Deep learning has seen rapid evolution in the past decade, accomplishing tasks that were previously unimaginable. At the same time, researchers strive to better understand and interpret the underlying mechanisms of the deep models, which are often justifiably regarded as "black boxes". Overcoming this deficiency will not only serve to suggest better learning architectures and training methods, but also extend deep learning to scenarios where interpretability is key to the application. One such scenario is signal detection and estimation, with gravitational wave detection as a specific example, where classic methods are often preferred for their interpretability. Nonetheless, while classic statistical detection methods such as matched filtering excel in their simplicity and intuitiveness, they can be suboptimal in terms of both accuracy and computational efficiency. Therefore, it is appealing to have methods that achieve ``the best of both worlds'', namely enjoying simultaneously excellent performance and interpretability. In this thesis, we aim to bridge this gap between modern deep learning and classic statistical detection, by revisiting the signal detection problem from a new perspective. First, to address the perceived distinction in interpretability between classic matched filtering and deep learning, we state the intrinsic connections between the two families of methods, and identify how trainable networks can address the structural limitations of matched filtering. Based on these ideas, we propose two trainable architectures that are constructed based on matched filtering, but with learnable templates and adaptivity to unknown noise distributions, and therefore higher detection accuracy. We next turn our attention toward improving the computational efficiency of detection, where we aim to design architectures that leverage structures within the problem for efficiency gains. By leveraging the statistical structure of class imbalance, we integrate hierarchical detection into trainable networks, and use a novel loss function which explicitly encodes both detection accuracy and efficiency. Furthermore, by leveraging the geometric structure of the signal set, we consider using signal space optimization as an alternative computational primitive for detection, which is intuitively more efficient than covering with a template bank. We theoretical prove the efficiency gain by analyzing Riemannian gradient descent on the signal manifold, which reveals an exponential improvement in efficiency over matched filtering. We also propose a practical trainable architecture for template optimization, which makes use of signal embedding and kernel interpolation. We demonstrate the performance of all proposed architectures on the task of gravitational wave detection in astrophysics, where matched filtering is the current method of choice. The architectures are also widely applicable to general signal or pattern detection tasks, which we exemplify with the handwritten digit recognition task using the template optimization architecture. Together, we hope the this work useful to scientists and engineers seeking machine learning architectures with high performance and interpretability, and contribute to our understanding of deep learning as a whole.

The upcoming Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GWs) from massive black hole binaries (MBHB). Finding the electromagnetic (EM) counterparts for these GW events will be crucial for understanding how and where MBHBs merge, measuring their redshifts, constraining the Hubble constant and the graviton mass, and for other novel science applications. However, due to poor GW sky localization, multi-wavelength, time-dependent electromagnetic (EM) models are needed to identify the right host galaxy. This dissertation investigates electromagnetic (EM) signatures to accompany compact black hole binaries, specifically those that occur prior to, during, and following the merger, as well as those originating via self-lensing flares (SLFs). Chapter 2 considers equal-mass merging massive black hole binaries (MBHBs) embedded in a circumbinary disk (CBD), using high-resolution two-dimensional simulations, with a 𝚪-law equation of state, incorporating viscous heating, shock heating, and radiative cooling. Beginning from before the decoupling limit and transitioning through into post-merger, distinct EM features are identified before, during, and after the merger. The main result is that the MBHB produces strong thermal X-ray emission until 1-2 days prior to the merger. However, as the binary decouples from the CBD, the X-ray-bright minidisks rapidly shrink in size, become disrupted, and the accretion rate drops precipitously. As a result, the thermal X-ray luminosity drops by orders of magnitude, and the source remains X-ray dark for several days, regardless of any post-merger effects such as gravitational wave (GW) recoil or mass loss. Looking for this abrupt spectral change where the thermal X-ray disappears is a tell-tale EM signature of LISA mergers that does not require extensive pre-merger monitoring. Chapter 3 follows up on and extends the results of Chapter~\ref{chap:ch2} by investigating the effects to the EM spectrum for unequal-mass MBHBs via comparable simulations. This work corroborates the findings of a several order of magnitude drop in the thermal X-ray luminosity near the time of merger, but with delayed timing than found in an equal-mass system, while the source still remains X-ray dark for hours post-merger. The main result, however, is a new signature, a sharp spike in the thermal X-ray emission just before the tell-tale steep drop occurs. This adds an additional EM signature that can be used to identify EM counterparts of LISA's unequal MBHBs before the merger and potentially measure the mass ratio of the system through EM means. Finally, Chapter 4 addresses the EM signature of self-lensing flares (SLFs). SLFs are expected to be produced once or twice per orbit by an accreting MBHB, if the eclipsing MBHBs are observed close to edge-on. Again, using high-resolution two-dimensional viscous hydrodynamical simulations of a CBD embedding a MBHB, a very high-cadence output of these hydrodynamical simulation is used as inputs for a general-relativistic ray-tracing code to produce synthetic spectra and phase-folded light curves. The main results show a significant periodic amplification of the flux with the characteristic shape of a sharp flare with a central dip, as the foreground black hole (BH) transits across the minidisk and shadow of the background BH, respectively. These corroborate previous conclusions based on the microlensing approximation and analytical toy models of the emission geometry. A realistic concern with incorporating a physical disk was that the CBD might obscure our view of the SLF, considering they only appreciably occur for a near edge-on line of sight. However, this work shows that the CBD is in fact more a friend than foe in the detection, because while the CBD does indeed block other sources of emission that constitute noise, the bent trajectories of the light from the lensed minidisks remain visible even for these edge-on configurations.

