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Abstract Proper orthogonal decomposition (POD) is widely used to compute a low-dimensional basis that underpins a subsequent dimension reduction or reduced-order modeling step. POD is data-driven in the sense that it requires a training dataset of …

Abstract In this talk, I review recent efforts on the development of registration methods for parametric model order reduction (MOR), with an emphasis on advection-dominated flows. In computer vision and pattern recognition, registration refers to the …

Abstract We propose a general framework for projection-based model order reduction using self-supervised machine learning [1]. For parametric elliptic equations, this approach is theoretically grounded in Céa’s Lemma. The proposed methodology, called …

Abstract During this talk, I will present the NIRB two-grid method, along with recent extensions applied to the Navier–Stokes equations, aimed at further reducing the computational cost of the algorithm. The NIRB two-grid method, introduced in [1], is …

Abstract In this talk, we present randomized methods that provide high-probability guarantees for the accuracy of reduced-order approximations of parametric partial differential equations (PDEs) with high-dimensional parameter sets. The underlying …

Abstract A broad class of problems in science and engineering involves the repeated solution of partial differential equations (PDEs) for different parameter values. Linear reduced-order models are a powerful tool for reducing the computational cost of …

Abstract The design of smart autonomous mechanical structures capable of performing real-time monitoring of their integrity and taking proactive measures during operation to prevent downtime or failure has become an active area of research. There is a …

Abstract To meet the rigorous demands of Best-Estimate Plus Uncertainty (BEPU) in modern nuclear engineering, it is essential to characterize safety margins and system dynamics with both high fidelity and high efficiency. Building upon foundational …

Abstract This talk presents the Polytope Division Method (PDM), a greedy algorithm for solving high-dimensional configuration optimization problems—such as those arising in model reduction and optimal experimental design—where one seeks an optimal …

Abstract Multi-query simulation settings require efficient surrogates for the underlying processes. We consider a family of kernel-based greedy schemes for approximating the solutions of PDEs, exemplified by elliptic boundary value problems [1]. The …

Abstract Joint work with Romain Verdière (Inria Grenoble) and Olivier Zahm (Inria Grenoble). During this talk, I will present a gradient-enhanced algorithm for high-dimensional function approximation that achieves superior accuracy on small datasets. This …

Abstract Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions over time, but ill-conditioning can make the parameter dynamics non-unique. We interpret this non-uniqueness as a gauge freedom: nullspace …

Abstract Among several recently proposed data-driven Reduced Order Models (ROMs), deep learning-based ROMs (DL-ROMs) have proven to be a successful strategy for constructing non-intrusive, highly accurate surrogates for the real-time solution of …

Documents and media Download the bibliographic references for the lectures Abstract The fourth and final presentation will address an often-asked question, formulated in the title of a contribution by John Römer in 1994: Who made the private tombs of …

Abstract Traditionally, model order reduction for parameterized systems relies on a so-called offline phase, in which reduced approximation spaces are constructed and the reduced parameterized system is built, followed by an online phase, where the …