Predicting the subcutaneous temperature in cryolipolysis using deep operator networks

Accurate monitoring of subcutaneous temperature is crucial for the safety and efficacy of cryolipolysis. However, existing measurement and simulation methods often require trade-offs between accuracy, depth, and computational efficiency. This study introduces a novel deep learning architecture, ConvD-DeepONet, specifically designed to predict subcutaneous temperature fields with both high accuracy and efficiency. The model effectively captures spatial information and produces multi-dimensional output, owing to the innovative integration of convolutional layers and the decoder network. An average absolute error (MAE) of 0.0038 ℃ and a root mean square error (RMSE) of 0.0083 ℃ are achieved, resulting in over a 50 % reduction compared to the baseline models. Moreover, each prediction is completed in just 5.9 ms, rendering it 120 times faster than traditional finite element method simulations. These results indicate that ConvD-DeepONet is a promising tool for real-time subcutaneous temperature prediction, with the potential to enhance the safety and efficacy of cryolipolysis.