CE46 - Modèles numériques, simulation, applications

Adaptive dynamical approximations via parallel tensor methods – ADAPT

Submission summary

ADAPT is a methodological project whose main objective is the setup of a parallel computational framework for adaptive tensor approximations, to be used in high-dimensional problems, and in particular the ones arising in Kinetic Theory and Uncertainty Quantification.
Tensor methods were intensively developed in the last decade since they represent a viable way to mitigate or overcome the curse of dimensionality, that makes the standard discretisations not affordable for high-dimensional problems. However, the tensor definition and the operations needed to solve the problems rely on intrinsically sequential algorithms. Moreover, in realistic problems, the tensor is not given, but it is specified through a set of equations and tensor data. Hence, it is difficult or impossible to assess a priori what format will have the best performances in terms of compression, and given the format, the number of terms to be used in order to ensure a prescribed accuracy on the solution representation.
In the proposed project, parallel tensor methods based on a divide and conquer strategy and avoiding communication will be defined, in order to foster the use of tensor methods within a High Performance Computing paradigm. Second, the goal is to propose methods that adapt dynamically the (hierarchical) tensor structure to enhance the compression while respecting a prescribed accuracy.
The resulting algorithms will be coded in an open source stand alone library, to be developed with the Inria Alpines team.
The two methodological needs addressed in the project make it possible to define parsimonious effective discretisations for high-dimensional problems in realistic contexts. In particular, applications in Kinetic Theory and Uncertainty Quantification will be considered.
In Kinetic Theory the ultimate goal is to propose efficient methods and algorithms, to be applied to several models used in physics and biology and to be used by the different communities. Then, in particular, we aim to perform simulations of electronic transport in semi-conductors in realistic setups. This problem is particularly important in energy production and semiconductor nano-film industrial applications.
The methods and the algorithms introduced will be based on the library developed in the project and will be integrated in the SIMOL code (developed in the Inria Matherials team, for simulations in condensed matter).
Concerning the Uncertainty Quantification, first, a semi-intrusive solver based on adaptive tensor discretisations will be proposed. This is intended to be a general tool to be used by the community and it will be tested on two relevant applications in cardiovascular modeling. The methods proposed will be also integrated in the Felisce code (developed in Inria Reo team, a general finite code for multi-physics).
Second, a particular focus will be put on the Data-Simulation interaction. This amounts to discover the underline structure of a parametric complex system solution by exploiting data coming from sparse, noisy and heterogeneous measurements. This is of the utmost relevance in a biomedical engineering context.

Project coordination

Damiano Lombardi (Centre de Recherche Inria de Paris)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Inria de Paris Centre de Recherche Inria de Paris

Help of the ANR 159,975 euros
Beginning and duration of the scientific project: November 2018 - 48 Months

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