Phd Position F/m Distributed Dimensionality Reduction for Large-scale Physical Simulations

Le descriptif de l’offre ci-dessous est en Anglais_

**Type de contrat**: CDD

**Niveau de diplôme exigé**: Bac + 5 ou équivalent

**Fonction**: Doctorant

**A propos du centre ou de la direction fonctionnelle**:
The Inria Grenoble research center groups together almost 600 people in 23 research teams and 7 research support departments.

Staff is present on three campuses in Grenoble, in close collaboration with other research and higher education institutions (University Grenoble Alpes, CNRS, CEA, INRAE,), but also with key economic players in the area.

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.

**Contexte et atouts du poste**:
While artificial intelligence is growing at a fast pace, the bulk of the world's computing power remains targeted at modeling and predicting physical phenomena, such as climate models, weather forecasting, or nuclear physics.
These simulations are run on highly parallel supercomputers on which both the hardware and the software are optimized for the task at hand. While the computing power of each processing unit is still increasing, the communication networks and the storage capabilities in these clusters do not follow such fast trends.
As a result, computing nodes produce outputs faster than what can be stored or sent to process elsewhere: These simulations are IO bound.

To reduce the communication burden, a promising venue is **is situ computations**, meaning that most of the data is processed locally by the nodes, and only meaningful aggregates are stored or sent over the network.
However, this is a difficult problem in general since meaningful information for the global simulation depends on the other nodes' output. The goal of this PhD is to** leverage machine learning techniques to bypass IO bottlenecks in the context of physics simulation on high-performance computing (HPC) clusters.**This work is thus placed in a broader ''Machine Learning for Science'' context, which aims at using ML to solve key problems arising in traditional sciences.

More specifically, we will focus on distributed dimensionality reduction techniques, which critically reduce the communication and storage needed to retain most of the information.

**Environment.** The PhD will take place at Inria Grenoble, in the Thoth team. This is a large team focused on machine learning, and in particular computer vision. Particular topics of interest include visual comprehension, hyperspectral imaging, numerical and parallel optimization, and unsupervised learning. A particular emphasis is put on interdisciplinary projects. The PhD will include frequent visits to the MIND team, at Inria Saclay. The two supervisors are young Inria researchers, with a strong track record in optimization and machine learning.

**Mission confiée**:

- The project will first focus on dimensionality reduction techniques, and in particular the standard PCA method. To fit the requirements imposed by the HPC setting, we will consider distributed incremental PCA methods [8], that work with streaming data split over many computing nodes. An important consideration in our context is that, unlike classical data stream, the data is not i.i.d. on the nodes, but stems from the domain partitioning imposed by the physics of the problem. The two main objectives are the following:

- **Benchmark existing methods**: This will require a thorough state-of-the-art review, as well as defining the

relevant metrics for evaluating data compression in physics simulations (communication/computation time/cost,
quality of the solution...). The benchmark will be realized with benchopt [3] and will benefit from the distributed
coding expertise of both supervisors.
- **Designing new efficient methods**: To account for the structure of physic simulations, we propose to investi
- gate how to efficiently leverage the inter-node communication to improve existing distributed PCA methods [5, 4]. The convergence of the proposed methods will be analyzed and we will provide tight convergence bounds.

While the initial focus will be on PCA, more advanced compression methods will be considered throughout the project, in particular with spatial compression [1, 2], mesh-based wavelets [7], or auto-encoders [6].

References
[1] Andrés Hoyos-Idrobo, Gaël Varoquaux, Jonas Kahn, and Bertrand Thirion. Recursive nearest agglomeration (ReNA): Fast clustering for approximation of structured signals. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(3):669-681, 2019.

[2] Milan Klöwer, Miha Razinger, Juan J. Dominguez, Peter D. Düben, and Tim N. Palmer. Compressing atmospheric data into its real information content. Nature Computational Science, 1(11):713-724, November 2021.