Generative AI for Robust Uncertainty Quantification in Astrophysical Inverse Problems

Context
Inverse problems, i.e. estimating underlying signals from corrupted observations, are ubiquitous in astrophysics, and our ability to solve them accurately is critical to the scientific interpretation of the data. Examples of such problems include inferring the distribution of dark matter in the Universe from gravitational lensing effects [1], or component separation in radio interferometric imaging [2].

Thanks to recent deep learning advances, and in particular deep generative modeling techniques (e.g. diffusion models), it now becomes not only possible to get an estimate of the solution of these inverse problems, but to perform Uncertainty Quantification by estimating the full Bayesian posterior of the problem, i.e. having access to all possible solutions that would be allowed by the data, but also plausible under prior knowledge.

Our team has in particular been pioneering such Bayesian methods to combine our knowledge of the physics of the problem, in the form of an explicit likelihood term, with data-driven priors implemented as generative models. This physics-constrained approach ensures that solutions remain compatible with the data and prevents “hallucinations” that typically plague most generative AI applications.

However, despite remarkable progress over the last years, several challenges still remain in the aforementioned framework, and most notably:

[Imperfect or distributionally shifted prior data] Building data-driven priors typically requires having access to examples of non corrupted data, which in many cases do not exist (e.g. all astronomical images are observed with noise and some amount of blurring), or might exist but may have distribution shifts compared to the problems we would like to apply this prior to.
This mismatch can bias estimations and lead to incorrect scientific conclusions. Therefore, the adaptation, or calibration, of data-driven priors from incomplete and noisy observations becomes crucial for working with real data in astrophysical applications.

[Efficient sampling of high dimensional posteriors] Even if the likelihood and the data-driven prior are available, correctly sampling from non-convex multimodal probability distributions in such high-dimensions in an efficient way remains a challenging problem. The most effective methods to date rely on diffusion models, but rely on approximations and can be expensive at inference time to reach accurate estimates of the desired posteriors.

The stringent requirements of scientific applications are a powerful driver for improved methodologies, but beyond the astrophysical scientific context motivating this research, these tools also find broad applicability in many other domains, including medical images [3].

PhD project
The candidate will aim to address these limitations of current methodologies, with the overall aim to make uncertainty quantification for large scale inverse problems faster and more accurate.
As a first direction of research, we will extend recent methodology concurrently developed by our team and our Ciela collaborators [4,5], based on Expectation-Maximization, to iteratively learn (or adapt) diffusion-based priors to data observed under some amount of corruption. This strategy has been shown to be effective at correcting for distribution shifts in the prior (and therefore leading to well calibrated posteriors). However, this approach is still expensive as it requires iteratively solving inverse problems and retraining the diffusion models, and is critically dependent on the quality of the inverse problem solver. We will explore several strategies including variational inference and improved inverse problem sampling strategies to address these issues.
As a second (but connected) direction we will focus on the development of general methodologies for sampling complex posteriors (multimodal/complex geometries) of non-linear inverse problems. Specifically we will investigate strategies based on posterior annealing, inspired from diffusion model sampling, applicable in situations with explicit likelihoods and priors.
Finally, we will apply these methodologies to some challenging and high impact inverse problems in astrophysics, in particular in collaboration with our colleagues from the Ciela institute, we will aim to improve source and lens reconstruction of strong gravitational lensing systems.
Publications in top machine learning conferences are expected (NeurIPS, ICML), as well as publications of the applications of these methodologies in astrophysical journals.

References
[1] Benjamin Remy, Francois Lanusse, Niall Jeffrey, Jia Liu, Jean-Luc Starck, Ken Osato, Tim Schrabback, Probabilistic Mass Mapping with Neural Score Estimation, https://www.aanda.org/articles/aa/abs/2023/04/aa43054-22/aa43054-22.html

[2] Tobías I Liaudat, Matthijs Mars, Matthew A Price, Marcelo Pereyra, Marta M Betcke, Jason D McEwen, Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging, RAS Techniques and Instruments, Volume 3, Issue 1, January 2024, Pages 505–534, https://doi.org/10.1093/rasti/rzae030

[3] Zaccharie Ramzi, Benjamin Remy, Francois Lanusse, Jean-Luc Starck, Philippe Ciuciu, Denoising Score-Matching for Uncertainty Quantification in Inverse Problems, https://arxiv.org/abs/2011.08698

[4] François Rozet, Gérôme Andry, François Lanusse, Gilles Louppe, Learning Diffusion Priors from Observations by Expectation Maximization, NeurIPS 2024, https://arxiv.org/abs/2405.13712

[5] Gabriel Missael Barco, Alexandre Adam, Connor Stone, Yashar Hezaveh, Laurence Perreault-Levasseur, Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problems, https://arxiv.org/abs/2407.17667

