DESCRIPTION :
We are opening a Ph.D. position in computer science as part of the ERC Starting Grant project Incorwave, which aims to develop advanced numerical and mathematical methods for passive seismic imaging. The research will focus on two key-directions: (1) the exploration of mixed-precision arithmetic in the context of high-order discontinuous discretization methods, and (2) the integration of machine learning techniques to complement and enhance traditional deterministic inversion approaches. Low-order arithmetic offers promises of important cost-reduction via the use of GPUs, and is commonly used in learning approaches, it has therefore become a central block of an efficient computational framework. The selected candidate will be able to collaborate closely with experts who will help guide the research direction. This work will contribute to the broader objective of improving passive seismic imaging by developing innovative computational frameworks for inversion. While initial development can
be conducted using standalone toolboxes, the final product should be integrated into the high-performance code hawen (https://ffaucher.gitlab.io/hawen-website/) with the support of the development team, enabling their application to real-world applications.
Mission confiée
The program will be divided into two main phases which corresponds to the mixed-precision arithmetic, and the investigation of learning techniques.
Phase 1: Mixed-precision HDG
The first phase concerns the use of mixed-precision arithmetic for Hybridizable discontinuous Galerkin (HDG) discretization. As the HDG involves several operations of (relatively small) dense matrices, mixed-precision and offloading should be emphasized. The first phase of the project will focus on the use of mixed-precision arithmetic within the framework of Hybridizable Discontinuous Galerkin (HDG) discretizations. Given that HDG methods inherently involve numerous operations on relatively small dense matrices, this phase will emphasize the potential of mixed-precision strategies and hardware offloading (e.g., to GPUs or specialized accelerators) to enhance computational efficiency without compromising numerical accuracy. In particular, since HDG methods rely on high-order polynomial approximations, special attention will be given to optimizing quadrature strategies, as they significantly impact both the performance and accuracy of the overall discretization scheme.
Phase 2: learning techniques in wave modeling and inversion
To address the inverse problem, we currently rely on a deterministic iterative optimization framework, which is computationally intensive as each iteration requires solving a potentially large-scale wave propagation problem. Moreover, the approach offers no guarantees regarding the global optimality of the solution, as we may fall into local minima. The objective of this research axis is to enhance the existing inversion framework by integrating learning-based strategies aimed at (1) reducing the overall computational cost, and (2) improving the quality and robustness of the reconstructed models. In particular, learning-based regularization techniques will be explored to guide the inversion process. For instance, generative models (e.g., variational autoencoders or generative adversarial networks) can be employed to learn low-dimensional priors from data, enabling the inversion to operate within realistic media. This data-driven regularization mitigates the
ill-posedness of the inverse problem.
Principales activités
The work program of the first part is as follow
* Extract a mini-app from Hawen related to the HDG matrix creation. This gives flexibility to the candidate with its own light framework to investigate the code.
* Investigate mixed-precision operations and efficient parallelism for (1) high-order quadrature rules, and (2) HDG dense-matrix operations.
* With the help of the developer's team, propagate the key-finding into the main app Hawen.
We envision the following for the second part:
* Learning-based regularization and their efficient combination with standard algorithm. Use of genetic algorithm to avoid local minima?
* Representation / Improvement of a given reconstruction (considered as an image) from apriori information (the measured data-set, simulations, map of uncertainty).
Code d'emploi : Thésard (h/f)
Niveau de formation : Bac+5
Temps partiel / Temps plein : Plein temps
Type de contrat : Contrat à durée indéterminée (CDI)
Compétences : C ++ (Langage de Programmation), Fortran (Programming Language), Genetic Algorithm, Python (Langage de Programmation), Machine Learning, Graphics Processing Unit (GPU), Julia, Technologies Informatiques, Axé sur le Succès, Innovation, Recherche, Algorithmes, Mathématiques, Simulations, Déchargement, Compétences de Modélisation, Imagerie, Programmation Scientifique
Courriel :
florian.faucher@inria.fr
Téléphone :
0139635511
Type d'annonceur : Employeur direct
