All three components of the current density are required to compute the heating rate due to free magnetic energy dissipation. Here we present a first test of a new model developed to determine if the times of increases in the resistive heating rate in active region (AR) photospheres are correlated with the subsequent occurrence of M and X flares in the corona. A data driven, 3 D, non-force-free magnetohydrodynamic model restricted to the near-photospheric region is used to compute time series of the complete current density and the resistive heating rate per unit volume $(Q(t))$ in each pixel in neutral line regions (NLRs) of 14 ARs. The model is driven by time series of the magnetic field ${bf B}$ measured by the Helioseismic & Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for ${bf B}$ in every AR pixel. For each AR, the cumulative distribution function (CDF) of the values of the NLR area integral $Q_i(t)$ of $Q(t)$ is found to be a scale invariant power law distribution essentially identical to the observed CDF for the total energy released in coronal flares. This suggests that coronal flares and the photospheric $Q_i$ are correlated, and powered by the same process. The model predicts spikes in $Q_i$ with values orders of magnitude above background values. These spikes are driven by spikes in the non-force free component of the current density. The times of these spikes are plausibly correlated with times of subsequent M or X flares a few hours to a few days later. The spikes occur on granulation scales, and may be signatures of heating in horizontal current sheets. It is also found that the times of relatively large values of the rate of change of the NLR unsigned magnetic flux are also plausibly correlated with the times of subsequent M and X flares, and spikes in $Q_i$.
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