Binary Black Hole Mergers

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

Nested sampling (NS) resolves the thermodynamics of an atomistic system from a single simulation, but its practical reach is limited by the Markov-chain updates needed to decorrelate walkers within each likelihood-constrained ensemble. Flow-based NS has removed this bottleneck for gravitational-wave (GW) inference, yet its transfer to atomistic systems is not merely a change of application. Comparing a GW150914-like binary-black-hole likelihood with an eight-particle two-dimensional Lennard-Jones (LJ) system of comparable dimensionality, we show that the two landscapes differ fundamentally: atomistic multimodality is discrete and combinatorial, generated by particle permutations separated by hard collision walls, and its coordinate coupling is dense and collective, whereas the GW posterior exhibits smooth degeneracies and localized parameter coupling. Guided by this diagnosis, we introduce NS-Flows: a single conditional normalizing flow, conditioned on the NS energy bound and trained on a sliding window of recent live sets, that replaces MCMC by direct parallel draws corrected by importance-weighted rejection resampling. Live sets supply data self-consistently, allowing flow training without structured priors or a pre-existing dataset. For LJ disks in PBC, the algorithm reduces energy evaluations by over two orders of magnitude and wall-clock time by roughly one third, an advantage that becomes increasingly favorable as the cost of the potential grows. The flow's generation efficiency further acts as a physical diagnostic: it varies non-monotonically along the annealing trajectory, is lowest in the dense disordered regime, and is quantitatively captured by the constrained ensemble's internal mode complexity together with target drift across the training window, identifying liquid-like ensembles, rather than prior-target separation, as the hard case for current flow architectures.

We introduce a continuous metric field framework trained by a single causal contrastive loss. The framework encodes a scene into coefficients of a fixed symmetric matrix basis, assembles them into a Lie algebra element, and exponentiates the result to a Riemannian or Lorentzian metric. Across dimensions, this field discovers the full spectrum of geometric structures: from obstacle-avoiding geodesics in robot navigation across planar and manipulator configuration spaces, to event horizons of black holes in Lorentzian spacetime. Extensive zero-shot generalization studies demonstrate that the field captures transferable geometric structure rather than memorizing specific configurations. In the black hole setting, the causal loss spontaneously evolves genuine black-hole-like structures with the correct Lorentzian signature. The same loss, the same architecture, and the same training protocol produce the full range of geometric phenomena across dimensions. The field knows geometry, and geometry knows physics.

We present a neural network surrogate model that emulates the NRSur7dq4 gravitational waveform model for precessing binary black hole mergers. The surrogate decomposes the waveform into constituent quantities and trains an independent multilayer perceptron (MLP) for each. We validate the surrogate against NRSur7dq4 on 10,000 waveforms spanning its full parameter space ($1 \leq q \leq 4$, $|χ_{A,B}| \leq 0.8$). For representative total masses between 60 and 300 $M_\odot$, median sky-averaged frequency-domain mismatches range from $8.0 \times 10^{-5}$ to $1.7 \times 10^{-4}$, with 95th percentiles below $10^{-3}$. On an NVIDIA L40S GPU the JAX surrogate evaluates a single waveform in about 1 ms end-to-end, roughly 10 times faster than the LALSimulation C implementation of NRSur7dq4, and sustains about 140 times the LALSimulation throughput at batch size 64, making it well suited for both low-latency parameter-estimation samplers and large-scale waveform generation. The full NRSur7dq4 NN waveform-to-likelihood pipeline is implemented in JAX and is differentiable. This is the first neural-network surrogate of a precessing numerical-relativity waveform model to combine validated NR-faithful accuracy with a fully differentiable, GPU-accelerated inference pipeline, enabling gradient-based inference approaches via automatic differentiation including Fisher information matrices, GPU-accelerated nested sampling, gradient-based MCMC and importance sampling.

