The use of ML in engineering has grown steadily to support a wide array of applications. Among these methods, deep neural networks have been widely adopted due to their performance and accessibility, but they require large, high-quality datasets. Experimental data are often sparse, noisy, or insufficient to build resilient data-driven models. Transfer learning, which leverages relevant data-abundant source domains to assist learning in data-scarce target domains, has shown efficacy. Parameter transfer, where pretrained weights are reused, is common but degrades under large domain shifts. Domain-adversarial neural networks (DANNs) help address this issue by learning domain-invariant representations, thereby improving transfer under greater domain shifts in a semi-supervised setting. However, DANNs can be unstable during training and lack a native means for uncertainty quantification. This study introduces a fully-supervised three-stage framework, the staged Bayesian domain-adversarial neural network (staged B-DANN), that combines parameter transfer and shared latent space adaptation. In Stage 1, a deterministic feature extractor is trained on the source domain. This feature extractor is then adversarially refined using a DANN in Stage 2. In Stage 3, a Bayesian neural network is built on the adapted feature extractor for fine-tuning on the target domain to handle conditional shifts and yield calibrated uncertainty estimates. This staged B-DANN approach was first validated on a synthetic benchmark, where it was shown to significantly outperform standard transfer techniques. It was then applied to the task of predicting critical heat flux in rectangular channels, leveraging data from tube experiments as the source domain. The results of this study show that the staged B-DANN method can improve predictive accuracy and generalization, potentially assisting other domains in nuclear engineering.

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