Concept

Inner product space

Related publications (32)

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini, Nicholas Mueller

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Philadelphia2024

The ABCD of topological recursion

Nicolas Gerson Orantin

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...

San Diego2024

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Jan Sickmann Hesthaven, Junming Duan

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

San Diego2023

Positive Definite Completions and Continuous Graphical Models

Kartik Waghmare

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

EPFL2023

Improving the use of the housing stock to reduce its environmental impact

Philippe Thalmann

In the future, the existing housing stock should be improved while less new dwellings are built. This improvement will take the form of energy-efficient renovation as well as by encouraging cohabitation and reducing the amount of living space occupied per ...

Swiss National Science Foundation2023

The first Grushin eigenvalue on cartesian product domains

Joachim Stubbe, Luigi Provenzano, Paolo Luzzini

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

WALTER DE GRUYTER GMBH2023

Asymmetric Construction of alpha,alpha-Disubstituted Piperazinones Enabled by Benzilic Amide Rearrangement

Jieping Zhu, Hua Wu, Yuping He

An unprecedent asymmetric catalytic benzilic amide rearrangement for the synthesis of a,a-disubstituted piperazinones is reported. The reaction proceeds via a domino [4+1] imidazolidination/formal 1,2-nitrogen shift/1,2-aryl or alkyl migration sequence, em ...

WILEY-V C H VERLAG GMBH2023

Leveraging topology, geometry, and symmetries for efficient Machine Learning

Michaël Defferrard

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

EPFL2022

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Daniel Kressner, Ulf David Persson, Alice Cortinovis

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

SIAM PUBLICATIONS2022

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

Alfio Quarteroni, Simone Deparis, Riccardo Tenderini, Stefano Pagani

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...

2022

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