PhD Position F/M Improving wave modeling and inversion in HPC framework

Contexte et atouts du poste Contexte et atouts du poste 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: the exploration of mixed-precision arithmetic in the context of high-order discontinuous discretization methods, and 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 ( 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 HDGThe 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 inversionTo 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 reducing the overall computational cost, and 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 high-order quadrature rules, and 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). Compétences Candidate profile Master degree Computer Sciences. Experience in scientific programming (e.g., Python, C++, Fortran, Julia) and parallelization. Avantages Subsidized meals Partial reimbursement of public transport costs Possibility of teleworking and flexible organization of working hours Professional equipment available (videoconferencing, loan of computer equipment, etc.) Social, cultural and sports events and activities Access to vocational training Social security coverage Rémunération 2300€ / month (before taxs) #J-18808-Ljbffr