LISA (Laser Interferometer Space Antenna) is a low-frequency gravitational wave observatory (0.1 mHz - 1 Hz) to be launched by ESA in 2035. It aims to observe several populations of relativistic binary stars: the white dwarf binaries in our Galaxy, super-massive black holes in coalescence, stellar-mass black holes captured by super-massive black holes in galactic nuclei, etc. In addition, we hope to observe stochastic gravitational wave signals from the primordial Universe.  Because of the dominant seismic noise at these frequencies, these sources cannot be observed by ground-based detectors.  Observing these sources will provide unique information about the history of the primordial Universe, the formation of large structures, the verification of the theory of general relativity and perhaps the nature of dark matter.
    We expect to detect thousands to tens of thousands of sources over the duration of the mission, with signals overlapping in time and frequency. In addition, we expect gaps in the data and artefacts from the instrument and the environment (for example, the impact of micro-meteorites or asteroid flybys). We need to detect all these sources and characterise them simultaneously: this problem is often called ‘global fit’ and is the main subject of PhD theses.

The project is divided into several parts.

1. Mathematical concept (statistics). 
Many gravitational wave signals dominate the data. The ‘noise’ is actually made up of very many weak sources, which overlap, creating a stochastic foreground. This complicates the concept of source ‘detectability’ and means that it has to be treated within a statistical framework. This mathematical framework is necessary even for detected sources in order to measure the quality of the solution found or when several solutions are identified to know their statistical compatibility.
2. Perform an analysis of simulated (realistic) data. 
The aim is to reliably detect and characterise all resolvable sources. These results will be used to create the catalogue of gravitational sources available to the scientific community. The main challenge is that some sources are correlated with each other and all sources are correlated with the shape and level of the noise. The simultaneous adjustment/detection of all the sources is a difficult problem because of the enormous dimensionality. We will approach this problem using (i) the Bayesian approach and (ii) the Machine learning approach (Autoencoders, Normalising flow, Simulation based inference)