Burnout is a significant public health concern affecting nearly half of the healthcare workforce. This paper presents the first end-to-end deep learning framework for predicting physician burnout based on electronic health record (EHR) activity logs, digital traces of physician work activities that are available in any EHR system. In contrast to prior approaches that exclusively relied on surveys for burnout measurement, our framework directly learns deep representations of physician behaviors from large-scale clinician activity logs to predict burnout. We propose the Hierarchical burnout Prediction based on Activity Logs (HiPAL), featuring a pre-trained time-dependent activity embedding mechanism tailored for activity logs and a hierarchical predictive model, which mirrors the natural hierarchical structure of clinician activity logs and captures physicians' evolving burnout risk at both short-term and long-term levels. To utilize the large amount of unlabeled activity logs, we propose a semi-supervised framework that learns to transfer knowledge extracted from unlabeled clinician activities to the HiPAL-based prediction model. The experiment on over 15 million clinician activity logs collected from the EHR at a large academic medical center demonstrates the advantages of our proposed framework in predictive performance of physician burnout and training efficiency over state-of-the-art approaches.