This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives. First, various adaptive sampling approaches for collocation points are investigated to verify their effectiveness in the mesh-free framework of PINNs, which allows automated construction of virtual representation without manual mesh generation. Then, the overall performance of the data-driven PINNs (DD-PINNs) framework is examined, which can utilize the acquired datasets in DT scenarios. Its scalability to more general physics is validated within parametric Navier-Stokes equations, where PINNs do not need to be retrained as the Reynolds number varies. In addition, since datasets can be often collected from different fidelity/sparsity in practice, multi-fidelity DD-PINNs are also proposed and evaluated. They show remarkable prediction performance even in the extrapolation tasks, with $42\sim62\%$ improvement over the single-fidelity approach. Finally, the uncertainty quantification performance of multi-fidelity DD-PINNs is investigated by the ensemble method to verify their potential in DT, where an accurate measure of predictive uncertainty is critical. The DD-PINN frameworks explored in this study are found to be more suitable for DT scenarios than traditional PINNs from the above perspectives, bringing engineers one step closer to seamless DT realization.

翻译：本研究从多维度探讨了物理信息神经网络（PINNs）在实现数字孪生（DT）中的潜力。首先，研究了配置点的多种自适应采样方法，验证其在PINNs无网格框架中的有效性——该框架无需手动生成网格即可自动构建虚拟表征。随后，考察了数据驱动型PINNs（DD-PINNs）框架的整体性能，该框架可有效利用数字孪生场景中获取的数据集。通过参数化纳维-斯托克斯方程验证了其向更普适物理问题的可扩展性：当雷诺数变化时，PINNs无需重新训练。此外，鉴于实际场景中数据集常具有不同保真度/稀疏性，本文提出并评估了多保真度DD-PINNs。即便在外推任务中，该模型仍展现出卓越的预测性能，相比单保真度方法提升达42%～62%。最后，采用集成方法研究了多保真度DD-PINNs的不确定性量化能力，以验证其在预测不确定性精准度量至关重要的数字孪生中的潜力。从上述维度分析，本研究所探索的DD-PINNs框架比传统PINNs更适配数字孪生场景，为工程师实现无缝数字孪生迈出了关键一步。