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We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure and control flow of the reference simulator. Our surrogates target stochastic simulators where the number of random variables itself can be stochastic and potentially unbounded. Our framework further enables an automatic replacement of the reference simulatorarXiv:1910.11950v2 fatcat:6ghgkxl7efgypbcthwhcvzar5q