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Geomagnetic storms play a critical role in space weather physics with thepotential for far reaching economic impacts including power grid outages, airtraffic rerouting, satellite damage and GPS disruption. The LFM-MIX is astate-of-the-art coupled magnetospheric-ionospheric model capable of simulatinggeomagnetic storms. Imbedded in this model are physical equations for turningthe magnetohydrodynamic state parameters into energy and flux of electronsentering the ionosphere, involving a set of input parameters. The exact valuesof these input parameters in the model are unknown, and we seek to quantify theuncertainty about these parameters when model output is compared toobservations. The model is available at different fidelities: a lower fidelitywhich is faster to run, and a higher fidelity but more computationally intenseversion. Model output and observational data are large spatiotemporal systems;the traditional design and analysis of computer experiments is unable to copewith such large data sets that involve multiple fidelities of model output. Wedevelop an approach to this inverse problem for large spatiotemporal data setsthat incorporates two different versions of the physical model. After aninitial design, we propose a sequential design based on expected improvement.For the LFM-MIX, the additional run suggested by expected improvementdiminishes posterior uncertainty by ruling out a posterior mode and shrinkingthe width of the posterior distribution. We also illustrate our approach usingthe Lorenz `96 system of equations for a simplified atmosphere, using knowninput parameters. For the Lorenz `96 system, after performing sequential runsbased on expected improvement, the posterior mode converges to the true valueand the posterior variability is reduced.

Parameter tuning for a multi-fidelity dynamical model of the magnetosphere