Parameter Estimation for Predictive Simulation of Oscillatory Systems with Model Discrepancy**This research was supported in part by the Air Force Office of Scientific Research grant AFOSR FA9550-11-1-0152. It was also supported by the Consortium for Advanced Simulation of Light Water Reactors (http://www.casl.gov), an Energy Innovation Hub, (http://www.energy.gov/hubs) for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy Contract No. DE-AC05-00OR22725.