Description du sujet de thèse

This doctoral research project, supported by the MITI (Mission pour les Initiatives Transverses et Interdiciplinaire) of the CNRS, lies at the interface between data science (INS2I) and gravitational astrophysics (IN2P3).

Its aim is to develop new signal processing tools to reconstruct the polarisation modes of gravitational waves from observational data and to characterise the polarisation state and its temporal dynamics. Estimating and characterising this polarisation information from gravitational waves will support the interpretation of astrophysical signals from black hole binaries or supernovae.

State of the art

Recent years have seen the emergence of a body of work on the analysis and characterisation of bivariate signals [1,2], i.e. time series associating two variables, thus describing over time a trajectory in a two-dimensional plane. This work has led to the introduction of new mathematical models and tools that make it possible to extend classical harmonic analysis to the bivariate case and to geometrically characterise the trajectory followed by the signal, which reflects the coupling between the two components of the signal. This characterisation is closely linked to the physical notion of polarisation, used in particular for vector waves such as electromagnetic or elastic waves.

These new approaches are particularly relevant to gravitational astronomy. Indeed, general relativity predicts the existence of two polarisation modes for gravitational waves [8]. The ground-based interferometers currently in operation, such as Virgo in Europe, LIGO in the United States and KAGRA in Japan, detect an astrophysical signal that is intrinsically bivariate.
Until now, little attention has been paid to measuring and characterising the polarisation of gravitational waves. Since each detector records a linear mixture of the two polarisation modes, their reconstruction from the observations of Virgo, LIGO and KAGRA is a ill-posed inverse problem, because of the limited number of detectors in operation and the low signal-to-noise ratio. However, with the improvement in instrumental sensitivity and the entry into service of new detectors such as LIGO India, this situation will gradually change over the next few years.

Hayama and colleagues have demonstrated the usefulness of gravitational wave polarisation measurements for supernova phenomenology [5]. More recently, progress has been made in the context of the two theses mentioned above, with the proposed use of Stokes parameters to characterise the polarisation state of gravitational signals [1] and the reconstruction of polarisations when the polarisation is fixed and known, and the position of the source in the sky is also known [2]. Solutions based on regularity constraints on the evolution of the polarisation state [6] or models derived from statistical learning [7] are currently being explored. However, all these studies lead to proofs of principle for simplified problems. There are currently no approaches that can be applied directly to the case of an astrophysical signal observed by the LIGO and Virgo detectors.


Scientific objectives

Accessing to the polarisation of gravitational waves is of major interest for astrophysics. It can provide valuable information about the dynamics of astrophysical sources. For example, in the case of mergers of binaries of compact objects (black holes and neutron stars), the detection of a change in polarisation would indicate a change in the inclination of the orbital plane of the binary and would therefore be an indicator of orbital precession. Similarly, analysing the polarisation of the modes of the protoneutron star formed after a supernova would provide key elements for understanding the processes involved in the gravitational collapse of the core of a massive star. Finally, it is possible to test gravitation by checking the polarisation of the quasi-normal modes of the black hole resulting from the merger of a compact binary.

This project lies at the interface between signal processing and gravitational astronomy. Its aim is to develop new algorithms enabling :
1. Reconstruct and denoise the polarisation modes of gravitational waves from observational data. This will require the introduction of regularisation schemes to constrain the solution of the inverse reconstruction problem, based on a priori assumptions derived from astrophysical models and constraints. The optimisation of these schemes will also involve the implementation of suitable algorithms, such as the structured low-rank approximations [3] dedicated to the bivariate case.
2. Define observables characterising the polarisation state and its temporal evolution. This includes, for example, the study of geometric invariants such as the geometric phase [4] or other invariants marking temporal variations in the intrinsic (polarisation) parameters of the signal.

The expected advances are numerous and will contribute to the two disciplinary areas of the project. For data science, methodological contributions are expected. The problems of approximation [3] or separation/de-noising are well known for the case of univariate signals, but taking into account the 'polarisation' dimension via bivariate models has not yet been considered. Inclusion of polarisation in waveform reconstruction. The inclusion of polarisation in the reconstruction of waveforms via a regularised inverse problem will also have potential applications beyond the scientific perimeter of the project due to the existence of polarised signals in other areas of physics.

Concerning 1. the promising solutions [6,7] currently being explored as part of the ANR RICOCHET project, which ends in 2026, offer interesting avenues on which this thesis proposal can build in order to obtain an algorithm applicable to LIGO and Virgo data.

Concerning 2. the study of polarisation dynamics via the definition of geometric invariants is a line of research that has emerged recently [4]. At the heart of this line of research is the search for representation spaces that are invariant to certain transformations. For example, the geometric phase [4] of bivariate signals is a quantity that is invariant by, among other things, temporal reparametrisation and phase shifting of the bivariate signal. It is therefore a marker that is robust to artefacts in the data, making it an interesting object for monitoring polarisation dynamics in a noisy environment. Work on the study and use of geometric phase in bivariate signal processing will therefore be carried out in this project to propose tools for monitoring the polarisation dynamics of gravitational waves.We therefore propose to explore an original methodological avenue in this part of the project, with potential validation on gravitational data and in the longer term in other scientific fields.

