Deterministic models are approximations of reality that are often easier to build and interpret than stochastic alternatives.  
 Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic models in practice.  
 Observation and process noise need to be added to adapt deterministic models to behave stochastically, such that they are capable of explaining and extrapolating from noisy data.
 Adding process noise to deterministic simulators can induce a failure in the simulator resulting in no return value for certain inputs -- a property we describe as ``brittle.''
 We investigate and address the wasted computation that arises from these failures, and the effect of such failures on downstream inference tasks.
 We show that performing inference in this space can be viewed as rejection sampling, and train a conditional normalizing flow as a proposal over noise values such that there is a low probability that the simulator crashes, increasing computational efficiency and inference fidelity for a fixed sample budget when used as the proposal in an approximate inference algorithm. In order to compensate for epistemic uncertainty due to modelling approximations and unmodeled aleatoric uncertainty, deterministic simulators are often "converted" to "stochastic" simulators by randomly perturbing the state at each time step. In practice, models adapted in this way often provide better inferences (Møller et al., 2011; Saarinen et al., 2008; Lv et al., 2008; Pimblott and LaVerne, 1990; Renard et al., 2013) . State-independent white noise with heuristically tuned variance is often used to perturb the state (Adhikari and Agrawal, 2013; Brockwell and Davis, 2016; Fox, 1997; Reddy and Clinton, 2016; Du and Sam, 2006; Allen, 2017; Mbalawata et al., 2013) . However, naively adding noise to the state will, in many applications, render the perturbed input state "invalid," inducing failure (Razavi et al., 2019; Lucas et al., 2013; Sheikholeslami et al., 2019) . These failures waste computational resources and reduce sample diversity, worsening inference performance. Examples of failure modes include ordinary differential equation (ODE) solvers not converging to the required tolerance in the allocated time, or, the state crossing into an unhandled configuration, such as solid bodies overlapping. Establishing the cause of failure is non-trivial and hence, the simulation artifact can be sensitive to seemingly inconsequential alterations to the state -a property we describe as "brittle." The principal contribution of this paper is a technique for minimizing this failure rate. We proceed by first framing sampling from brittle simulators as rejection sampling. We then eliminate rejections by learning the state-dependent density over perturbations that do not induce failure, using conditional autoregressive flows (Papamakarios et al., 2017) . Doing so renders the joint distribution unchanged and retains the interpretability afforded by the simulator, but improves sample efficiency. We show that using the learned proposal increases the fidelity of the inference results attainable on a range of examples. In this paper we have tackled reducing simulator failures caused by naively perturbing the input state. We achieve this by defining these simulators as rejection samplers and learning a conditional autoregressive flow to estimate the state-dependent proposal distribution conditioned on acceptance. We show that using this learned proposal reduces the variance of inference results when used as the proposal in a subsequent approximate inference scheme. This work has readily transferable practical contributions in the scientific community where naively modified simulation platforms are widely deployed.
We learn a conditional autoregressive flow to propose perturbations that don't induce simulator failure, improving inference performance.
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