Sorbonne Université

PhD position in Computer Science and Numerical Analysis

Deep Neural Networks and Differential Equations

Sorbonne Université, Paris, Fr

Laboratoire Jacques Louis Lions – INRIA Paris and Laboratoire d’informatique de Paris 6

More information :

Advisors and contacts: (Laboratoire Jacques-Louis Lions), (Laboratoire d’informatique de Paris 6)

Starting date : October 2020

Keywords: Machine Learning, Deep Neural Networks, Numerical Analysis, Differential Equations

Differential equations form one of the bedrocks of scientific computing, while neural networks have emerged as the preferred tool of modern machine learning. They offer complementary strengths: the modelling power and interpretability of differential equations, and the approximation and generalization power of deep neural networks.  The objective of the thesis is to develop links between DNNs and DEs in order to start answering central questions like: how could DNNs be used to solve PDEs, how the concepts of numerical analysis could be adapted to DNNs, how to develop hybrid models incorporating both NN modules and ODE/PDE solvers? On the application side, we will focus on PDEs arising from environmental applications. The PhD is at the interplay of machine learning and numerical analysis and will be co-supervised by specialists of the two domains.

Working Environment

The candidate will work at SCAI (Sorbonne Center for Artificial Intelligence) in Paris, under the supervision of Julien Salomon (numerical analysis) and Patrick Gallinari (Machine Learning).

Candidate profile

Master or engineering degree in computer science or applied mathematics. The topic is at the crossroad of machine learning and numerical analysis. The candidate should have a strong scientific background with specialization in one of the two domains, good technical skills in programming. Experience of project development with machine learning platforms such as PyTorch or TensorFlow is a plus.


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