcement learning methods is the parameter sensitivity of our core learning algorithms. In many large-scale applications, online computation and function approximation represent key…

Artificial Intelligence · Computer Science 2016-10-25 Martha White , Adam White

We consider a class of stochastic programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error. The Clarke subdifferential and surrogate functions are not…

Optimization and Control · Mathematics 2025-05-13 Boyang Shen , Junyi Liu

In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…

Numerical Analysis · Mathematics 2018-02-12 Stefan Hain , Mario Ohlberger , Mladjan Radic , Karsten Urban

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

Optimization and Control · Mathematics 2021-08-25 Kainat Khowaja , Mykhaylo Shcherbatyy , Wolfgang Karl Härdle

In this paper, we leverage ideas from model-based control to address the sample efficiency problem of reinforcement learning (RL) algorithms. Accelerating learning is an active field of RL highly relevant in the context of time-varying…

Systems and Control · Electrical Eng. & Systems 2023-05-23 Ibrahim Ahmed , Marcos Quinones-Grueiro , Gautam Biswas

We introduce a local surrogate approach for explainable time-series forecasting. An initially non-interpretable predictive model to improve the forecast of a classical time-series 'base model' is used. 'Explainability' of the correction is…

Machine Learning · Statistics 2025-01-17 Alfredo Lopez , Florian Sobieczky

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

Numerical Analysis · Mathematics 2019-09-11 Marie Billaud-Friess , Anthony Nouy

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…

Numerical Analysis · Mathematics 2014-05-16 Fabien Casenave , Alexandre Ern , Tony Lelièvre

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Optimization and Control · Mathematics 2014-07-30 Matthew J. Zahr , Charbel Farhat