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Modelling Subgrid-scale Scalar Dissipation Rate in Turbulent Premixed Flames using Gene Expression Programming and Deep Artificial Neural Networks

In the present study, Gene Expression Programming (GEP) will be used for training a model for subgrid scale (SGS) scalar dissipation rate (SDR) for a large range of filter widths, using a database of statistically planar turbulent premixed flames, featuring different turbulence intensities and heat release parameters. GEP is based on the idea to iteratively improve a population of model candidates using the survival-of-the-fittest concept. The resulting model is a mathematical expression that can be easily implemented, shared with the community and analyzed for physical consistency, as illustrated in this work. Efficient evaluation of the cost function and a smart choice of basis functions have been found to be essential for a successful optimization process. The GEP based model has been found to outperform an existing algebraic model from the literature. However, the optimization process was found to be quite intricate and the SGS SDR closure turned out to be difficult. Some of these problems have been explained using the model-agnostic interpretation method which requires the existence of a trained artificial neural network (ANN). ANNs are known for their ability to represent complex functional relationships and serve as an additional benchmark solution for the GEP based model.