# Development of a CFD-Suitable Deep Neural Network Model for Laminar Burning Velocity
## 1 Introduction  
The first concepts of non-biological brains were analyzed during World War II by [PERSON] and [PERSON] [1]. Since then, multilayer deep neural networks (DNNs) have been widely used for numerous research and practical applications. In machine learning, the algorithm learns from the data, using various transformations of inputs, without a user or programmer giving it explicit instructions [2]. Various other machine learning (ML) algorithms can also be used as a replacement for neural networks since studies show that the performance of all ML algorithms depends greatly on the problem itself [3, 4]. In general, an artificial neural network (ANN) performs better in finding complex behavior and patterns in large amounts of data. As stated by studies, multi-layer ANNs, such as deep neural networks (DNN) can reproduce any function with arbitrary precision [5, 6]. Simulation of turbulent premixed combustion is challenging numerically due to the wide range of spatial and temporal scales involved in turbulence and combustion chemistry. Therefore, to perform practically relevant simulations, various simplified modeling approaches are usually employed, e.g., RANS treatment of turbulence or simplified combustion rate estimations instead of direct modeling of chemical kinetics. The most common approach to avoid chemical simulation is to formulate a used combustion model in a way that chemistry would be replaced by a simpler estimation of laminar burning velocity (LBV), e.g., from the correlations based on the experiments. There are several examples of ANN and other ML methods for the application in the prediction of combustible mixture properties in the literature. In 2018, [PERSON] et al. [7] createdthree ML models--ANN, SVM and multivariable regression (MR)--for LBVs of mixtures of air with one of seven hydrocarbons from methane up to n-heptane. The best performance was obtained by ANN model in terms of R\({}^{2}\), RMSE and MAE. In 2019, [PERSON] et al. [8] were able to create DNN which could predict laminar burning velocities of HyCONG gas blends with an R-squared value approximately equal to 0.999 and a number of neurons up to 20. Concentrations of blend constituents were used as inputs. Authors showed that an increase in network weight number decreased the testing error, which means that DNN with more weights should have higher accuracy. Similar behavior was noticed for the number of epochs used for model optimization. However, while more complex networks can show better results, they also are slower and have a higher risk of overfitting. In 2020, [PERSON] et al. [9] developed methodology to improve the accuracy of laminar flame ML simulations, starting from data preparation, model creation and finishing with model evaluation and results interpretation. [PERSON] et al. presented a light neural network (as it only had up to five neurons in each layer), which could get good predictions in a short amount of time [10]. Their neural network could be used in real-time and had the mean squared error equal to 0.3023 (m/s)\({}^{2}\) with hydrogen-air mixtures for laminar burning velocity predictions. In their work, 577 observations were used for the training of DNN. Part of them had a high spread and this can lower prediction accuracy. Since the amount of available experimental data was insufficient to train the neural network, the study generated new points (up to 7300 observations) for training. [PERSON] and [PERSON] [11] analyzed syngas mixtures and created multiple linear regression model to predict their LBVs with error <10%. Their model was derived partly from the measured velocities, and partly from the predictions using FPCM-1 kinetic mechanism. In 2021, [PERSON] et al. [12] compared four different machine learning algorithms predicting laminar burning velocities of hydrogen-methane mixtures. Their study showed that the DNN model can give much better predictions than other popular algorithms such as support vector machines (SVM) or random forest while predicting velocities for hydrogen-methane mixtures.