Stakeholders constantly make assumptions in the development of deep learning (DL) frameworks. These assumptions are related to various types of software artifacts (e.g., requirements, design decisions, and technical debt) and can turn out to be invalid, leading to system failures. Existing approaches and tools for assumption management usually depend on manual identification of assumptions. However, assumptions are scattered in various sources (e.g., code comments, commits, pull requests, and issues) of DL framework development, and manually identifying assumptions has high costs (e.g., time and resources). To overcome the issues of manually identifying assumptions in DL framework development, we constructed a new and largest dataset (i.e., AssuEval) of assumptions collected from the TensorFlow and Keras repositories on GitHub; explored the performance of seven traditional machine learning models (e.g., Support Vector Machine, Classification and Regression Trees), a popular DL model (i.e., ALBERT), and a large language model (i.e., ChatGPT) of identifying assumptions on the AssuEval dataset. The experiment results show that: ALBERT achieves the best performance (f1-score: 0.9584) of identifying assumptions on the AssuEval dataset, which is much better than the other models (the 2nd best f1-score is 0.6211, achieved by ChatGPT). Though ChatGPT is the most popular large language model, we do not recommend using it to identify assumptions in DL framework development because of its low performance on the task. Fine-tuning ChatGPT specifically for assumption identification could improve the performance. This study provides researchers with the largest dataset of assumptions for further research (e.g., assumption classification, evaluation, and reasoning) and helps practitioners better understand assumptions and how to manage them in their projects.