Machine Learning-based Algorithms for the Futur Upstream Tracker Standalone Tracking Performance of LHCb at the LHC

This proposal focuses on enhancing tracking performance for the LHCb experiments during Run 5 at the Large Hadron Collider (LHC) through the exploration of various machine learning-based algorithms. The Upstream Tracker (UT) sub-detector, a crucial component of the LHCb tracking system, plays a vital role in reducing the fake track rate by filtering out incorrectly reconstructed tracks early in the reconstruction process. As the LHCb detector investigates rare particle decays, studies CP violation in the Standard Model, and study the Quark-Gluon plasma in PbPb collisions, precise tracking becomes increasingly important.

With upcoming upgrades planned for 2035 and the anticipated increase in data rates, traditional tracking methods may struggle to meet the computational demands, especially in nucleus-nucleus collisions where thousands of particles are produced. Our project will investigate a range of machine learning techniques, including those already demonstrated in the LHCb’s Vertex Locator (VELO), to enhance the tracking performance of the UT. By applying diverse methods, we aim to improve early-stage track reconstruction, increase efficiency, and decrease the fake track rate. Among these techniques, Graph Neural Networks (GNNs) are a particularly promising option, as they can exploit spatial and temporal correlations in detector hits to improve tracking accuracy and reduce computational burdens.

This exploration of new methods will involve development work tailored to the specific hardware selected for deployment, whether it be GPUs, CPUs, or FPGAs, all part of the futur LHCb’s data architecture. We will benchmark these algorithms against current tracking methods to quantify improvements in performance, scalability, and computational efficiency. Additionally, we plan to integrate the most effective algorithms into the LHCb software framework to ensure compatibility with existing data pipelines.

Caliste-3D CZT: development of a miniature, monolithic and hybrid gamma-ray imaging spectrometer with improved efficiency in the 100 keV to 1 MeV range and optimised for detection of the Compton effect and sub-pixel localisation

Multi-wavelength observation of astrophysical sources is the key to a global understanding of the physical processes involved. Due to instrumental constraints, the spectral band from 0.1 to 1 MeV is the one that suffers most from insufficient detection sensitivity in existing observatories. This band allows us to observe the deepest and most distant active galactic nuclei, to better understand the formation and evolution of galaxies on cosmological scales. It reveals the processes of nucleosynthesis of the heavy elements in our Universe and the origin of the cosmic rays that are omnipresent in the Universe. The intrinsic difficulty of detection in this spectral range lies in the absorption of these very energetic photons after multiple interactions in the material. This requires good detection efficiency, but also good localisation of all the interactions in order to deduce the direction and energy of the incident photon. These detection challenges are the same for other applications with a strong societal and environmental impact, such as the dismantling of nuclear facilities, air quality monitoring and radiotherapy dosimetry.

The aim of this instrumentation thesis is to develop a versatile '3D' detector that can be used in the fields of astrophysics and nuclear physics, with improved detection efficiency in the 100 keV to 1 MeV range and Compton events, as well as the possibility of locating interactions in the detector at better than pixel size.

Several groups around the world, including our own, have developed hard X-ray imaging spectrometers based on high-density pixelated semiconductors for astrophysics (CZT for NuSTAR, CdTe for Solar Orbiter and Hitomi), for synchrotron (Hexitec UK, RAL) or for industrial applications (Timepix, ADVACAM). However, their energy range remains limited to around 200 keV (except for Timepix) due to the thinness of the crystals and their intrinsic operating limitations. To extend the energy range beyond MeV, thicker crystals with good charge carrier transport properties are needed. This is currently possible with CZT, but several challenges need to be overcome.

The first challenge was the ability of manufacturers to produce thick homogeneous CZT crystals. Advances in this field over the last 20 years mean that we can now foresee detectors up to at least 10 mm thick (Redlen, Kromek).

The main remaining technical challenge is the precise estimation of the charge generated by the interaction of a photon in the semiconductor. In a pixelated detector where only the X and Y coordinates of the interaction are recorded, increasing the thickness of the crystal degrades spectral performance. Obtaining Z interaction depth information in a monolithic crystal theoretically makes it possible overcome the associated challenge. This requires the deployment of experimental methods, physical simulations, the design of readout microelectronics circuits and original data analysis methods. In addition, the ability to localise interactions in the detector to better than the size of a pixel will help to solve this challenge.

