Publications related to Manifold

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland

We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...

OXFORD UNIV PRESS2021

Realizing doubles: a conjugation zoo

Jérôme Scherer

Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...

CAMBRIDGE UNIV PRESS2021

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

Auke Ijspeert, Jonas Buchli, Ludovic Righetti

Oscillators have two main limitations: their synchronization properties are limited (i.e., they have a finite synchronization region) and they have no memory of past interactions (i.e., they return to their intrinsic frequency whenever the entraining signa ...

SIAM PUBLICATIONS2021

Structure-Preserving Reduced Basis Methods For Poisson Systems

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

AMER MATHEMATICAL SOC2021

Efficient implementation of atom-density representations

Michele Ceriotti, Guillaume André Jean Fraux, Till Junge, Félix Benedito Clément Musil, Michael John Willatt, Max David Veit, Alexander Jan Goscinski

Physically motivated and mathematically robust atom-centered representations of molecular structures are key to the success of modern atomistic machine learning. They lie at the foundation of a wide range of methods to predict the properties of both materi ...

2021

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Uniformly perfect finitely generated simple left orderable groups

Yash Lodha

We show that the finitely generated simple left orderable groups G(rho) constructed by the first two authors in Hyde and Lodha [Finitely generated infinite simple groups of homeomorphisms of the real line. Invent. Math. (2019), doi:10.1007/s00222-01900880- ...

CAMBRIDGE UNIV PRESS2021

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Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Collapse-invariant properties of spaces equipped with signals or directions

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Realizing doubles: a conjugation zoo

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

Structure-Preserving Reduced Basis Methods For Poisson Systems

Efficient implementation of atom-density representations

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Uniformly perfect finitely generated simple left orderable groups

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Collapse-invariant properties of spaces equipped with signals or directions

Realizing doubles: a conjugation zoo

Uniformly perfect finitely generated simple left orderable groups

Efficient implementation of atom-density representations

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

Structure-Preserving Reduced Basis Methods For Poisson Systems

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances