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Stephen R. Green

Publications and source records attributed to Stephen R. Green.

At least 37 records · Page 2Linked to original sources
arXiv2023

Flow Matching for Scalable Simulation-Based Inference

Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional problems can be challenging. Building on recent advances in generative modeling, we here present flow matching posterior estimation (FMPE), a technique for SBI using continuous normalizing flows. Like diffusion models, and in contrast to discrete flows, flow matching allows for unconstrained architectures, providing enhanced flexibility for complex data modalities. Flow matching, therefore, enables exact density evaluation, fast training, and seamless scalability to large architectures--making it ideal for SBI. We show that FMPE achieves competitive performance on an established SBI benchmark, and then demonstrate its improved scalability on a challenging scientific problem: for gravitational-wave inference, FMPE outperforms methods based on comparable discrete flows, reducing training time by 30% with substantially improved accuracy. Our work underscores the potential of FMPE to enhance performance in challenging inference scenarios, thereby paving the way for more advanced applications to scientific problems.

cs.LG↗
arXiv2023

Group equivariant neural posterior estimation

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

cs.LG↗
arXiv2023

Real-time gravitational-wave science with neural posterior estimation

We demonstrate unprecedented accuracy for rapid gravitational-wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational-wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from O(day) to a minute per event. Our networks are trained using simulated data, including an estimate of the detector-noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters, and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm -- called "DINGO" -- sets a new standard in fast-and-accurate inference of physical parameters of detected gravitational-wave events, which should enable real-time data analysis without sacrificing accuracy.

gr-qc↗
arXiv2023

Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference

We combine amortized neural posterior estimation with importance sampling for fast and accurate gravitational-wave inference. We first generate a rapid proposal for the Bayesian posterior using neural networks, and then attach importance weights based on the underlying likelihood and prior. This provides (1) a corrected posterior free from network inaccuracies, (2) a performance diagnostic (the sample efficiency) for assessing the proposal and identifying failure cases, and (3) an unbiased estimate of the Bayesian evidence. By establishing this independent verification and correction mechanism we address some of the most frequent criticisms against deep learning for scientific inference. We carry out a large study analyzing 42 binary black hole mergers observed by LIGO and Virgo with the SEOBNRv4PHM and IMRPhenomXPHM waveform models. This shows a median sample efficiency of $\approx 10\%$ (two orders-of-magnitude better than standard samplers) as well as a ten-fold reduction in the statistical uncertainty in the log evidence. Given these advantages, we expect a significant impact on gravitational-wave inference, and for this approach to serve as a paradigm for harnessing deep learning methods in scientific applications.

gr-qc↗
arXiv2022

Adapting to noise distribution shifts in flow-based gravitational-wave inference

Deep learning techniques for gravitational-wave parameter estimation have emerged as a fast alternative to standard samplers $\unicode{x2013}$ producing results of comparable accuracy. These approaches (e.g., DINGO) enable amortized inference by training a normalizing flow to represent the Bayesian posterior conditional on observed data. By conditioning also on the noise power spectral density (PSD) they can even account for changing detector characteristics. However, training such networks requires knowing in advance the distribution of PSDs expected to be observed, and therefore can only take place once all data to be analyzed have been gathered. Here, we develop a probabilistic model to forecast future PSDs, greatly increasing the temporal scope of DINGO networks. Using PSDs from the second LIGO-Virgo observing run (O2) $\unicode{x2013}$ plus just a single PSD from the beginning of the third (O3) $\unicode{x2013}$ we show that we can train a DINGO network to perform accurate inference throughout O3 (on 37 real events). We therefore expect this approach to be a key component to enable the use of deep learning techniques for low-latency analyses of gravitational waves.

gr-qc↗
arXiv2022

Gamma-radiation sky maps from compact binaries

We study sky maps and light curves of gamma-ray emission from neutron stars in compact binaries, and in isolation. We briefly review some gamma-ray emission models, and reproduce sky maps from a standard isolated pulsar in the Separatrix Layer model. We consider isolated pulsars with several variations of a dipole magnetic field, including superpositions, and predict their gamma-ray emission. Our results provide new heuristics on what can and cannot be inferred about the magnetic field configuration of pulsars from high-energy observations. We find that typical double-peak light curves can be produced by pulsars with significant multipole structure beyond a single dipole. For binary systems, we also present a simple approximation that is useful for rapid explorations of binary magnetic field structure. Finally, we predict the gamma-ray emission pattern from a compact black hole-neutron star binary moments before merger by applying the Separatrix Layer model to data simulated in full general relativity; we find that face-on observers receive little emission, equatorial observers see one broad peak, and more generic observers typically see two peaks.

