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Register a new userLarge-Scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant
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We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time-delay gravitational lenses for Hubble constant ($H_0$) determination. Our BNN was trained on synthetic HST-quality images of strongly lensed active galactic nuclei (AGN) with lens galaxy light included. The BNN can accurately characterize the posterior PDFs of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into ensemble $H_0$ inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of $9.3$% per lens in the inferred $H_0$. A simple combination of 200 test-set lenses results in a precision of 0.5 $textrm{km s}^{-1} textrm{ Mpc}^{-1}$ ($0.7%$), with no detectable bias in this $H_0$ recovery test. The computation time for the entire pipeline -- including the training set generation, BNN training, and $H_0$ inference -- translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for $H_0$ inference.
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We propose a new model of Bayesian Neural Networks to not only detect the events of compact binary coalescence in the observational data of gravitational waves (GW) but also identify the full length of the event duration including the inspiral stage. This is achieved by incorporating the Bayesian approach into the CLDNN classifier, which integrates together the Convolutional Neural Network (CNN) and the Long Short-Term Memory Recurrent Neural Network (LSTM). Our model successfully detect all seven BBH events in the LIGO Livingston O2 data, with the periods of their GW waveforms correctly labeled. The ability of a Bayesian approach for uncertainty estimation enables a newly defined `awareness state for recognizing the possible presence of signals of unknown types, which is otherwise rejected in a non-Bayesian model. Such data chunks labeled with the awareness state can then be further investigated rather than overlooked. Performance tests with 40,960 training samples against 512 chunks of 8-second real noise mixed with mock signals of various optimal signal-to-noise ratio $0 leq rho_text{opt} leq 18$ show that our model recognizes 90% of the events when $rho_text{opt} >7$ (100% when $rho_text{opt} >8.5$) and successfully labels more than 95% of the waveform periods when $rho_text{opt} >8$. The latency between the arrival of peak signal and generating an alert with the associated waveform period labeled is only about 20 seconds for an unoptimized code on a moderate GPU-equipped personal computer. This makes our model possible for nearly real-time detection and for forecasting the coalescence events when assisted with deeper training on a larger dataset using the state-of-art HPCs.
In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect between training sets and the distribution of real-world objects can introduce bias when BNNs are applied to data. This is a common challenge in astrophysics and cosmology, where the unknown distribution of objects in our Universe is often the science goal. In this work, we incorporate BNNs with flexible posterior parameterizations into a hierarchical inference framework that allows for the reconstruction of population hyperparameters and removes the bias introduced by the training distribution. We focus on the challenge of producing posterior PDFs for strong gravitational lens mass model parameters given Hubble Space Telescope (HST) quality single-filter, lens-subtracted, synthetic imaging data. We show that the posterior PDFs are sufficiently accurate (i.e., statistically consistent with the truth) across a wide variety of power-law elliptical lens mass distributions. We then apply our approach to test data sets whose lens parameters are drawn from distributions that are drastically different from the training set. We show that our hierarchical inference framework mitigates the bias introduced by an unrepresentative training sets interim prior. Simultaneously, given a sufficiently broad training set, we can precisely reconstruct the population hyperparameters governing our test distributions. Our full pipeline, from training to hierarchical inference on thousands of lenses, can be run in a day. The framework presented here will allow us to efficiently exploit the full constraining power of future ground- and space-based surveys.
We seek to achieve the Holy Grail of Bayesian inference for gravitational-wave astronomy: using deep-learning techniques to instantly produce the posterior $p(theta|D)$ for the source parameters $theta$, given the detector data $D$. To do so, we train a deep neural network to take as input a signal + noise data set (drawn from the astrophysical source-parameter prior and the sampling distribution of detector noise), and to output a parametrized approximation of the corresponding posterior. We rely on a compact representation of the data based on reduced-order modeling, which we generate efficiently using a separate neural-network waveform interpolant [A. J. K. Chua, C. R. Galley & M. Vallisneri, Phys. Rev. Lett. 122, 211101 (2019)]. Our scheme has broad relevance to gravitational-wave applications such as low-latency parameter estimation and characterizing the science returns of future experiments. Source code and trained networks are available online at https://github.com/vallis/truebayes.
It is well known that measurements of H0 from gravitational lens time delays scale as H0~1-k_E where k_E is the mean convergence at the Einstein radius R_E but that all available lens data other than the delays provide no direct constraints on k_E. The properties of the radial mass distribution constrained by lens data are R_E and the dimensionless quantity x=R_E a(R_E)/(1-k_E)$ where a(R_E) is the second derivative of the deflection profile at R_E. Lens models with too few degrees of freedom, like power law models with densities ~r^(-n), have a one-to-one correspondence between x and k_E (for a power law model, x=2(n-2) and k_E=(3-n)/2=(2-x)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of k_E and hence H0. Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates of H0 from gravitational lens time delays are more accurate than ~10%, regardless of the reported precision.
Future large-scale surveys with high resolution imaging will provide us with a few $10^5$ new strong galaxy-scale lenses. These strong lensing systems however will be contained in large data amounts which are beyond the capacity of human experts to visually classify in a unbiased way. We present a new strong gravitational lens finder based on convolutional neural networks (CNNs). The method was applied to the Strong Lensing challenge organised by the Bologna Lens Factory. It achieved first and third place respectively on the space-based data-set and the ground-based data-set. The goal was to find a fully automated lens finder for ground-based and space-based surveys which minimizes human inspect. We compare the results of our CNN architecture and three new variations (invariant views and residual) on the simulated data of the challenge. Each method has been trained separately 5 times on 17 000 simulated images, cross-validated using 3 000 images and then applied to a 100 000 image test set. We used two different metrics for evaluation, the area under the receiver operating characteristic curve (AUC) score and the recall with no false positive ($mathrm{Recall}_{mathrm{0FP}}$). For ground based data our best method achieved an AUC score of $0.977$ and a $mathrm{Recall}_{mathrm{0FP}}$ of $0.50$. For space-based data our best method achieved an AUC score of $0.940$ and a $mathrm{Recall}_{mathrm{0FP}}$ of $0.32$. On space-based data adding dihedral invariance to the CNN architecture diminished the overall score but achieved a higher no contamination recall. We found that using committees of 5 CNNs produce the best recall at zero contamination and consistenly score better AUC than a single CNN. We found that for every variation of our CNN lensfinder, we achieve AUC scores close to $1$ within $6%$.
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