Stochastic simulators need suitable parameter values to reproduce observed behaviour in complex systems. Searching for these values through repeated simulations makes frequent recalibration computationally expensive. We develop an amortized optimizer that uses simulations collected in advance to learn how to choose parameters that make simulated outcomes agree with observations. Once fitted, it maps new observations to feasible parameters without further simulator calls. The method retains alternative parameter settings that can explain similar observations and compares their responses, avoiding the conflicting labels that arise when training a single parameter regressor. Historical observations also provide supervision by showing which simulated responses agree with the data, even when the underlying parameters are unknown. Experiments across four simulators compare calibration accuracy and query time. Dedicated cost analyses quantify traffic preparation and the recorded financial reuse costs. On new traffic targets, local correction more than halves query time relative to empirical and surrogate selection; a learned inverse is faster still, with similar mean error. In a retrospective comparison on real financial data, our method returns parameters about $1.07\times10^{7}$ times faster than a 10-minute Gaussian-process Bayesian optimization search, with mean calibration error 3.06% higher. Reusing simulation work across observations supports repeated parameter updates when the available time is too short for a new search.

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