Title: Quantitative modelling of type Ia supernovae spectral time series: Constraining the explosion physics

Abstract: Multiple explosion mechanisms have been proposed to explain type Ia supernovae (SNe Ia). Empirical modelling tools have also been developed that allow for fast, customised modelling of individual SNe and direct comparisons between observations and explosion model predictions. Such tools have provided useful insights, but the subjective nature with which empirical modelling is performed makes it difficult to obtain robust constraints on the explosion physics or expand studies to large populations of objects. Machine learning accelerated tools have therefore begun to gain traction. In this paper, we present riddler, a framework for automated fitting of SNe Ia spectral sequences up to shortly after maximum light. We train a series of neural networks on realistic ejecta profiles predicted by the W7 and N100 explosion models to emulate full radiative transfer simulations and apply nested sampling to determine the best-fitting model parameters for multiple spectra of a given SN simultaneously. We show that riddler is able to accurately recover the parameters of input spectra and use it to fit observations of two well-studied SNe Ia. We also investigate the impact of different weighting schemes when performing quantitative spectral fitting and show that best-fitting models and parameters are highly dependent on the assumed weighting schemes and priors. As spectroscopic samples of SNe Ia continue to grow, automated spectral fitting tools such as riddler will become increasingly important to maximise the physical constraints that can be gained in a quantitative and consistent manner.