astro-ph.HE↗
arXiv2022

Using machine learning to parametrize postmerger signals from binary neutron stars

There is growing interest in the detection and characterization of gravitational waves from postmerger oscillations of binary neutron stars. These signals contain information about the nature of the remnant and the high-density and out-of-equilibrium physics of the postmerger processes, which would complement any electromagnetic signal. However, the construction of binary neutron star postmerger waveforms is much more complicated than for binary black holes: (i) there are theoretical uncertainties in the neutron-star equation of state and other aspects of the high-density physics, (ii) numerical simulations are expensive and available ones only cover a small fraction of the parameter space with limited numerical accuracy, and (iii) it is unclear how to parametrize the theoretical uncertainties and interpolate across parameter space. In this work, we describe the use of a machine-learning method called a conditional variational autoencoder (CVAE) to construct postmerger models for hyper/massive neutron star remnant signals based on numerical-relativity simulations. The CVAE provides a probabilistic model, which encodes uncertainties in the training data within a set of latent parameters. We estimate that training such a model will ultimately require $\sim 10^4$ waveforms. However, using synthetic training waveforms as a proof-of-principle, we show that the CVAE can be used as an accurate generative model and that it encodes the equation of state in a useful latent representation.

gr-qc↗
arXiv2021

Nonlinear effects in the black hole ringdown: absorption-induced mode excitation

Gravitational-wave observations of black hole ringdowns are commonly used to characterize binary merger remnants and to test general relativity. These analyses assume linear black hole perturbation theory, in particular that the ringdown can be described in terms of quasinormal modes even for times approaching the merger. Here we investigate a nonlinear effect during the ringdown, namely how a mode excited at early times can excite additional modes as it is absorbed by the black hole. This is a third-order secular effect: the change in the black-hole mass causes a shift in the mode spectrum, so that the original mode is projected onto the new ones. Using nonlinear simulations, we study the ringdown of a spherically-symmetric scalar field around an asymptotically anti-de Sitter black hole, and we find that this "absorption-induced mode excitation" (AIME) is the dominant nonlinear effect. We show that this effect takes place well within the nonadiabatic regime, so we can analytically estimate it using a sudden mass-change approximation. Adapting our estimation technique to asymptotically-flat Schwarzschild black holes, we expect AIME to play a role in the analysis and interpretation of current and future gravitational wave observations.

gr-qc↗
arXiv2021

New metric reconstruction scheme for gravitational self-force calculations

Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a "no-string" radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of "gauge completion" as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the "gauge completion". We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order self-force calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.

gr-qc↗
arXiv2020

Teukolsky formalism for nonlinear Kerr perturbations

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed into a pure gauge part plus a zero mode (infinitesimal perturbation of the mass and spin) plus a perturbation arising from a certain scalar ("Debye-Hertz") potential, plus a so-called "corrector tensor." The scalar potential is a solution to the spin $-2$ Teukolsky equation with a source. This source, as well as the tetrad components of the corrector tensor, are obtained by solving certain decoupled ordinary differential equations involving the stress tensor. As we show, solving these ordinary differential equations reduces simply to integrations in the coordinate $r$ in outgoing Kerr-Newman coordinates, so in this sense, the problem is reduced to the Teukolsky equation with source, which can be treated by a separation of variables ansatz. Since higher order perturbations are subject to a linearized Einstein equation with a stress tensor obtained from the lower order perturbations, our method also applies iteratively to the higher order metric perturbations, and could thus be used to analyze the nonlinear coupling of perturbations in the near-extremal Kerr spacetime, where weakly turbulent behavior has been conjectured to occur. Our method could also be applied to the study of perturbations generated by a pointlike body traveling on a timelike geodesic in Kerr, which is relevant to the extreme mass ratio inspiral problem.

