PhD Position F/M Bayesian optimal sensor placement using model gradients: a majorize-then-optimize strategy

The Centre Inria de l’Université de Grenoble groups together almost 600 people in 22 research teams and 8 research support departments.

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

The Centre Inria de l’Université Grenoble Alpes 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.

The PhD thesis will take place at the Université Grenoble Alpes in the Inria-AIRSEA team. This project is funded by Numpex, the French exascale supercomputing program (https://numpex.org/). Scientific collaboration with fellow academics from Numpex is anticipated.

Bayesian optimal sensor placement is critical in various applications, particularly in scenarios where data acquisition is expensive (satelite observation, buoys in the ocean, underground drill etc). The primary challenge lies in determining the optimal locations where to observe the system in order to best inference a specific parameter of interest. While linear models and Gaussian priors are well-understood and relatively straightforward to handle, the problem becomes significantly more complex when dealing with models that are numerically costly to evaluate. This is especially true for large-scale, nonlinear and nonGaussian systems for which evaluating the numerical model is prohibitively expensive.

Recently, a gradient-based approach has been proposed to alleviate this computational burden. The strategy behind this approach is to minimize a bound of the so-called Expected Information Gain (EIG), which is relatively easy to work with, rather than minimizing the EIG itself. In principle, this bound serves as a surrogate for the EIG which providing a computationally favorable way to guide the sensor placement. This is because the error-bound can be evaluated and optimized much more efficiently than the actual error, which requires numerous expensive numerical simulations of the numerical model.

The objective of this project is to address various numerical aspects associated with the gradient-based solution for the Bayesian optimal sensor placement problem. The project has three main goals:

• Firstly, we seek to enhance our understanding of the majorize-then-minimize approach used in the gradient-based solution. We will achieve this by comparing the solutions obtained from the bound-based approach with those obtained from the conventional EIG-based approach. Ultimately, we hope to use the bound-based approach as a preconditioning step for the EIG-based solution to improve its accuracy.
• Secondly, we will employ randomized linear algebra methods to accelerate the computation of the bound which, in the high-dimensional setting, can still be quite expensive to compute. This will help to improve the computational efficiency of the gradient-based approach, making it more practical for large-scale systems.
• Finally, we will address the challenge of incorporating physical constraints into the sensor placement problem. Specifically, we will investigate how to take into account the constraints (physical/technical/financial) on the way the system can be observed, in order to obtain more realistic and practical sensor placement solutions.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (90 days / year) and flexible organization of working hours
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

1st and 2nd year: 2100 euros gross salary /month
 
 3rd year: 2190 euros gross salary / month