Data-driven soft sensors are essential for achieving accurate perception through reliable state inference. However, developing representative soft sensor models is challenged by issues such as missing labels, domain adaptability, and temporal coherence in data. To address these challenges, we propose a deep Particle Flow Bayes (DPFB) framework for cross-domain soft sensor modeling in the absence of target state labels. In particular, a sequential Bayes objective is first formulated to perform the maximum likelihood estimation underlying the cross-domain soft sensing problem. At the core of the framework, we incorporate a physics-inspired particle flow that optimizes the sequential Bayes objective to perform an exact Bayes update of the model extracted latent and hidden features. As a result, these contributions enable the proposed framework to learn a rich approximate posterior feature representation capable of characterizing complex cross-domain system dynamics and performing effective time series unsupervised domain adaptation (UDA). Finally, we validate the framework on a complex industrial multiphase flow process system with complex dynamics and multiple operating conditions. The results demonstrate that the DPFB framework achieves superior cross-domain soft sensing performance, outperforming state-of-the-art deep UDA and normalizing flow approaches.
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