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Photospheric vector magnetograms from Helioseismic and Magnetic Imager onboard the Solar Dynamic Observatory are utilized as the boundary conditions toextrapolate both non-linear force-free and potential magnetic fields in solarcorona. Based on the extrapolations, we are able to determine the free magneticenergy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in61 ARs were analyzed. We compare FME with ARs' flare index (FI) and find thatthere is a weak correlation ($<60\%$) between FME and FI. FME shows slightlyimproved flare predictability relative to total unsigned magnetic flux of ARsin the following two aspects: (1) the flare productivity predicted by FME ishigher than that predicted by magnetic flux and (2) the correlation between FIand FME is higher than that between FI and magnetic flux. However, thisimprovement is not significant enough to make a substantial difference intime-accumulated FI, rather than individual flare, predictions.

Statistical study of free magnetic energy and flare productivity of solar active regions