gr-qc↗
arXiv2020

Complete parameter inference for GW150914 using deep learning

The LIGO and Virgo gravitational-wave observatories have detected many exciting events over the past five years. As the rate of detections grows with detector sensitivity, this poses a growing computational challenge for data analysis. With this in mind, in this work we apply deep learning techniques to perform fast likelihood-free Bayesian inference for gravitational waves. We train a neural-network conditional density estimator to model posterior probability distributions over the full 15-dimensional space of binary black hole system parameters, given detector strain data from multiple detectors. We use the method of normalizing flows---specifically, a neural spline normalizing flow---which allows for rapid sampling and density estimation. Training the network is likelihood-free, requiring samples from the data generative process, but no likelihood evaluations. Through training, the network learns a global set of posteriors: it can generate thousands of independent posterior samples per second for any strain data consistent with the prior and detector noise characteristics used for training. By training with the detector noise power spectral density estimated at the time of GW150914, and conditioning on the event strain data, we use the neural network to generate accurate posterior samples consistent with analyses using conventional sampling techniques.

astro-ph.IM↗
arXiv2020

Gravitational-wave parameter estimation with autoregressive neural network flows

We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, ϕ_0, t_c, d_L)$ prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal $ϕ_0$ posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins $(χ_{1z}, χ_{2z})$ and binary inclination $θ_{JN}$, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw $10^4$ posterior samples.

astro-ph.IM↗
arXiv2019

Excited hairy black holes: dynamical construction and level transitions

We study the dynamics of unstable Reissner-Nordström anti-de Sitter black holes under charged scalar field perturbations in spherical symmetry. We unravel their general behavior and approach to the final equlibrium state. In the first part of this work, we present a numerical analysis of massive charged scalar field quasinormal modes. We identify the known mode families - superradiant modes, zero-damped modes, AdS modes, and the near-horizon mode - and we track their migration under variation of the black hole and field parameters. We show that the zero-damped modes become superradiantly unstable for large RNAdS with large gauge coupling; the leading unstable mode is identified with the near-horizon condensation instability. In the second part, we present results of numerical simulations of perturbed large RNAdS, showing the nonlinear development of these unstable modes. For generic initial conditions, charge and mass are ransferred from the black hole to the scalar field, until an equilibrium solution with a scalar condensate is reached. We use results from the linear analysis, however, to select special initial data corresponding to an unstable overtone mode. We find that these data evolve to produce a new equilibrium state - an excited hairy black hole with the scalar condensate in an overtone configuration. This state is, however, unstable, and the black hole eventually decays to the generic end state. Nevertheless, this demonstrates the potential relevance of overtone modes as transients in black hole dynamics.

gr-qc↗
arXiv2018

Extended I-Love relations for slowly rotating neutron stars

Observations of gravitational waves from inspiralling neutron star binaries---such as GW170817---can be used to constrain the nuclear equation of state by placing bounds on stellar tidal deformability. For slowly rotating neutron stars, the response to a weak quadrupolar tidal field is characterized by four internal-structure-dependent constants called "Love numbers." The tidal Love numbers $k_2^\text{el}$ and $k_2^\text{mag}$ measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the rotational-tidal Love numbers $\mathfrak{f}^\text{o}$ and $\mathfrak{k}^\text{o}$ measure those raised by couplings between the applied field and the neutron star spin. In this work we compute these four Love numbers for perfect fluid neutron stars with realistic equations of state. We discover (nearly) equation-of-state independent relations between the rotational-tidal Love numbers and the moment of inertia, thereby extending the scope of I-Love-Q universality. We find that similar relations hold among the tidal and rotational-tidal Love numbers. These relations extend the applications of I-Love universality in gravitational-wave astronomy. As our findings differ from those reported in the literature, we derive general formulas for the rotational-tidal Love numbers in post-Newtonian theory and confirm numerically that they agree with our general-relativistic computations in the weak-field limit.

gr-qc↗
arXiv2016

Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability

We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordstrom-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.

gr-qc↗
arXiv2016

A Simple, Heuristic Derivation of our "No Backreaction" Results

We provide a simple discussion of our results on the backreaction effects of density inhomogeneities in cosmology, without mentioning one-parameter families or weak limits. Emphasis is placed on the manner in which "averaging" is done and the fact that one is solving Einstein's equation. The key assumptions and results that we rigorously derived within our original mathematical framework are thereby explained in a heuristic way.

gr-qc↗
arXiv2015

Superradiant instabilities of asymptotically anti-de Sitter black holes

We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension $d\ge4$. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, $\mathcal{E}$. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that $\mathcal{E}<0$, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.

gr-qc↗