Multi-messenger analysis of core-collapse supernovae

Core-collapse supernovae play a crucial role in the stellar evolution of massive stars, the birth of neutron stars and black holes, and the chemical enrichment of galaxies. How do they explode? The explosion mechanism can be revealed by the analysis of multi-messenger signals: the production of neutrinos and gravitational waves is modulated by hydrodynamic instabilities during the second following the formation of a proto-neutron star.
This thesis proposes to use the complementarity of multi-messenger signals, using numerical simulations of the stellar core- collapse and perturbative analysis, in order to extract physical information on the explosion mechanism.
The project will particularly focus on the multi-messenger properties of the stationary shock instability ("SASI") and the corotational instability ("low T/W") for a rotating progenitor. For each of these instabilities, the signal from different species of neutrinos and the gravitational waves with different polarization will be exploited, as well as the correlation between them.

INVESTIGATION OF THE NUCLEAR TWO-PHOTON DECAY

The nuclear two-photon, or double-gamma decay is a rare decay mode in atomic nuclei whereby a nucleus in an excited state emits two gamma rays simultaneously. Even-even nuclei with a first excited 0+ state are favorable cases to search for a double-gamma decay branch, since the emission of a single gamma ray is strictly forbidden for 0+ to 0+ transitions by angular momentum conservation. The double-gamma decay still remains a very small decay branch (<1E-4) competing with the dominant (first-order) decay modes of atomic internal-conversion electrons (ICE) or internal positron-electron (e+-e-) pair creation (IPC).

The thesis project has two distinct experimental parts: First, we store bare (fully-stripped) ions in their excited 0+ state in the heavy-ion storage ring (ESR) at the GSI facility to search for the double-gamma decay in several nuclides. For neutral atoms the excited 0+ state is a rather short-lived isomeric state with a lifetime of the order of a few tens to hundreds of nanoseconds. At relativistic energies available at GSI, however, all ions are fully stripped of their atomic electrons and decay by ICE emission is hence not possible. If the state of interest is located below the pair creation threshold the IPC process is not possible either. Consequently, bare nuclei are trapped in a long-lived isomeric state, which can only decay by double-gamma emission to the ground state. The decay of the isomers is identified by so-called time-resolved Schottky Mass Spectroscopy. This method allows to distinguish the isomer and the ground state by their (very slightly) different revolution time in the ESR, and to observe the disappearance of the isomer peak in the mass spectrum with a characteristic decay time. Successful experiment establishing the double-gamma decay in several nuclides (72Ge, 98Mo, 98Zr) were already performed and a new experiment has been accepted by the GSI Programme Committee and its realization is planned for 2025.

The second part concerns the direct observation of the emitted photons using gamma-ray spectroscopy. While the storage ring experiments allow to measure the partial lifetime for the double gamma decay, further information on the nuclear properties can be only be achieved by measuring the photon themselves. A test experiment has been performed to study its feasibility and the plans a more detailed study should be developed with the PhD project.

Towards a high spatial resolution pixel detector for particle identification: new detectors contribution to physics

Future experiments on linear colliders (e+e-) with low hadronic background require improvements in the spatial resolution of pixel vertex detectors to the micron range, in order to determine precisely the primary and secondary vertices for particles with a high transverse momentum. This kind of detector is set closest to the interaction point. This will provide the opportunity to make precision lifetime measurements of short-lived charged particles. We need to develop pixels arrays with a pixel dimension below the micron squared. The proposed technologies (DOTPIX: Quantum Dot Pixels) should give a significant advance in particle tracking and vertexing. Although the principle of these new devices has been already been studied in IRFU (see reference), this doctoral work should focus on the study of real devices which should then be fabricated using nanotechnologies in collaboration with other Institutes. This should require the use of simulation codes and the fabrication of test structures. Applications outside basics physics are X ray imaging and optimum resolution sensors for visible light holographic cameras.

The galaxy clusters in the XMM-Euclid FornaX deep field

The XMM Heritage project on the DEEP Euclid Fornax field aims to characterize distant galaxy clusters by comparing X-ray and optical/IR detections. The two methods call on very different cluster properties; ultimately, their combination will make it possible to set the free parameters of the Euclid cluster selection function over the entire WIDE survey, and thus constitute a fundamental ingredient for Euclid cosmological analysis.

The targeted redshift range ([1-2]) has never been systematically explored, despite being a critical area for the use of clusters in cosmology.
With FornaX, for the first time we'll have access to a large volume at these redshifts, enabling us to statistically quantify the evolution of clusters: role of AGNs in the properties of intracluster gas? Are there massive gas-deficient clusters? What are the respective biases of X-ray and optical detection?
The thesis work will involve (1) building and validating the X-ray cluster catalog; (2) correlating it with the optical/IR catalogs obtained by Euclid; and (3) studying the combined X-ray and optical evolution of the clusters.

All the algorithms for detecting and characterizing clusters in XMM images already exist, but we'll be pushing detection even further by using artificial intelligence techniques (combining spatial and spectral information on sources).
The complex problem of spatial correlation between XMM and Euclid cluster catalogs will also involve AI.

