Publications related to Optimal control of geodesics in Riemannian manifolds

Escaping from saddle points on Riemannian manifolds

Nicolas Henri Bernard Flammarion, Yue Sun

We consider minimizing a nonconvex, smooth function f on a Riemannian manifold M. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manif ...

2019

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromi ...

2019

Renormalization of quantum field theory on Riemannian manifolds

In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allow ...

2019

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Dynamical Reduced Basis Methods for Hamiltonian Systems

Cecilia Pagliantini

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...

2019

A finite element framework based on bivariate simplex splines on triangle configurations

Xiaodong Wei, Juan Cao

Recently, triangle configuration based bivariate simplex splines (referred to as TCB-spline) have been introduced to the geometric computing community. TCB-splines retain many attractive theoretic properties of classical B-splines, such as partition of uni ...

ELSEVIER SCIENCE SA2019

Numerical Approximation Of Orthogonal Maps

Marco Picasso, Alexandre Caboussat, Dimitrios Gourzoulidis

Orthogonal maps are the solutions of the mathematical model of paper-folding, also called the origami problem. They consist of a system of first-order fully nonlinear equations involving the gradient of the solution. The Dirichlet problem for orthogonal ma ...

2019

Current and pressure gradient triggering and nonlinear saturation of low-n edge harmonic oscillations in tokamaks

Jonathan Graves, Wilfred Anthony Cooper, Antoine Pierre Emmanuel Alexis Merle, Daniele Brunetti, Andreas Kleiner

Non-axisymmetric free-boundary equilibrium computations are shown to represent nonlinearly saturated external kink modes and external kink-like sidebands coupled to pressure-driven infernal modes. In this study of edge harmonic oscillations associated with ...

IOP PUBLISHING LTD2019

A Moment‐Based Kinetic Model for Efficient Numerical Implementation

Paolo Ricci, Rogério Manuel Cabete De Jesus Jorge, Baptiste Jimmy Frei

A drift-kinetic and a gyrokinetic model able to describe the plasma dynamics in the tokamak periphery are presented, which take into account electromagnetic fluctuations at all relevant scales, allowing for comparable amplitudes of background and fluctuati ...

2019

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Annalisa Buffa, Rafael Vazquez Hernandez

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10, 12, 11], optimal convergence rates of the AIGM can be proved when suitable approximation cla ...

2019

Optimal control of geodesics in Riemannian manifolds

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Escaping from saddle points on Riemannian manifolds

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Renormalization of quantum field theory on Riemannian manifolds

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Dynamical Reduced Basis Methods for Hamiltonian Systems

A finite element framework based on bivariate simplex splines on triangle configurations

Numerical Approximation Of Orthogonal Maps

Current and pressure gradient triggering and nonlinear saturation of low-n edge harmonic oscillations in tokamaks

A Moment‐Based Kinetic Model for Efficient Numerical Implementation

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Renormalization of quantum field theory on Riemannian manifolds

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Escaping from saddle points on Riemannian manifolds

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Dynamical Reduced Basis Methods for Hamiltonian Systems

A finite element framework based on bivariate simplex splines on triangle configurations

Current and pressure gradient triggering and nonlinear saturation of low-n edge harmonic oscillations in tokamaks

Numerical Approximation Of Orthogonal Maps

A Moment‐Based Kinetic Model for Efficient Numerical Implementation