L'astronomie gravitationnelle a débuté en septembre 2015 avec la première détection de la fusion de deux trous noirs par LIGO. Depuis lors, plusieurs fusions de trous noirs et une fusion d'étoiles à neutrons ont été observées. Advanced Virgo a rejoint les deux observatoires LIGO dans la prise de données en août 2017, augmentant fortement les capacités de localisation du réseau. Afin d'exploiter pleinement le potentiel scientifique de ce nouveau domaine, un énorme effort expérimental est nécessaire pour améliorer la sensibilité des interféromètres. Cette thèse, développée dans ce contexte, est composée de deux parties. La première concerne Advanced Virgo : nous avons développé un budget de bruit automatique pour le bruit de fréquence du laser et nous avons effectué des mesures de caractérisation optique pour les cavités de bras kilométriques. Des pertes aller-retour aussi faibles que 80 ppm ont été mesurées. Elles sont parmi les plus basses jamais mesurées avec un faisceau de cette taille. La deuxième partie concerne la conception et le développement d'une cavité de filtrage de 300 m, un prototype pour démontrer la production de lumière squeezing dépendante de la fréquence avec les propriétés nécessaires pour une réduction du bruit quantique à large bande dans KAGRA, Advanced Virgo et Advanced LIGO. Nous avons contribué à la fois aux phases de conception et d'intégration du projet. Nous avons d'abord fait le design optique de la cavité, y compris les spécifications pour l'optique de la cavité et une estimation détaillée des sources de dégradation pour le squeezing. Nous avons donc développé un système de contrôle pour les miroirs, assemblé les suspensions et finalement aligné et mis la cavité en résonance avec la lumière laser / Gravitational wave astronomy has started in September 2015 with the first detection of a binary black-hole merger by LIGO. Since then, several black-hole mergers and a binary neutron star merger have been observed. Advanced Virgo joined the two LIGO detector in the observation run, in August 2017, highly increasing the localization capabilities of the network. In order to fully exploit the scientific potential of this new-born field, a huge experimental effort is needed to bring the instruments at their design sensitivity and to further improve them. This thesis, developed in this context, it is composed of two parts. The first is about Advanced Virgo: we have developed an automatic noise budget for the laser frequency noise and we have performed optical characterization measurements for the kilometric arm cavities. Round trip Losses as low as 80 ppm have been measured. They are among the lowest ever measured for beams of these size. The second part is about the design and development of a 300 m filter cavity, a prototype to demonstrate the frequency dependent squeezing production with properties needed for a broadband quantum noise reduction in the future upgrades of KAGRA, Advanced Virgo and Advanced LIGO. We have contributed to the design and integration phases of the project. We have first made the optical design of the cavity, including the the specifications for the main cavity optics and a detailed estimation of the squeezing degradation sources. We have then developed a local control system for the mirrors, assembled the suspensions, and finally aligned and brought the cavity in resonance with the laser light

L'existence des ondes gravitationnelles (OG) est l'une des prédictions les plus intéressantes de la théorie de la Relativité Générale d'Einstein. La découverte expérimentale des OG serait donc un test important de la théorie elle-même et permettra d'ouvrir une nouvelle fenêtre d'observation en particulier dans les régions de l'Univers inaccessible à l'observation électromagnétique. Les détecteurs interférométriques, comme Virgo, sont les dispositifs les plus prometteurs pour la détection d’OG. Actuellement, leur sensibilité n'est pas encore suffisante pour avoir un taux d'observation de quelques événements/an. Un intense programme expérimental pour l’améliorer est en cours. Particulièrement, les prochaines générations de détecteurs d'OG, aux basses fréquences, seront limitées par l'effet de la pression de radiation (PR) sur les miroirs suspendus. Ce phénomène, pas encore observé expérimentalement, est l'objet d'un champ de recherche très actif. Mon travail ici présenté vise à la construction d'un détecteur pour l'étude des effets quantiques de la PR dans les détecteurs d’OG: QuRaG. Il sera constitué d'un interféromètre de Michelson suspendu dont chaque bras sera une cavité Fabry-Pérot de très haute finesse, dans laquelle seulement le miroir de fond sera suspendu et sensible au bruit quantique de la PR. Durant ma thèse j'ai participé activement au R&D de tous les sous-systèmes de QuRaG. Par conséquent, le travail que j'ai fait porte sur divers aspects du projet dont les problématiques appartiennent à différents domaines de la physique. Mon travail présenté ici démontre que QuRaG sera réalisable et qu’il observera le bruit de la PR dans la bande de fréquences attendue. / The existence of gravitational waves (GW) is one of the most interesting predictions of the theory of general relativity of Einstein. The experimental discovery of GW would be an important test of the theory itself. In addition, the detection of GW will open a new window of observation especially in those regions of the Universe inaccessible to electromagnetic observations. Interferometers, as Virgo are the most promising devices for the detection of GW. Currently, the sensitivity of these detectors is not yet sufficient to have a detection rate of few events/year. Therefore, an intense experimental program to improve the sensitivity is underway. Specifically, the sensitivity of the next generations of GW detectors, at low frequencies, will be limited by the effect of the radiation pressure (RP) on the suspended mirrors. This phenomenon not yet observed experimentally in the ground based GW detectors band, is currently the subject of a very active research field. My work presented here aims at building a detector for studying quantum effects of RP in GW detectors: the QuRaG experiment. It will consist of a suspended Michelson interferometer where each arm will be a high finesse Fabry-Pérot cavity, in which only the end mirror will be further suspended and then sensitive to the RP noise. During my PhD I have actively participated to the R&D of all QuRaG subsystems. Therefore, the work that I have done deals with various aspects of the project whose related problems belong to different domains of physics. My work described in this manuscript demonstrates that QuRaG is realizable and that it will be able to observe the RP noise in the expected frequency range.