The complementary nature of the two teams is central to achieving these objectives. The team based at Gipsa-lab has considerable expertise in the analysis of bivariate signals and in the development of geometric approaches that exploit polarisation information.

The team based at the APC has recognised expertise in the simulation, analysis, use and interpretation of experimental data from the LIGO, Virgo and Kagra interferometers.

Role of the PhD student

The role of the PhD student will be to carry out research at the interface between signal processing and gravitational astrophysics, with a view to the operational transfer of signal processing algorithms developed for astrophysicists.

The PhD student's research work will therefore range from the proposal of new data processing approaches (for the reconstruction of polarised gravitational signals and for the study of the polarisation dynamics of gravitational waves via geometric invariants), to validation on simulated data and possibly on real data. The tests developped by the PhD student will be carried out on simulations derived from the codes of the LIGO-Virgo-KAGRA collaboration (signal simulation, realistic instrument noise), enabling them to be validated in realistic situations and, ultimately, the inclusion of the codes developed in the collaboration's processing pipelines.

Over the next four years, the LIGO, Virgo and KAGRA detectors are scheduled to carry out two observation campaigns: the final part of the current O4 campaign is due to end in October 2025, and the O5 campaign is planned to start in the last quarter of 2027. One objective will be to apply the methods developed during the thesis to the observational data associated with O4 or O5.

The PhD student will be assigned to Gipsa-lab. His/her research work will take place in the two laboratories involved in the project (Gipsa-lab and APC). Regular visits to the two sites and constant interaction with researchers from the two teams will ensure the interdisciplinary nature of the work carried out. A special effort will be made to ensure that the results of the work are accessible to both scientific communities, through participation in conferences on gravitational astrophysics and data science. Similarly, the results obtained will be published in journals from both communities.

References
[1] , Une approche générique pour l'analyse et le filtrage des signaux bivariés, Julien Flamant, Thèse de doctorat, École Centrale de Lille, 2018.
[2] Outils mathématiques et de traitement du signal pour l'étude polarimétrique des ondes gravitationnelles, Cyril Cano, Thèse de doctorat, Université Grenoble Alpes, 2022.
[3] Structured low-rank matrix completion for forecasting in time series analysis, Jonathan Gillard and Konstantin Usevich, International Journal of Forecasting, Volume 34, Issue 4, 2018.
[4] The geometric phase of bivariate signals, N. Le Bihan, J. Flamant and P.O Amblard, European Conference on Signal and Image Processing, Lyon, 2024.
[5] Hayama et al, Circular polarizations of gravitational waves from core-collapse supernovae: a clear indication of rapid rotation, Phys. Rev. Lett, vol 116 151102, 2016 https://arxiv.org/abs/1606.01520
[6] Y Pilavci et al, Time and Covariance Smoothing for Polarized Bivariate Signals, IEEE SSP Conference, 2025
[7] P Palud et al, Synthetic-data-driven Plug-and-Play method for inverse problems on bivariate signals, IEEE SSP Conference, 2025

[8] M Isi, Parametrizing gravitational-wave polarizations, Class. Quantum Grav. 40 203001, 2025

Contexte de travail

The Gipsa-lab is a joint research laboratory of the CNRS, Grenoble-INP -UGA and the University of Grenoble Alpes. It is under agreement with Inria and the Observatory of Sciences of the Universe of Grenoble. He conducts theoretical and applied research on AUTOMATICS, SIGNAL, IMAGES, SPEECH, COGNITION, ROBOTICS and LEARNING.
Multidisciplinary and at the interface between the human, the physical and digital worlds, our research is confronted with measurements, data, observations from physical, physiological and cognitive systems. They focus on the design of methodologies and algorithms for processing and extracting information, decisions, actions and communications that are viable, efficient and compatible with physical and human reality. Our work is based on mathematical and computer theories for the development of models and algorithms, validated by hardware and software implementations.
By relying on its platforms and partnerships, Gipsa-lab maintains a constant link with applications in a wide variety of fields: health, environment, energy, geophysics, embedded systems, mechatronics, processes and industrial systems, telecommunications, networks, transport and vehicles, operational safety and security, human-computer interaction, linguistic engineering, physiology and biomechanics, etc.
Due to the nature of its research, Gipsa-lab is in direct and constant contact with the economic environment and society.
Its potential as teacher-researchers and researchers is invested in training at the level of universities and engineering schools on the Grenoble site (Grenoble Alpes University).
Gipsa-lab develops its research through 16 teams or themes organized into 4 divisions:
• Automatic and Diagnosis (PAD)
• Data Science (PSD)
• Speech and Cognition (PPC)
• Geometries, Learning, Information and Algorithms (GAIA).
The staff supporting research (38 engineers and technicians) is distributed in the common services distributed within 2 divisions:
• The Administrative and Financial Pole
• The Technical Pole
Gipsa-lab has around 150 permanent staff, including 70 teacher-researchers and 41 researchers. It also welcomes guest researchers and post-docs.
Gipsa-lab supervises nearly 150 theses, including around 50 new ones each year. All the theses carried out in the laboratory are financed and supervised by teacher-researchers and researchers, including 50 holders of an HDR.
Finally, around sixty Master's trainees come each spring to swell the ranks of the laboratory.

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Contraintes et risques

None identified

Informations complémentaires

Beginners accepted