Transfer learning has been highlighted as a promising framework to increase the accuracy of the data-driven model in the case of data sparsity, specifically by leveraging pretrained knowledge to the training of the target model. The objective of this study is to evaluate whether the number of requisite training samples can be reduced with the use of various transfer learning models for predicting, for example, the chemical source terms of the data-driven reduced-order modeling (ROM) that represents the homogeneous ignition of a hydrogen/air mixture. Principal component analysis is applied to reduce the dimensionality of the hydrogen/air mixture in composition space. Artificial neural networks (ANNs) are used to regress the reaction rates of principal components, and subsequently, a system of ordinary differential equations is solved. As the number of training samples decreases in the target task, the ROM fails to predict the ignition evolution of a hydrogen/air mixture. Three transfer learning strategies are then applied to the training of the ANN model with a sparse dataset. The performance of the ROM with a sparse dataset is remarkably enhanced if the training of the ANN model is restricted by a regularization term that controls the degree of knowledge transfer from source to target tasks. To this end, a novel transfer learning method is introduced, Parameter control via Partial Initialization and Regularization (PaPIR), whereby the amount of knowledge transferred is systemically adjusted in terms of the initialization and regularization schemes of the ANN model in the target task.
