Phd Position F/m Deep Learning Meets Numerical

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 Sophia Antipolis - Méditerranée center counts 34 research teams as well as 7 support departments. The center's staff (about 500 people including 320 Inria employees) is made up of scientists of different nationalities (250 foreigners of 50 nationalities), engineers, technicians and administrative staff. 1/3 of the staff are civil servants, the others are contractual agents. The majority of the center’s research teams are located in Sophia Antipolis and Nice in the Alpes-Maritimes. Four teams are based in Montpellier and two teams are hosted in Bologna in Italy and Athens. The Center is a founding member of Université Côte d'Azur and partner of the I-site MUSE supported by the University of Montpellier.

**Contexte et atouts du poste**:
Cardiac Arrhythmias are a major healthcare issue. For instance, atrial fibrillation (AF) is the most common cardiac arrhythmia, characterised by chaotic electrical activation of the atria, preventing synchronized contraction. More than 6 million Europeans suffer from it and age is the most powerful predictor of risk. Life-threatening complications and fast progression to persistent or permanent forms call for as early as possible diagnosis and effective treatment.

Arrhythmias are often treated with anti-arrhythmic drugs, with limited efficacy and safety. Catheter ablation, an invasive procedure, is more effective. This procedure is by no means optimized, however, and arrhythmias may reoccur. The efficacy of first-time ablation may range from 30%-75% depending on the individual patient and disease, such that multiple ablation procedures may be recommended.

It is critical to understand whether an ablation procedure is likely to benefit a particular patient, and whether the arrhythmia is likely to reoccur in this patient, to maximize positive patient outcomes and ensure judicious resource allocation in our healthcare systems. Currently, there are no decision support tools enabling clinicians to access integrated patient data together with predictive models to facilitate prognosis and treatment planning.

**Mission confiée**:
Deep Learning has become a major paradigm for data analysis and modelling in the numerical world for semantic data analysis (vision, natural language processing) and games. It is now beginning to play an important role for scientific computing, in domains dealing with the modelling of complex physical processes, such as physics, mechanics or environmental and health sciences, and for industry sectors that exploit intensive simulations, like aeronautics or energy. It is particularly promising for problems involving processes that are not fully understood or when physics-based simulation models are too costly. We focus here on the modelling of complex dynamical systems arising from the observation of natural phenomena with the objective of developing the interplay between two families of approaches, Deep Neural Networks (DNNs) and Differential Equations (DEs). Partial differential equations (PDEs) play a prominent role for modelling complex system dynamics in applied mathematics, physics and other disciplines. However, in many situations, solving PDEs remains complex and challenging for numerical analysis: the governing equations of the underlying system may not be fully known, the state space may be extremely large or the dynamics too complex, the computation cost may be too high or the physical phenomenon may be loosely known. The availability of huge quantities of data, coming from simulations or observations, opens new opportunities for data-driven discovery and modelling of complex natural phenomena dynamics, a new research direction. The benefits could be extremely important: faster model development, reduction of simulation cost, improved modelling quality, targeting problems beyond the reach of traditional approaches.

The scientific objective of this project is to combine the advantages of biophysics and deep learning methods, and to develop hybrid models exploiting the complementarity of the two approaches. The objective is to exploit optimally the large amounts of available data together with well-known properties of biophysical cardiac dynamics. Besides, this would also enable us to propose a data-driven correction of biophysical model error. Finally, we will seek a principled integration of uncertainty quantification within this framework. This will encompass both uncertainty on the training data and in the prediction. The vast amount of knowledge in numerical analysis and data assimilation will be leveraged to guide the machine learning formulation.

**Principales activités**:
The main activities will be to propose new methods at the interface between physics-based and data-driven approaches in collaboration with