  Time series domain adaptation stands as a pivotal and intricate challenge
with diverse applications, including but not limited to human activity
recognition, sleep stage classification, and machine fault diagnosis. Despite
the numerous domain adaptation techniques proposed to tackle this complex
problem, they primarily focus on domain adaptation from a single source domain.
Yet, it is more crucial to investigate domain adaptation from multiple domains
due to the potential for greater improvements. To address this, three important
challenges need to be overcome: 1). The lack of exploration to utilize
domain-specific information for domain adaptation, 2). The difficulty to learn
domain-specific information that changes over time, and 3). The difficulty to
evaluate learned domain-specific information. In order to tackle these
challenges simultaneously, in this paper, we introduce PrOmpt-based domaiN
Discrimination (POND), the first framework to utilize prompts for time series
domain adaptation. Specifically, to address Challenge 1, we extend the idea of
prompt tuning to time series analysis and learn prompts to capture common and
domain-specific information from all source domains. To handle Challenge 2, we
introduce a conditional module for each source domain to generate prompts from
time series input data. For Challenge 3, we propose two criteria to select good
prompts, which are used to choose the most suitable source domain for domain
adaptation. The efficacy and robustness of our proposed POND model are
extensively validated through experiments across 50 scenarios encompassing four
datasets. Experimental results demonstrate that our proposed POND model
outperforms all state-of-the-art comparison methods by up to $66\%$ on the
F1-score.
