Generalized Approach to Matched Filtering using Neural Networks

Abstract

Gravitational wave science is a pioneering field with rapidly evolving data analysis methodology currently assimilating and inventing deep learning techniques. The bulk of the sophisticated flagship searches of the field rely on the time-tested matched filtering principle within their core. In this paper, we make a key observation on the relationship between the emerging deep learning and the traditional techniques: matched filtering is formally equivalent to a particular neural network. This means that a neural network can be constructed analytically to exactly implement matched filtering, and can be further trained on data or boosted with additional complexity for improved performance. Moreover, we show that the proposed neural network architecture can outperform matched filtering, both with or without knowledge of a prior on the parameter distribution. When a prior is given, the proposed neural network can approach the statistically optimal performance. We also propose and investigate two different neural network architectures MNet-Shallow and MNet-Deep, both of which implement matched filtering at initialization and can be trained on data. MNet-Shallow has simpler structure, while MNet-Deep is more flexible and can deal with a wider range of distributions. Our theoretical findings are corroborated by experiments using real LIGO data and synthetic injections, where our proposed methods significantly outperform matched filtering at false positive rates above $5\times 10^{-3}\%$. The fundamental equivalence between matched filtering and neural networks allows us to define a "complexity standard candle" to characterize the relative complexity of the different approaches to gravitational wave signal searches in a common framework. Finally, our results suggest new perspectives on the role of deep learning in gravitational wave detection.

arXiv comment18 pages, 13 figures

References in corpus (64)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Multi-messenger Observations of a Binary Neutron Star Merger
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• Advanced LIGO
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?
• Detection, Measurement and Gravitational Radiation
• The PyCBC search for gravitational waves from compact binary coalescence
• FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries
• Measuring gravitational waves from binary black hole coalescences: I. Signal to noise for inspiral, merger, and ringdown
• Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo
• The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
• Search templates for gravitational waves from inspiraling binaries: Choice of template spacing
• Matched filtering of gravitational waves from inspiraling compact binaries: Computational cost and template placement
• Analysis Framework for the Prompt Discovery of Compact Binary Mergers in Gravitational-wave Data
• A guide to LIGO-Virgo detector noise and extraction of transient gravitational-wave signals
• Deep Learning for Real-time Gravitational Wave Detection and Parameter Estimation: Results with Advanced LIGO Data
• A chi-squared time-frequency discriminator for gravitational wave detection
• Characterization of transient noise in Advanced LIGO relevant to gravitational wave signal GW150914
• PyCBC Inference: A Python-based parameter estimation toolkit for compact binary coalescence signals
• Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates
• Deep Neural Networks to Enable Real-time Multimessenger Astrophysics
• Searching for periodic sources with LIGO
• Matching matched filtering with deep networks in gravitational-wave astronomy
• An excess power statistic for detection of burst sources of gravitational radiation
• Implementing a search for aligned-spin neutron star -- black hole systems with advanced ground based gravitational wave detectors
• Detecting binary compact-object mergers with gravitational waves: Understanding and Improving the sensitivity of the PyCBC search
• Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters
• Analysis of LIGO data for gravitational waves from binary neutron stars
• Low-latency analysis pipeline for compact binary coalescences in the advanced gravitational wave detector era
• Gravitational-wave parameter estimation with autoregressive neural network flows
• PyCBC Live: Rapid Detection of Gravitational Waves from Compact Binary Mergers
• Convolutional neural networks: a magic bullet for gravitational-wave detection?
• GEO 600 and the GEO-HF upgrade program: successes and challenges
• Application of machine learning algorithms to the study of noise artifacts in gravitational-wave data
• Real-Time Detection of Gravitational Waves from Binary Neutron Stars using Artificial Neural Networks
• Gravitational Wave Denoising of Binary Black Hole Mergers with Deep Learning
• Fast evaluation of multi-detector consistency for real-time gravitational wave searches
• Image-based deep learning for classification of noise transients in gravitational wave detectors
• Deep-Learning continuous gravitational waves
• Aperture synthesis for gravitational-wave data analysis: Deterministic Sources
• Transient Classification in LIGO data using Difference Boosting Neural Network
• Detection and Classification of Supernova Gravitational Waves Signals: A Deep Learning Approach
• A New Method to Observe Gravitational Waves emitted by Core Collapse Supernovae
• How effective is machine learning to detect long transient gravitational waves from neutron stars in a real search?
• Random template banks and relaxed lattice coverings
• Applying deep neural networks to the detection and space parameter estimation of compact binary coalescence with a network of gravitational wave detectors
• Efficient Gravitational-wave Glitch Identification from Environmental Data Through Machine Learning
• Deep-Learning Continuous Gravitational Waves: Multiple detectors and realistic noise
• Classifying the unknown: discovering novel gravitational-wave detector glitches using similarity learning
• Eccentricity Estimate for Black Hole Mergers with Numerical Relativity Simulations
• Detection of Gravitational Waves Using Bayesian Neural Networks
• Comparison of various methods to extract ringdown frequency from gravitational wave data
• Improved deep learning techniques in gravitational-wave data analysis
• Optimizing gravitational-wave searches for a population of coalescing binaries: Intrinsic parameters
• A robust machine learning algorithm to search for continuous gravitational waves
• Lightning-Fast Gravitational Wave Parameter Inference through Neural Amortization
• Likelihood-ratio ranking of gravitational-wave candidates in a non-Gaussian background
• A power filter for the detection of burst sources of gravitational radiation in interferometric detectors
• Deep learning merger masses estimation from gravitational waves signals in the frequency domain
• Deep Networks and the Multiple Manifold Problem
• Characterization of Gravitational Waves Signals Using Neural Networks

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• Ensemble of Deep Convolutional Neural Networks for real-time gravitational wave signal recognition
• Efficient Gravitational Wave Template Bank Generation with Differentiable Waveforms
• Gravitational-Wave Searches for Cosmic String Cusps in Einstein Telescope Data using Deep Learning
• SiGMa-Net: Deep learning network to distinguish binary black hole signals from short-duration noise transients
• Identifying and Mitigating Machine Learning Biases for the Gravitational Wave Detection Problem
• Nonlinear noise regression in gravitational-wave detectors with convolutional neural networks
• Boosting the Efficiency of Parametric Detection with Hierarchical Neural Networks
• Architectural Optimization and Feature Learning for High-Dimensional Time Series Datasets
• Learning and Interpreting Gravitational-Wave Features from CNNs with a Random Forest Approach
• Using machine learning to auto-tune chi-squared tests for gravitational wave searches
• Sequence modeling of higher-order wave modes of binary black hole mergers
• Unveiling gravitational waves from core-collapse supernovae with MUSE