The AInstein architecture introduced an unsupervised neural method for solving the Riemannian Einstein equations on arbitrary manifolds. This Physics Informed Neural Network approach (PINN) is extended here to Lorentzian signature, validated by recovering the maximally extended Schwarzschild geometry, and tested as novel search method for arbitrary black hole solutions. The topology is built into the architecture by treating $S^{2}$ globally through its standard embedding, such that the network learns an ambient metric on the manifold $\mathbb{R}^{2} \times \mathbb{R}^{3}$, where Penrose coordinates are chosen for $\mathbb{R}^2$ and the metric on $S^{2}$ is obtained by pullback. The architecture is first trained with the objective of recovering the Schwarzschild metric via losses encoding the vacuum Einstein equation, a quadratic Weyl scalar constraint, and the $SO(3)$ symmetry of the resultant metric; directly motivated by the Birkhoff--Jebsen theorem. Following this, the objective is generalised to use the Petrov speciality index, a horizon curvature anchor, and a trapped-surface constraint, to allow search for algebraically general Petrov type I solutions, finding potentially novel general-type Lorentzian Einstein metrics with a genuinely trapped interior.

Pulsar timing arrays (PTAs) provide a unique window into nanohertz gravitational waves (GWs), but extracting astrophysical parameters from noisy, long-baseline timing residuals remains computationally challenging with traditional Bayesian techniques due to the high dimensionality of the parameter space, complex and correlated noise models, and the cost of repeated likelihood evaluations. We introduce a Transformer with a physics-informed positional-encoding framework for the efficient inference of eccentric binary black holes in relativistic orbits from PTA data. Our approach embeds analytical GW phase evolution directly into the model through structured positional encodings, enabling the network to learn physically meaningful representations from raw PTA timing residuals. We then use generative models, including discrete and continuous conditional normalizing flows, to infer posterior distributions within a simulation-based inference framework. Across a range of signal-to-noise ratios, the proposed method achieves improved accuracy, sharper posteriors, and faster inference compared to physics-agnostic baselines. While presented for deterministic white-noise signals, the modular framework readily generalizes to realistic PTA analyses incorporating red noise and additional components. This work highlights the potential of physics-aware deep learning models as scalable alternatives to conventional inference pipelines for next-generation PTA datasets.

Gravitational Waves (GWs) represent the newest window of astronomy, furthering our understanding of compact objects like black holes and neutron stars in the Universe. The signal from two merging neutron stars is especially interesting since it brings the prospect of concordant electromagnetic and neutrino emissions. Such multi-messenger observations have a transformational impact on fundamental physics, nuclear matter, astrophysics, and gravity. It was first witnessed in 2017 with the detection of the binary neutron star (BNS) merger GW170817. However, searching for BNS signals in real-time in the LIGO-Virgo-KAGRA (LVK) GW detectors presents a computational challenge, as the data streaming out must be matched against $\sim$ million reference waveforms, which requires up to a thousand CPU cores. We present a different approach using neural networks to learn the presence of a signal in the data. Our algorithm, called Aframe, was deployed in the LVK's fourth observing run and was the first artificial intelligence (AI)-enabled search to detect multiple binary black holes (BBHs) live. In this work, we demonstrate that the approach extends to the lower-mass BNS regime, and is the first AI-enabled search that achieves sensitivity comparable to matched-filter pipelines at lower computational and latency costs. The challenge of the longer-duration BNS signals is addressed by heterodyning the data, following which the network architecture used for BBHs is sufficient to distinguish signal versus background. We also show that this analysis requires a single non-flagship GPU for online deployment. Furthermore, the design and adoption of inference-as-a-service tools allow rapid offline analysis using a distributed pool of GPU resources. Hence, aside from the use case of rapid online data analysis, we also establish the use of Aframe for efficient archival data analysis.

The detection of gravitational waves has revolutionized our ability to explore fundamental aspects of the Universe. Traditionally, modeled gravitational-wave signals have been identified using template-based matched filtering, followed by coincidence analysis across multiple detectors in the signal-to-noise ratio time series. Recent advances in Machine Learning and Deep Learning have sparked growing interest in their application to both signal detection and parameter estimation. In this study, a hybrid Deep Learning strategy is proposed that leverages the effectiveness of Transformer encoders alongside well-established Convolutional Neural Network architectures in an attempt to estimate the intrinsic and extrinsic parameters of non-precessing binary black hole systems. The primary focus of this work is point estimation, producing single best-fit values for each parameter rather than full posterior distributions. This method is evaluated on both simulated signals embedded in Gaussian noise and real gravitational-wave events, and it demonstrates strong predictive performance and robustness across key astrophysical parameters.

