Where 𝐺 ",! is the hybridization free energy with index i predicted by the model of weight parameters ω, ⟨𝐺 ",! ⟩ is the expectation of the model ensemble. Here, the threshold of model deviation was set to 0.6, and the top 16 duplexes with error index greater than the threshold were taken as candidates per iteration. After obtaining hybridization free energies of these candidates, they are added to the training data for subsequent retraining. During the iterative process of the active learning, as the number of iterations increases, the mean RMSE of the train set gradually rises from the initial value of 0.236 and eventually reaches 0.334 (Figure ). Meanwhile, the number of candidates steadily decreases from the initial count of 642 and eventually reaches 0 (Figure ). 132 duplexes were selected by the active learning method, and along with the initial training data, a total of 196 duplexes were used as the final training data. To evaluate the model performance, the test set consisting of 48 duplexes was randomly generated based on the above sequence design principle, including 24 perfect duplexes and 24 duplexes with dangles, and their hybridization free energies were obtained. Melting curves and thermodynamic parameters of 244 duplexes are elaborated in Supplementary Note 3. The results show that the best-fit values of hybridization free energies of 244 duplexes range from -14.7 to -5.58 kcal/mol (Figure ). There is a significant negative correlation between the length of the stack domain and the hybridization free energy, with the Pearson correlation coefficient being -0.925. The results indicate that increasing the length of stack domains contribute to improve the stability of the duplex.