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 and stability of the calculation of NN emulation Jacobians is presented. The term "emulation" is defined to distinguish NN emulations from other NN models. It was shown that, for NN emulations, the introduced ensemble technique can be successfully applied to significantly reduce uncertainties in NN emulation Jacobias to reach the accuracy 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, 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 reduces the magnitudes of the extreme outliers and, (c) in general, significantly reduces the number of larger errors, (d) nonlinear ensemble is able to account for nonlinear correlations between ensemble members and improves significantly the accuracy of the NN emulation as compared with the linear conservative ensemble in terms of systematic (bias), random, and lager errors.