Low-rank approximate inverse for preconditioning tensor-structured linear systems

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable distance to the inverse operator. It provides a sequence of approximations that are defined as the projections of the inverse operator in an increasing sequence of linear subspaces of operators. These subspaces are obtained by the tensorization of bases of operators that are constructed from successive rank-one corrections. In order to handle high-order tensors, approximate projections are computed in low-rank Hierarchical Tucker subsets of the successive subspaces of operators. Some desired properties such as symmetry or sparsity can be imposed on the approximate inverse operator during the correction step, where an optimal rank-one correction is searched as the tensor product of operators with the desired properties. Numerical examples illustrate the ability of this algorithm to provide efficient preconditioners for linear systems in tensor format that improve the convergence of iterative solvers and also the quality of the resulting low-rank approximations of the solution

Validation de systèmes de conduite autonome par modèle probabiliste basé sur un dictionnaire

International audienceValidation of autonomous driving systems remains one of the biggest challenges that car manufacturers must tackle in order to provide safe driverless cars. The complexity of this task stems from several factors: the multiplicity of vehicles, embedded systems, use cases, and the high level of reliability that is required for the driving system to be at least as safe as a human driver. In order to circumvent these issues, large scale simulation that reproduces physical conditions is intensively used to test driverless cars. Therefore, this validation step produces a massive amount of data that needs to be processed. In this paper, we present a new method applied to time-series produced by autonomous driving numerical simulations. It is a dictionary-based method that consists in three steps: automatic segmentation of each time-series, regime dictionary construction, and clustering of produced categorical sequences. We present the time-series specific structure and the proposed method's advantages for processing such data, compared to state-of-the-art reference methods

Validation de systèmes de conduite autonome par modèle probabiliste basé sur un dictionnaire

International audienceValidation of autonomous driving systems remains one of the biggest challenges that car manufacturers must tackle in order to provide safe driverless cars. The complexity of this task stems from several factors: the multiplicity of vehicles, embedded systems, use cases, and the high level of reliability that is required for the driving system to be at least as safe as a human driver. In order to circumvent these issues, large scale simulation that reproduces physical conditions is intensively used to test driverless cars. Therefore, this validation step produces a massive amount of data that needs to be processed. In this paper, we present a new method applied to time-series produced by autonomous driving numerical simulations. It is a dictionary-based method that consists in three steps: automatic segmentation of each time-series, regime dictionary construction, and clustering of produced categorical sequences. We present the time-series specific structure and the proposed method's advantages for processing such data, compared to state-of-the-art reference methods