This work proposes a novel solution to predict pulsar timing residuals with limited data, addressing the critical challenge of data scarcity across spin-frequency subgroups of millisecond pulsars in PTA datasets. The proposed solution applies a Long Short-Term Memory (LSTM) network optimized using the model-agnostic meta-learning algorithm, enabling rapid adaptation to new frequency domain by fine-tuning the LSTM network with only a few-shot of ground truth timing residuals. Particle swarm optimization algorithm is also used for automatic hyperparameter optimization, leading to improved prediction accuracy. Our solution, evaluated on the second data release of the International Pulsar Timing Array (IPTA), demonstrates robust generalization with accurate predictions in three metrics across high-frequency test frequency domains, while requiring only 10% of the timing residuals from these domains for model fine-tuning. Furthermore, our lightweight structure only costs 16.86 MB CPU memory and 18 milliseconds for single-step residual prediction. All these characteristics make our solution highly suitable for real-world applications, where effective and real-time predictions of pulsar timing residuals are essential-particularly in resource-constrained environments with limited computational power, memory, or energy availability.

Astrophysical observations from Earth are subject to weather, environmental, and scientific constraints that lead to sparse, irregular light curves. On the eve of the Vera C. Rubin Observatory Legacy Survey of Space and Time, its dataset offers unprecedented opportunities for transient science. Yet a key challenge remains its cadence, sparse and irregular across six bands, limiting inference. Interpolation helps mitigate this, with Gaussian Processes the standard, but they struggle with cross-band correlations, require a priori kernel specification, and must be fit to each light curve individually, hence scaling poorly. Here, we introduce the neural process family for light curve reconstruction, combining the probabilistic framework of Gaussian Processes with the scalability of deep learning. By meta-learning on diverse simulated transients, Attentive Neural Processes shift the bulk of computation to training, enabling rapid, amortized inference with a class-agnostic model. Evaluated on realistic Rubin cadences across 15 transient classes, we show that even an unoptimized, out-of-the-box Attentive Neural Process consistently outperforms all benchmarks -- a suite of Gaussian Processes and neural networks -- on every tested metric, spanning regression quality, astrophysical feature recovery, and probabilistic calibration. Our model interpolates all bands simultaneously in microseconds, over four orders of magnitude faster than the next-best neural benchmark and five faster than Gaussian Processes, demonstrating the potential of neural processes for the nightly Rubin alert stream. Attentive Neural Processes avoid the overconfidence of standard neural networks and the underconfidence of Gaussian Processes, delivering sharp, well-calibrated uncertainties. This work establishes the neural process family as a scalable, probabilistic foundation for real-time transient science in the Rubin era.

We present a machine learning framework for testing general relativity (GR) with gravitational wave signals from binary black hole mergers. Using the source parameters of 173 BBH events from the GWTC catalog as a realistic astrophysical population, we generate simulated GR waveforms and construct beyond GR (BGR) waveforms by applying controlled phase deformations. We introduce a response function formalism that provides a systematic framework for quantifying how any observable responds to modifications of GR. We train convolutional neural networks (CNNs) on two input representations: whitened waveforms and a response function type observable derived from the waveform mismatch, which isolates the effect of phase deviations from the bulk signal. Using response functions as the CNN input improves the classification sensitivity by a factor of approximately 33 compared to whitened waveforms, demonstrating that the choice of observable representation is as important as the classifier architecture. We study the fundamental limits of this classification through Bayes optimal error analysis, averaging methods that reveal coherent patterns hidden in noise, and a comparison between CNN accuracy and a single feature classifier as a proxy for human performance. At all deformation scales, the CNN outperforms the best single feature approach. We extend the framework to physically motivated theories using the parameterized post Einsteinian (ppE) formalism and apply it to massive gravity, where the classifier detects deviations for graviton masses of order $m_g \sim 10^{-23}\;\mathrm{eV}/c^2$ with aLIGO design sensitivity.

