Publication

On the stability of Reduced Basis methods for Stokes Equations in parametrized domains

Publications associées (32)

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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

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Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

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Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...

AIP Publishing2022

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

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Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...

Cambridge University Press2022

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The lattice Green's function method (LGFM) is the discrete counterpart of the continuum boundary element method and is a natural approach for solving intrinsically discrete solid mechanics problems that arise in atomistic-continuum coupling methods. Here, ...

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DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

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SIAM PUBLICATIONS2022

High-order geometric integrators for nonadiabatic molecular quantum dynamics and their applications to explore conical intersections

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Accurate simulations of molecular quantum dynamics are crucial for understanding numerous natural processes and experimental results. Yet, such high-accuracy simulations are challenging even for relatively simple systems where the Born-Oppenheimer approxim ...

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Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-cen ...

AIP Publishing2022

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EPFL2021

Model order reduction of flow based on a modular geometrical approximation of blood vessels

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We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

2021

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Yinlin Hu, Wei Wang

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

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Optimal radial basis for density-based atomic representations

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The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

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