Inverse problems seek to reconstruct the unknown model parameters characterizing the system under investigation from measured data. More precisely, nonlinear inverse problems start by considering a nonlinear operator between the parameters, and acquired information / observation about them, i.e., data or measurements. This operator constructs a model for the available data, assumed to depend only on these parameters. Since the inverse problem is the inverse of the forward problem, this operator is often referred to as the forward operator. n nonlinear inverse problems, the forward operator being nonlinear, the model parameters depend in a nonlinear way of the state of the system and therefore on the observations available on it.
However, inverse problems are typically ill-posed, as opposed to the well-posed problems (verifying existence, uniqueness, and stability of the solution(s)). Also inverse problems are also typically ill-conditioned, i.e., a small change in the input induce a large change in the response. Hence, to tackles them, nonlinear regularization functionals are often introduced in the objective function to prevent overfitting. The specific context of this internship sits when the resulting minimization problem also involves inequality constraints on the model parameters or some functions of them. These constraints are important to avoid invalid or non-significant values for the model parameters.
Task:
- Design and compare different numerical solving algorithms associated to different constrained nonlinear optimization methods.
- Evaluate and compare these algorithms both formally and numerically using various (synthetic or real) benchmark cases including network tomography, network properties inference, etc. These tasks will be realized under supervision of senior (postdoc-level) researcher.
Duration: from 3 months to 1 year (max.)
Candidate profile:
- if MSc thesis: the candidate must be following the last year of the curriculum in, e.g., Applied/ Numerical mathematics, Math/Mechanical engineering, Theoretical computer science, Computer science engineering. Detailed coordinates of MSc promotor and his/her academic affiliation must be provided in the CV application form.
- if internship: the candidate must have completed his MSc (in one of these disciplines). Copy of the MSc diploma/certificate shall be included in annex of the CV. The internship can also be considered as part of post-MSc graduation or PhD graduation program.
- Good knowledge of networked systems is considered as a plus.
Note well: candidate must have obtained their University degree from an academic institution of one of the EU country.
Starting date: Jan.1st, 2023 (earliest) - Sep.30, 2023 (latest)