General-relativistic magnetohydrodynamic (GR-MHD) simulations are essential for studying black hole accretion, relativistic jets, and magnetic reconnection, yet their computational cost severely limits systematic parameter exploration. We investigate neural operator surrogates for two astrophysically relevant simulation scenarios produced by the Black Hole Accretion Code (\texttt{BHAC}). First, a Physics Informed Fourier Neural Operator (PINO) is trained on the special-relativistic resistive MHD (SRRMHD) evolution of the Orszag-Tang vortex over a range of resistivities spanning the Sweet-Parker and fast reconnection regimes. By embedding the governing equations as an additional loss term evaluated at finer temporal resolution than the available data supervision, the model learns dynamics at time steps where no simulation data is provided, enabling recovery of plasmoid formation that a data-only baseline trained on the same sparse snapshots fails to reproduce. To our knowledge, the present work is the first application of a physics informed neural operator to special relativistic resistive MHD, and the first to investigate the capability of such models to resolve plasmoid formation in SRRMHD. In a second line of investigation, an OFormer-style Transformer Neural Operator is trained on the evolution of spine-sheath relativistic jets created with \texttt{BHAC}, in special-relativistic MHD (SRMHD). The model is directly applied on the adaptive mesh, highlighting the need for linear attention due to long sequences. The neural surrogate model is capable of capturing most of the major details, especially in early predictions. To our knowledge, this constitutes the first application of a neural operator directly on a high resolution adaptive mesh refinement grid in the context of MHD simulations.

While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources. Current approaches to finetuning diffusion models rely on a large number of observations with varying forward operators, which can be difficult to collect for many applications, and thus lead to overfitting when the measurement set is small. We propose a method for tuning a prior from only a single observation by combining existing diffusion priors into a single product-of-experts prior and identifying the exponents that maximize the Bayesian evidence. We validate our method on real-world inverse problems, including black hole imaging, where the true prior is unknown a priori, and image deblurring with text-conditioned priors. We find that the evidence is often maximized by priors that extend beyond those trained on a single dataset. By generalizing the prior through exponent weighting, our approach enables posterior sampling from both tempered and combined diffusion models, yielding more flexible priors that improve the trustworthiness of the resulting posterior image distribution.

Stellar and AGN-driven feedback processes affect the distribution of gas on a wide range of scales, from within galaxies well into the intergalactic medium. Yet, it remains unclear how feedback, through its connection to key galaxy properties, shapes the radial gas density profile in the host halo. We tackle this question using suites of the EAGLE, IllustrisTNG, and Simba cosmological hydrodynamical simulations, which span a variety of feedback models. We develop a random forest algorithm that predicts the radial gas density profile within haloes from the total halo mass and five global properties of the central galaxy: gas and stellar mass; star formation rate; mass and accretion rate of the central black hole (BH). The algorithm reproduces the simulated gas density profiles with an average accuracy of $\sim$83-90% over the halo mass range $10^{9.5} \, \mathrm{M}_{\odot} < M_{\rm 200c} < 10^{15} \, \mathrm{M}_{\odot}$ and redshift interval $0<z<4$. For the first time, we apply Sobol statistical sensitivity analysis to full cosmological hydrodynamical simulations, quantifying how each feature affects the gas density as a function of distance from the halo centre. Across all simulations and redshifts, the total halo mass and the gas mass of the central galaxy are the most strongly tied to the halo gas distribution, while stellar and BH properties are generally less informative. The exact relative importance of the different features depends on the feedback scenario and redshift. Our framework can be readily embedded in semi-analytic models of galaxy formation to incorporate halo gas density profiles consistent with different hydrodynamical simulations. Our work also provides a proof of concept for constraining feedback models with future observations of galaxy properties and of the surrounding gas distribution.