Curriculum-Transfer-Learning-Based Physics-Informed Neural Networks for Simulating Long-Term-Evolution Convection-Diffusion Behaviors on Curved Surfaces

Physics-informed neural networks (PINNs) encode prior physical knowledge into neural networks, alleviating the need for extensive data volume within the network. However, for long-term problems involving time-dependent partial differential equations, the traditional PINN exhibits poor stability and struggles to obtain effective solutions. To address this challenge, a novel physics-informed neural network based on curriculum learning and transfer learning (CTL-PINN) was introduced. The main idea of this method is to transform the problem of long-term course simulation into multiple short-term course simulation problems within this time domain. Under the concept of curriculum learning, and step by step from simpleness to difficulty, the scope of the time domain to be solved was gradually expanded by training the PINN within small time quanta. Furthermore, the transfer learning method was adopted to transfer across the time domain based on the curriculum learning, and the PINN was gradually employed for solution, thus to achieve long-term simulation of convection-diffusion behaviors on curved surfaces. The CTL-PINN was combined with the extrinsic surface operator processing technology to simulate long-term convection-diffusion behaviors on complex surfaces, and the effectiveness and robustness of the improved physics-informed neural network were verified through multiple numerical examples.