Physical restriction neural networks with restarting strategy for solving mathematical model of thermal heat equation for early diagnose breast cancer

Abstract

Breast cancer is a serious health concern for women in both developed and developing countries, and early diagnosis is crucial for an effective treatment. One possible approach of detection is by observing abnormal surface temperatures of the breast. To study the thermal behavior of the human breast, this research paper employs the two-dimensional heat equation’s partial differential equation (PDE). In fact, we propose a method called r-PINN-Adam, which uses Physics-Informed Neural Networks (PINN) with a restarting strategy to solve the PDE thermal analysis. PINN is a method that incorporates physical law in each dataset to solve PDE problems, while Adam is used to update the weights of the ANN and minimize the loss function. The restarting process monitors the progress of the loss values, and if no improvement is made, the process is restarted with the best weights as the initial input to the next cycle. This approach ensures that the method finds the smallest value of the loss function, and it is also more efficient as no time is wasted on iterations that do not significantly improve the results. The PDE thermal analysis was solved for normal and tumorous breasts to study the temperature behavior surrounding the cancer. The proposed r-PINN-Adam method was compared to the basic PINN and other optimizers in terms of accuracy and efficiency. The numerical results indicated that our proposed method yields competitive results compared to state-of-the-art methods, while significantly reducing computational time.

Keywords

• Breast cancer
• PINN
• Adam
• Restarting
• PDE thermal analysis