Reducing uncertainties in neural network Jacobians and improving accuracy of neural network emulations with NN ensemble approaches

A new application of the NN ensemble technique to improve the accuracy (reduce uncertainty) of NN emulation Jacobians is presented. It is shown that the introduced ensemble technique can be successfully applied to significantly reduce uncertainties in NN emulation Jacobians and to reach the accuracy of NN Jacobian calculations that is sufficient for the use in data assimilation systems. An NN ensemble approach is also applied to improve the accuracy of NN emulations themselves. Two ensembles linear (or conservative) and nonlinear (uses an additional averaging NN to calculate the ensemble average) were introduced and compared. The ensemble approaches: (a) significantly reduce the systematic and random error in NN emulation Jacobian, (b) significantly reduce the magnitudes of the extreme outliers and, (c) in general, significantly reduce the number of larger errors. It is also shown that the nonlinear ensemble is able to account for nonlinear correlations between ensemble members and to improve significantly the accuracy of the NN emulation as compared to the linear conservative ensemble in terms of systematic (bias), random, and larger errors.