tech&fest 2025

INRIA - Stage - STATIFY - Towards expressive and tractable surrogate models for large scale inverse problems

Description

Internship Master 2 - Required level: BAC + 4 Who we are? Inria is the French national research institute dedicated to digital science and technology. World-class research, technological innovation and entrepreneurial risk are its DNA. Its 215 agile project teams, most of which are joint with academic partners, involve more than 3,900 scientists in tackling the challenges of digital technology, often at the interface with other disciplines. https://inria.fr/fr Inria is headquartered in Rocquencourt and has 9 research centres. Inria Grenoble is active in the fields of high-performance computing, verification and embedded systems, modeling of the environment at multiple levels, and data science and artificial intelligence. The center is a top-level scientific institute with an extensive network of international collaborations in Europe and the rest of the world. Context: This internship will be done within an ongoing collaboration between Statify Inria team, Ipag laboratory (UGA), and Inria's software development service. Recently Inria’s Statify research team has developed a scientific library based on the so-called xLLiM (Gaussian Locally-Linear Mapping) model, whose target is the resolution of Bayesian inverse problems using physical direct models and simulations from them (https://gitlab.inria.fr/kernelo-mistis/kernelo-gllim-is). In the current implementation, the model is learned from training data using a batch implementation requiring to upload all data into memory, which can limit its use to moderate volumes of data. In terms of expressiveness, the current parameterization is tailored for real-valued data and assumes only two options for the noise part of the model. Contact: in addition to the application to the platform, more information can be requested by contacting florence.forbes@inria.fr, sylvain.doute@univ-grenoble-alpes.fr, stan.borkowski@inria.fr, luc.meyer@inria.fr Objective of the internship: The goal of this internship is to extend the approach with three new functionalities, namely: • Implementation of an incremental learning of the model parameters to allow reading the data sequentially and going beyond hardware limitations, • Extension of the noise modelling to parsimonious parametrization by introducing an additional latent component, • Reformulate the model with complex-valued Gaussian distributions to handle complex valued data. These improvements should be implemented efficiently in C++ and binded to python. These functionalities will have to be developed and then implemented in the current GLLiM frame-work (xLLiM toolbox and application PlanetGLLiM). Validation analyses of the resulting new proce-dures will have to be conducted, assessing their efficiency, accuracy, and scalability. The goal is to test and improve the performance of the GLLiM model in two specific domains: space remote sensing in high-dimensional settings, and medical imaging analysis, with a particular emphasis on Magnetic Reso-nance Imaging (MRI). Assignment: • Mathematical formulation of one or more extensions for the GLLiM method • Implementation of the extensions in Python and in C++ • Performing tests and benchmarks • Integrating your code into the existing xLLiM code base • Testing for non-regression of xLLiM and PlanetGLLiM • Writing documentation Profile and Skills: • Good programming skills in C++ and Python • Familiarity with probability & statistics, eg. Gaussian mixtures, EM algorithm, Bayesian models • Solid understanding of mathematics, especially linear algebra and optimization. • Experience with Github, GitLab, CI, Docker • Analytical and modeling skills: writing specifications, requirement documents, and user docu-mentation Useful link: https://team.inria.fr/statify/ Additional information: - Périod: march 2025 - Duration: 6 months - Location: Montbonnot-Saint-Martin - Contact to Apply: jobs.inria.fr Offre n°2024-08275

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