Uncertainty quantification and optimization of spray break-up submodel using regularized multi-task neural nets.

For a high-fidelity simulation of engine combustion, parameters of a spray atomization break-up submodel needs to be optimized for the specified conditions to match with the non-reactive experiment. The well-accepted KH-RT spray breakup model include at least 6 parameters and they are not independent of each other, thus cannot be optimized independently. Properly tuning is time-consuming and often need expertise-guide. We propose a regularized multi-task neural nets approach to find optimal submodel parameters $\theta $ at the working condition X that minimizes ``error'' $\epsilon $. The proposed model includes two neural nets: a predictor and an autoencoder. Predictor is trained to predict the submodel parameters $\theta $ for a given X and $\epsilon $. The optimal $\theta $ then can be estimated by setting $\epsilon $ as zero. Autoencoder is used to learn a latent representation of a pair of (X, $\theta )$, which is encouraged by a regularization term to share the same latent space as the predictor. For an unseen condition X and estimated optimal $\epsilon $, we can use the autoencoder to find similar (X, $\theta )$ pairs from the training data to interpret the predictor prediction and quantify the uncertainty.