  Recently, artificial neural networks have been gaining momentum in the field
of gravitational wave astronomy, for example in surrogate modelling of
computationally expensive waveform models for binary black hole inspiral and
merger. Surrogate modelling yields fast and accurate approximations of
gravitational waves and neural networks have been used in the final step of
interpolating the coefficients of the surrogate model for arbitrary waveforms
outside the training sample. We investigate the existence of underlying
structures in the empirical interpolation coefficients using autoencoders. We
demonstrate that when the coefficient space is compressed to only two
dimensions, a spiral structure appears, wherein the spiral angle is linearly
related to the mass ratio. Based on this finding, we design a spiral module
with learnable parameters, that is used as the first layer in a neural network,
which learns to map the input space to the coefficients. The spiral module is
evaluated on multiple neural network architectures and consistently achieves
better speed-accuracy trade-off than baseline models. A thorough experimental
study is conducted and the final result is a surrogate model which can evaluate
millions of input parameters in a single forward pass in under 1ms on a desktop
GPU, while the mismatch between the corresponding generated waveforms and the
ground-truth waveforms is better than the compared baseline methods. We
anticipate the existence of analogous underlying structures and corresponding
computational gains also in the case of spinning black hole binaries.
