Transfer learning-based physics-informed DeepONets for the adaptive evolution of digital twin models for dynamic systems

Digital twins have been widely applied as an important tool for digital transformation across various industries. In practical applications, digital twin virtual models must continuously evolve based on changes in physical entities. However, current research primarily focuses on providing general frameworks for evolving digital twin models, lacking specific implementations. To address this issue, this work develops a modified physics-informed deep operator networks (DeepONets) method based on transfer learning. The physics-informed DeepONets is adopted to construct the foundational digital twin model of the physical entity, which is capable of long-term prediction. Then, transfer learning is applied, leveraging the interaction between the physical entity and the virtual model to obtain the evolved digital twin model by fine-tuning. The evolved digital twin model can identify changes in the physical entity and perform long-term prediction. Both digital twin models require only the initial conditions for long-term predictions. This method is tested on three typical nonlinear dynamic systems, including the Duffing system, the Van der Pol system, and the Lorenz system. The results indicate that the digital twin model can adaptively evolve and achieve accurate long-term prediction using only a portion of the data collected from the physical entity without prior knowledge of changes in the physical entity, demonstrating the effectiveness of the proposed method.