Project website: https://fornax.cosmostat.org/

DEVELOPMENT OF AN AI-BASED FRAMEWORK IN NEUTRINO PHYSICS: A FOCUS ON TIME SERIES EVENT RECONSTRUCTION AND MULTIVARIATE SCIENCE ANALYSES

Neutrinoless double beta decay (0nßß) represents a pivotal area of research in nuclear physics, offering profound insights into neutrino properties and the potential violation of lepton number conservation. The CUPID experiment is at the forefront of this investigation, employing advanced scintillating bolometers at cryogenic temperatures to minimize radioactive background noise. It aims to achieve unprecedented sensitivity in detecting 0nßß decay using lithium molybdate (Li2MoO4) crystals. These crystals are particularly advantageous due to their scintillation properties and the high Q-value of the decay process, which lies above most environmental gamma backgrounds. In turn this endeavour will require operating a fine grained array of 1596 dual heat/light detectors with excellent energy resolution. The proposed thesis integrates artificial intelligence (AI) techniques to enhance data analysis, reconstruction, and modeling for the CUPID experiment demonstrators and the science exploitation of CUPID.

The thesis will focus on two primary objectives:
1. Improved Time Series Event Reconstruction Techniques
- CNN based denoising and comparison against optimal classical techniques
2. Multivariate science analysis of a large neutrino detector array
- Analysis of Excited States: The study will use Geant4 simulations together with the CUPID background model as training data to optimize the event classification and hence science potential for the analysis of 2nßß decay to excited states.

Probing Gluon Dynamics in the Proton via the Exclusive Phi Meson Photoproduction with CLAS12

Protons and neutrons are made of partons (quarks and gluons) that interact via the strong force, governed by Quantum Chromodynamics (QCD). While QCD can be computed at high energies, its complexity reveals itself at low energies, requiring experimental inputs to understand nucleon properties like their mass and spin. The experimental extraction of the Generalized Parton Distributions (GPDs), which describe the correlation of the partons longitudinal momenta and transverse positions within nucleons, provide critical insights into these fundamental properties.
This thesis focuses on analyzing data from the CLAS12 detector, an experiment part of Jefferson Lab's research infrastructure, one the 17 National Laboratory in the USA. CLAS12, a 15-meter-long fixed-target detector with large acceptance, is dedicated to hadronic physics, particularly GPDs extraction. The selected student will study the exclusive photoproduction of the phi meson (gamma p->phi p’), which is sensitive to gluon GPDs, still largely unexplored. The student will develop a framework to study this reaction in the leptonic decay channel (phi -> e+e-) and develop a novel Graph Neural Network-based algorithm to enhance the scattered proton detection efficiency.
The thesis will aim at extracting the cross section of the photoproduction of the phi, and interpret it in term of the proton's internal mass distribution. Hosted at the Laboratory of Nucleon Structure (LSN) at CEA/Irfu in Saclay, this project involves international collaboration within the CLAS collaboration, travel to Jefferson Lab for data collection, and presentations at conferences. Proficiency in particle physics, programming (C++/Python), and English is required. Basic knowledge of particle detectors and Mahine Learning is advantageous but not mandatory.

Search for new physics through resonant di-Higgs production

Since the discovery of the Higgs boson (H) in 2012 by the ATLAS and CMS experiments, and after more than 10 years of studying its properties, especially thanks to the large Run 2 datasets from the LHC collected by both collaborations between 2015 and 2018, everything seems to indicate that we have finally completed the Standard Model (SM), as it was predicted sixty years ago. However, despite the success of this theory, many questions remain unanswered, and in-depth studies of the scalar sector of the SM could provide us with hints about how to address them.

The study of double Higgs boson (HH) production is currently of particular interest to the high-energy physics community, as it constitutes the best experimental handle to access the H self coupling, and consequently the Higgs potential V(H). Due to its direct links with the electroweak phase transition (EWPT), the shape of V(H) is particularly relevant for beyond the Standard Model (BSM) theories that attempt, for instance, to explain primordial baryogenesis and the matter-antimatter asymmetry in our universe. Some of these models predict an expanded scalar sector, involving the existence of additional Higgs bosons, often interacting preferentially with the SM Higgs.

The CMS group at CEA-Saclay/IRFU/DPhP therefore wishes to offer a PhD position focused on the search for resonant HH production, concentrating on the H(bb)H(tautau) channel, with the aim of constraining these models, for the first time involving a complete characterization of the BSM signal and its interferences with the SM. The selected student would participate in well-established research activities within the CMS collaboration and the CEA group, in connection with several institutes in France and abroad.