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.

本研究从不同角度探索了物理信息神经网络在数字孪生中的潜力，包括验证自适应采样方法在免网格框架中的有效性、评估数据驱动的 PINN 框架的性能，验证其在参数化 Navier-Stokes 方程中的可扩展性，提出了多保真度的数据驱动 PINN 方法，并评估其在不同的预测任务中的预测性能，最后通过集合方法研究了多保真度的数据驱动 PINN 方法的不确定性量化性能，证实了其在数字孪生中的潜力。