Scott E. Field

Som Dev Bishoyi, Scott E. Field, Stephen R. Lau

Several theoretical and astrophysical problems - including gravitational-wave modeling for extreme mass-ratio inspirals - require accurate time-domain solutions of the spin-weight $s=-2$ Teukolsky equation in Boyer-Lindquist coordinates. Because such simulations are performed on finite computational domains, they typically introduce an artificial outer boundary where nontrivial boundary conditions must be imposed. If these conditions are inaccurate, then spurious reflections and slowly-growing unphysical modes may corrupt long-time evolutions. We develop and implement exact radiation outer boundary conditions for the Bardeen-Press equation (a harmonic moment of the $a=0$ Teukolsky equation), making the artificial boundary transparent at any finite radius. We also construct near-to-far field teleportation kernels that map field data recorded at finite radius $r_1$ to the data reaching $r_2 > r_1$. The possible choice $r_2 = \infty$ corresponds to asymptotic waveform evaluation, that is propagation of the data to future null infinity. We show that both boundary and teleportation kernels are well approximated by exponential sums, with associated error bounds. Implemented in a time-domain solver, our kernel-based boundary conditions eliminate unphysical late-time growth and give the correct late-time decay rates, affording efficient long-duration simulations for waveform modeling and related blackhole perturbation calculations.

Brendan Keith, Akshay Khadse, Scott E. Field

We introduce a gravitational waveform inversion strategy that discovers mechanical models of binary black hole (BBH) systems. We show that only a single time series of (possibly noisy) waveform data is necessary to construct the equations of motion for a BBH system. Starting with a class of universal differential equations parameterized by feed-forward neural networks, our strategy involves the construction of a space of plausible mechanical models and a physics-informed constrained optimization within that space to minimize the waveform error. We apply our method to various BBH systems including extreme and comparable mass ratio systems in eccentric and non-eccentric orbits. We show the resulting differential equations apply to time durations longer than the training interval, and relativistic effects, such as perihelion precession, radiation reaction, and orbital plunge, are automatically accounted for. The methods outlined here provide a new, data-driven approach to studying the dynamics of binary black hole systems.

Dwyer S. Deighan, Scott E. Field, Collin D. Capano et al.

Gravitational-wave detection strategies are based on a signal analysis technique known as matched filtering. Despite the success of matched filtering, due to its computational cost, there has been recent interest in developing deep convolutional neural networks (CNNs) for signal detection. Designing these networks remains a challenge as most procedures adopt a trial and error strategy to set the hyperparameter values. We propose a new method for hyperparameter optimization based on genetic algorithms (GAs). We compare six different GA variants and explore different choices for the GA-optimized fitness score. We show that the GA can discover high-quality architectures when the initial hyperparameter seed values are far from a good solution as well as refining already good networks. For example, when starting from the architecture proposed by George and Huerta, the network optimized over the 20-dimensional hyperparameter space has 78% fewer trainable parameters while obtaining an 11% increase in accuracy for our test problem. Using genetic algorithm optimization to refine an existing network should be especially useful if the problem context (e.g. statistical properties of the noise, signal model, etc) changes and one needs to rebuild a network. In all of our experiments, we find the GA discovers significantly less complicated networks as compared to the seed network, suggesting it can be used to prune wasteful network structures. While we have restricted our attention to CNN classifiers, our GA hyperparameter optimization strategy can be applied within other machine learning settings.