Abstract: Periodic patterns are a fundamental characteristic of time series in natural world, with significant implications for a range of disciplines, from economics to cloud systems. However, the current literature on periodicity detection faces two key challenges: limited robustness in real-world scenarios and a lack of memory to leverage previously observed time series to accelerate and improve inference on new data. To overcome these obstacles, this paper presents AmortizedPeriod, an innovative approach to periodicity identification based on amortized variational inference that integrates Bayesian statistics and deep learning. Through the Bayesian generative process, our method flexibly captures the dependencies of the periods, trends, noise, and outliers in time series, while also considering missing data and irregular periods in a robust manner. In addition, it utilizes the evidence lower bound of the log-likelihood of the observed time series as the loss function to train a deep attention inference network, facilitating knowledge transfer from the seen time series (and their labels) to unseen ones. Experimental results show that AmortizedPeriod surpasses the state-of-the-art methods by a large margin of $28.5\%$ on average in terms of micro $F_1$-score, with at least $55\%$ less inference time.