\texttt{calypso}: a Parameter-Conditioned Stochastic Surrogate Model for Circumbinary Accretion Time-Series

Abstract

We present calypso, a parameter-conditioned stochastic surrogate model for circumbinary accretion flows. We represent the total and individual accretion time series in a PCA basis and model the resulting coefficients as draws from a multivariate Gaussian distribution over the latent PCA coefficients. We specifically include the aleatoric uncertainty of the time series in the model, enabling the emulator to capture the inherent stochasticity of the accretion process and the long-term modulation due to disk precession. We further explore the epistemic uncertainty in the model due to limited training data and interpolation in the ($e_{\rm b}$, $q_{\rm b}$) parameter space and find that the data does not support inclusion of this added variance term. We present the properties of existing simulation suites of circumbinary accretion, and run new simulations to fill in gaps in the parameter space, as well as a set of 13 test simulations for validation of the emulator. We publish calypso as a pip-installable Python package with an open-source codebase and comprehensive documentation, and demonstrate use-cases for current and upcoming transient surveys. We additionally derive a closed-form Gaussian likelihood that enables direct inference of ($e_{\rm b}$, $q_{\rm b}$) from observed accretion-rate time series.