# Development of a CFD-Suitable Deep Neural Network Model for Laminar Burning Velocity
## 1 Introduction
[PERSON] et al. [13] used several ML methods to predict the research octane numbers of several spark ignition fuels. Study evaluated multiple ML algorithms using 10-fold cross validation, which ensured that results are less influenced by noise and more accurately reflects real capabilities of these models. In this study SVM gave best predictions out of all tested methods. [PERSON] et al. [14] created a quantitative structure-property relationship (QSPR) model for the estimation of LBVs of hydrocarbons and oxygenated hydrocarbons based on their underlying fuel structures. A set of molecular groups as well as pressure, temperature and equivalence ratio served as input parameters to an ANN, which has been trained based on a large database of training data for 124 different compounds. Recently, [PERSON] et al. [15] compared 16 ML algorithms for the prediction of hydrocarbon and oxygenated fuels LBVs and found out that the Gaussian or Tree-based methods gave high predictions with most of those models explaining over 90% of all data. [PERSON] et al. [16] created ML-QSPR model to screen fuels based on their predicted properties. In our previous work [17], we created a DNN for the prediction of the laminar burning velocity of hydrogen-air mixtures with a coefficient of determination approximately equal to 0.985. However, this model was too slow to be used practically (in CFD calculations)--the testing script could make a million predictions in around 45 s, compared to the Malet correlation [18], with which predictions could be made under the same conditions in less than a second. For complex combustion cases, increases in observation quantity can highly improve predictions of neural networks. However, as the network starts to learn the way to solve the problem, this effect gets less visible. In the end, if the model overlearns on data, it can even start to mimic the noise. Therefore, the goal should be to obtain a high enough amount of well-balanced data. Since there are more data in the specific region, the more trustworthy prediction can be made by the neural network. To achieve more accurate predictions, aberrant outliers may need to be removed from the data. As suggested by [PERSON], this can be carried out with the so-called 'double-D' algorithm [19]. The algorithm itself has many names, however, the idea behind it is to use a double standard deviation as a removal condition. However, it is more useful when the database has a very large number of observations. Since the amount of experimental data on hydrogen-air LBV in the literature is not that large, this method might not significantly improve predictions as the neural network might not have enough data to learn well. On the other hand, it could be a direction for future work. Moreover, outliers have a significant influence on the mean value as it is one of the neural network's measures based on which it decides how the final model will look like. Luckily, the model can also be evaluated using mean absolute error (MAE) instead. The influence on a model based on MAE compared to a model based on mean squared error (MSE) was analyzed by [PERSON] [20]. It is much less affected by outliers but error can be influenced by the number of observations. As pointed out by [PERSON] [21], each metric has its advantages and disadvantages. Due to this, it would be wise to have the MSE as a side evaluator as well and not trust in a single measure (MAE) blindly. As the presented research overview shows, most of the related studies to date have focused on the development of stand-alone ML models of combustible mixtures' properties. While there are works considering the implementation of such a model into a CFD code [10], this has not been performed up to now. Consequentially, when developing, there is less pressure to create lean and fast, but sufficiently accurate models, and their suitability is not tested in CFD frameworks. In addition, the last, but main step, producing a working, research or application suitable CFD-ANN code is never performed.