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We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…

Numerical Analysis · Mathematics 2020-10-30 Felix Black , Philipp Schulze , Benjamin Unger

In the context of model order reduction of parametric elliptic problems, we present a methodology to reconstruct a conforming flux from a given reduced solution, that is locally conservative with respect to the underlying finite element…

Numerical Analysis · Mathematics 2019-11-20 Stephan Rave , Felix Schindler

The performance of a reinforcement learning (RL) system depends on the computational architecture used to approximate a value function. Deep learning methods provide both optimization techniques and architectures for approximating nonlinear…

Machine Learning · Computer Science 2021-06-21 John D. Martin , Joseph Modayil

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of…

Numerical Analysis · Mathematics 2025-11-19 Maxime Dalery , Genevieve Dusson , Virginie Ehrlacher , Alexei Lozinski

An element based adaptation method is developed for an anisotropic a posteriori error estimator. The adaptation does not make use of a metric, but instead equidistributes the error over elements using local mesh modifications. Numerical…

Numerical Analysis · Mathematics 2016-12-20 Edward Boey , Yves Bourgault , Thierry Giordano

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…

Numerical Analysis · Mathematics 2023-08-08 Efthymios N. Karatzas , Francesco Ballarin , Gianluigi Rozza

We present an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations, based on elliptic reconstruction techniques [10, 9, 3, 5]. In addition to its original application (to derive…

Numerical Analysis · Mathematics 2019-10-30 Mario Ohlberger , Stephan Rave , Felix Schindler

In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved…

Optimization and Control · Mathematics 2024-02-19 Hendrik Kleikamp

We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…

Optimization and Control · Mathematics 2026-03-10 Mickael Binois , Jeffrey Larson

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop…

Optimization and Control · Mathematics 2023-03-08 Xiaonan Lu , Mark Cannon

A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…

Numerical Analysis · Mathematics 2025-12-01 Philippe-André Luneau , Jean Deteix

Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive…

Numerical Analysis · Mathematics 2026-05-18 Zhiwei Gao , George Karniadakis

Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…

Optimization and Control · Mathematics 2026-05-26 Nataša Krejić , Nataša Krklec Jerinkić , Sanja Rapajić , Luka Rutešić

Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…

Numerical Analysis · Mathematics 2023-08-30 Jonah A. Reeger

One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that…

Machine Learning · Computer Science 2020-11-03 Ilja Kuzborskij , Nicolò Cesa-Bianchi

In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…

Systems and Control · Electrical Eng. & Systems 2025-03-03 Johannes Teutsch , Christopher Narr , Sebastian Kerz , Dirk Wollherr , Marion Leibold

Creating accurate spatial representations that take into account uncertainty is critical for autonomous robots to safely navigate in unstructured environments. Although recent LIDAR based mapping techniques can produce robust occupancy…

Computer Vision and Pattern Recognition · Computer Science 2020-07-02 Anthony Tompkins , Ransalu Senanayake , Fabio Ramos

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Computational Engineering, Finance, and Science · Computer Science 2021-09-24 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi

Model order reduction usually consists of two stages: the offline stage and the online stage. The offline stage is the expensive part that sometimes takes hours till the final reduced-order model is derived, especially when the original…

Numerical Analysis · Mathematics 2023-01-20 Lihong Feng , Luigi Lombardi , Giulio Antonini , Peter Benner

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

Computer Vision and Pattern Recognition · Computer Science 2020-03-23 Huu Le , Christopher Zach