PhD opportunities

Quantifying Uncertainties in Physics-Informed Machine Learning

Thesis proposal

Area of expertiseGeoscience and Geoengineering
Doctoral SchoolGRNE - Géosciences, Ressources Naturelles et Environnement
SupervisorM. Hervé CHAURIS
Co-supervisorM. Nicolas DESASSIS
Research unitGeosciences
ContactCHAURIS Hervé
Starting dateOctober 1st 2021
KeywordsMachine Learning, uncertainties, seismic imaging, Physics-Informed Neural Network
AbstractRecently, Physics-informed Neural Networks (PINN) have been proposed to explicitly introduce the Physics inside Machine Learning. On one side, Machine Learning is able to extract information out of the data. On the other side, the conclusions are not always consistent with the physics. This is a strong limitation, but it offers the possibility to extend the capabilities of Machine Learning. The objective of the of PINN approaches is to update the weights of the neural network to fit the observed data and to obey to the physics (Raissi et al., 2019).
The objective of the PhD work is to quantify the PINN uncertainties. From a starting initial solution, the network learning leads currently towards a deterministic solution. The stochastic gradient is more general, but a unique solution is determined, without uncertainties. Here, we propose to recast the PINN in a Bayesian context to derive a posterior probability.
The applications are related to seismic imaging. The traditional approach (without Machine Learning) is the Full Waveform Inversion (Chauris, 2019). The Bayesian approach is here pertinent, as Full Waveform Inversion may easily converge towards a local minimum with the deterministic approaches. The objective is to demonstrate on synthetic
ED 398 Géosciences, Ressources Naturelles et Environnement
Proposition de sujet de thèse pour la rentrée universitaire 2021-2022
and real data sets how the PINN strategy could avoid these local minima and to obtain the posterior probability density functions for different parameters (velocity, density) influencing the wave propagation.
ProfileThe PhD student should have a strong background in maths and physics, as well as good capabilities in scientific programming. He/she should be interested in geophysical applications.

Specific Requirements
The project is co-funded by AI4Sciences (Artificial Intelligence for the Sciences, There are no requirements based on nationality or age, but applicants should not have lived or carried out their main activity (work, studies, etc.) in France for more than 12 months in the last 3 years
FundingAutre type de financement