PINN Fine-tuning Scheme for Distributed Parameter Systems Modeling with Dynamic Loss Balance*

Driven by the industrial demand for enhanced system safety and control performance, the modeling of distributed parameter systems has drawn significant attention. In this paper, a physics-informed neural network (PINN) fine-tuning scheme, consisting of pre-training and fine-tuning phases, is proposed for modeling distributed parameter systems, while dropout techniques is incorporated to prevent overfitting. During the pre-training phase, the network primarily focuses on training with higher-magnitude loss components, while a variable weighting method adjusts the emphasis according to different training phases. During the fine-tuning phase, the pre-trained model is refined using boundary and initial conditions. Consequently, effective distributed parameter system modeling is achieved for scenarios with a limited number of sensors. The effectiveness of the proposed scheme is demonstrated through a benchmark study on a nonlinear one-dimensional thermal process.