  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.
