The spin distribution of binary black hole mergers contains key information concerning the formation channels of these objects, and the astrophysical environments where they form, evolve and coalesce. To quantify the suitability of deep learning to characterize the signal manifold of quasi-circular, spinning, non-precessing binary black hole mergers, we introduce a modified version of WaveNet trained with a novel optimization scheme that incorporates general relativistic constraints of the spin properties of astrophysical black holes. The neural network model is trained, validated and tested with 1.5 million $ell=|m|=2$ waveforms generated within the regime of validity of NRHybSur3dq8, i.e., mass-ratios $qleq8$ and individual black hole spins $ | s^z_{{1,,2}} | leq 0.8$. Using this neural network model, we quantify how accurately we can infer the astrophysical parameters of black hole mergers in the absence of noise. We do this by computing the overlap between waveforms in the testing data set and the corresponding signals whose mass-ratio and individual spins are predicted by our neural network. We find that the convergence of high performance computing and physics-inspired optimization algorithms enable an accurate reconstruction of the mass-ratio and individual spins of binary black hole mergers across the parameter space under consideration. This is a significant step towards an informed utilization of physics-inspired deep learning models to reconstruct the spin distribution of binary black hole mergers in realistic detection scenarios.
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