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Recently, artificial neural networks have been gaining momentum in the fieldof gravitational wave astronomy, for example in surrogate modelling ofcomputationally expensive waveform models for binary black hole inspiral andmerger. Surrogate modelling yields fast and accurate approximations ofgravitational waves and neural networks have been used in the final step ofinterpolating the coefficients of the surrogate model for arbitrary waveformsoutside the training sample. We investigate the existence of underlyingstructures in the empirical interpolation coefficients using autoencoders. Wedemonstrate that when the coefficient space is compressed to only twodimensions, a spiral structure appears, wherein the spiral angle is linearlyrelated to the mass ratio. Based on this finding, we design a spiral modulewith 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 isevaluated on multiple neural network architectures and consistently achievesbetter speed-accuracy trade-off than baseline models. A thorough experimentalstudy is conducted and the final result is a surrogate model which can evaluatemillions of input parameters in a single forward pass in under 1ms on a desktopGPU, while the mismatch between the corresponding generated waveforms and theground-truth waveforms is better than the compared baseline methods. Weanticipate the existence of analogous underlying structures and correspondingcomputational gains also in the case of spinning black hole binaries.

Autoencoder-driven Spiral Representation Learning for Gravitational Wave Surrogate Modelling