Unbiasing Truncated Backpropagation Through Time

Truncated Backpropagation Through Time (truncated BPTT) is a widespread method for learning recurrent computational graphs. Truncated BPTT keeps the computational benefits of Backpropagation Through Time (BPTT) while relieving the need for a complete backtrack through the whole data sequence at every step. However, truncation favors short-term dependencies: the gradient estimate of truncated BPTT is biased, so that it does not benefit from the convergence guarantees from stochastic gradient theory. We introduce Anticipated Reweighted Truncated Backpropagation (ARTBP), an algorithm that keeps the computational benefits of truncated BPTT, while providing unbiasedness. ARTBP works by using variable truncation lengths together with carefully chosen compensation factors in the backpropagation equation. We check the viability of ARTBP on two tasks. First, a simple synthetic task where careful balancing of temporal dependencies at different scales is needed: truncated BPTT displays unreliable performance, and in worst case scenarios, divergence, while ARTBP converges reliably. Second, on Penn Treebank character-level language modelling, ARTBP slightly outperforms truncated BPTT

A domain decomposition strategy to efficiently solve structures containing repeated patterns

This paper presents a strategy for the computation of structures with repeated patterns based on domain decomposition and block Krylov solvers. It can be seen as a special variant of the FETI method. We propose using the presence of repeated domains in the problem to compute the solution by minimizing the interface error on several directions simultaneously. The method not only drastically decreases the size of the problems to solve but also accelerates the convergence of interface problem for nearly no additional computational cost and minimizes expensive memory accesses. The numerical performances are illustrated on some thermal and elastic academic problems

On the initial estimate of interface forces in FETI methods

The Balanced Domain Decomposition (BDD) method and the Finite Element Tearing and Interconnecting (FETI) method are two commonly used non-overlapping domain decomposition methods. Due to strong theoretical and numerical similarities, these two methods are generally considered as being equivalently efficient. However, for some particular cases, such as for structures with strong heterogeneities, FETI requires a large number of iterations to compute the solution compared to BDD. In this paper, the origin of the bad efficiency of FETI in these particular cases is traced back to poor initial estimates of the interface stresses. To improve the estimation of interface forces a novel strategy for splitting interface forces between neighboring substructures is proposed. The additional computational cost incurred is not significant. This yields a new initialization for the FETI method and restores numerical efficiency which makes FETI comparable to BDD even for problems where FETI was performing poorly. Various simple test problems are presented to discuss the efficiency of the proposed strategy and to illustrate the so-obtained numerical equivalence between the BDD and FETI solvers

L’action régionale de la Médiathèque de la Cité des sciences et de l’industrie

Depuis son ouverture en 1986, la Cité des sciences et de l’industrie a développé une politique d’action régionale à laquelle la Médiathèque a participé activement en partageant son expérience en matière de constitution et de gestion de fonds scientifiques et techniques avec les professionnels et les ibliothécaires territoriaux

Influence of strain-induced crystallization on the crack driving force in fracture behavior of rubber

International audienceFatigue crack growth resistance increases with the loading ratio due to strain-induced crystallization, even if the peak stress increases. Recent experiments have allowed determination of the strain-induced crystallization (SIC) distribution around a crack tip during uninterrupted fatigue tests. The purpose of this work is to compare spatial distributions of crystallinity in a cracked sample at different elongations between one experiment and simulation results based on our model

Analyse de stabilité d'une nappe fibrée en compression

National audienceL'objectif de ce travail est de modéliser le flambement de nappes fibrées lorsque les câbles sont soumis à une compression axiale. Nous réalisons une analyse de stabilité multi- échelles basée sur le résultat de [1], qui permet de réduire le problème à une cellule élémentaire 2D et de modéliser les modes propres sous forme d'ondes de Bloch. Nous avons choisi de nous placer dans le cas particulier d'une flexion circulaire, mais la méthode proposée est valable pour des chargement plus généraux