Modeling of distributed parameter systems based on independent partial derivative-physics-informed neural network

Abstract

Physics-informed neural networks (PINNs) have attracted considerable interest due to their capacity to incorporate established physical principles, thus facilitating efficient training with a limited amount of observed data. This approach ensures that the results of supervised learning are in accordance with the governing physical laws of the system, thereby enhancing the interpretability of models. However, existing research predominantly employs a single network architecture to simultaneously learn the information of the partial differential equations (PDEs). Such architectures typically require large network sizes to learn the system characteristics, which leads to prolonged training times and inefficiencies. This paper introduces a novel modeling framework, termed the independent partial derivative-physics-informed neural network (IPD-PINN). In contrast to conventional methodologies, IPD-PINN employs a network comprising multiple subnetworks, with each subnetwork dedicated to the learning of individual partial derivatives in the PDEs. The modular network structure allows for flexible and scalable adjustments to the size of each subnetwork, accommodating modeling tasks of varying complexities. Consequently, the entire network is capable of reducing the required training time while maintaining precise modeling accuracy. The efficacy of the proposed IPD-PINN method is demonstrated through two simulation case studies, which highlight its potential to improve the efficiency and accuracy of IPD-PINN modeling.