A Hessian-based transfer learning approach for artificial neural networks based chemical kinetics with a sparse dataset

One of the primary challenges in high-fidelity numerical simulations of turbulent reacting flows stems from the prohibitive computational cost of evaluating chemical reaction source terms of the thermo-chemical variables. Although data-driven approaches are increasingly adopted in chemically reactive flow simulations to accelerate the evaluation of the chemical source terms, the data acquisition process is often challenging due to the inherent case-specific and high-dimensional nature of combustion systems. In the present study, we adopt regularization-based transfer learning methods to leverage pre-trained knowledge obtained from a previous task to train the target neural network model with a sparse training dataset. This study demonstrates that the overall performance of a neural network model with a sparse dataset can be remarkably enhanced by using regularization-based transfer learning methods demonstrated for both zero-and two-dimensional chemically reactive flow simulations. Moreover, a Hessian-based transfer learning method is introduced illustrating that additional performance gains can be achieved by transferring curvature-based knowledge obtained from a previous task to the target neural network model. The efficiency of the Hessian-based transfer learning method is analyzed for various scenarios and is found to outperform the baseline transfer learning method when task similarity and data sparsity in the target task are high.