Reduced order models based on the transport of a lower dimensional manifold representation of the thermochemical state, such as Principal Component (PC) transport and Machine Learning (ML) techniques, have been developed to reduce the computational cost associated with the Direct Numerical Simulations (DNS) of reactive flows. Both PC transport and ML normally require an abundance of data to exhibit sufficient predictive accuracy, which might not be available due to the prohibitive cost of DNS or experimental data acquisition. To alleviate such difficulties, similar data from an existing dataset or domain (source domain) can be used to train ML models, potentially resulting in adequate predictions in the domain of interest (target domain). This study presents a novel probabilistic transfer learning (TL) framework to enhance the trust in ML models in correctly predicting the thermochemical state in a lower dimensional manifold and a sparse data setting. The framework uses Bayesian neural networks, and autoencoders, to reduce the dimensionality of the state space and diffuse the knowledge from the source to the target domain. The new framework is applied to one-dimensional freely-propagating flame solutions under different data sparsity scenarios. The results reveal that there is an optimal amount of knowledge to be transferred, which depends on the amount of data available in the target domain and the similarity between the domains. TL can reduce the reconstruction error by one order of magnitude for cases with large sparsity. The new framework required 10 times less data for the target domain to reproduce the same error as in the abundant data scenario. Furthermore, comparisons with a state-of-the-art deterministic TL strategy show that the probabilistic method can require four times less data to achieve the same reconstruction error.

翻译：基于热化学状态低维流形表示传输的降阶模型（如主成分传输和机器学习技术）已被开发用于降低反应流直接数值模拟的计算成本。然而，主成分传输和机器学习通常需要大量数据才能达到足够的预测精度，而由于直接数值模拟或实验数据获取的高昂成本，这些数据可能难以获得。为缓解此类困难，可利用现有数据集或源域中的相似数据训练机器学习模型，从而在目标域中实现充分预测。本研究提出一种新型概率迁移学习框架，以增强机器学习模型在低维流形及稀疏数据场景下正确预测热化学状态的置信度。该框架采用贝叶斯神经网络与自编码器降低状态空间维度，并将知识从源域扩散至目标域。新框架被应用于不同数据稀疏性条件下的一维自由传播火焰解。结果表明，存在最优知识迁移量，该量取决于目标域可用数据量及域间相似性。在大稀疏度案例中，迁移学习可将重建误差降低一个数量级。相较于数据充足场景，新框架在目标域中仅需十分之一的数据即可达到相同误差。此外，与现有确定性迁移学习策略的对比显示，概率方法实现同等重建误差所需数据量可减少四倍。