The Laser Interferometer Space Antenna (LISA), to be launched in 2034, will detect gravitational waves (GWs) of various astrophysical and cosmological origin, in the range 1mHz-1Hz.
The GWs of cosmological origin will be detected in the form of a cosmological background noise. The cosmological processes at work are not well known, and some are speculative, meaning that their spectral characteristics are very uncertain.
An added complexity is that the instrumental noise characteristics of the LISA instrument are poorly known, and will be difficult to measure in-flight. This means that distinguishing the instrumental noise from the cosmological GW backgrounds is going to be particularly complicated.

One hope might be to exploit the stationarity of the cosmological signal and the non-stationarity of the instrumental noise. This is the objective of the internship, which is split into 2 parts.

Part 1: To start with, the intern is expected to study, understand in detail and reproduce the results of a paper entitled "Separation of stationary and non-stationary sources with a generalized eigenvalue problem" by Hara et al., Neural Networks 33 (2012).

Part 2: The intern will next have to investigate the type of non-stationary instrumental noise and the type of stationary cosmological signal one might expect in LISA. The intern will then apply the separation method of Part 1 to a superposition of signal and noise.

The intern will gain knowledge on on statistical methods in data analysis, on cosmology, on the LISA mission, and will have a chance to apply the data analysis learned methods using Python in an area of active research for the LISA community.