Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective

TL;DR

Realizing digital twins for fluid dynamics requires fast, generalizable surrogates that adapt to changing Reynolds numbers ($Re$) and data fidelities. The paper first evaluates adaptive sampling for data-free PINNs, showing limitations at higher $Re$, and then proposes data-driven PINNs (DD-PINNs) that incorporate labeled guide data to stabilize training; it further extends DD-PINNs to parametric NS equations and to multi-fidelity data with uncertainty quantification. Key findings include that random sampling often outperforms domain-specific adaptive schemes for DD-PINNs, while DD-PINNs achieve better generalization across unseen $Re$ and benefit from higher-fidelity guides; multi-fidelity DD-PINNs can yield superior extrapolation and realistic predictive uncertainty. The work demonstrates a viable path toward DT deployments by delivering mesh-free, data-informed, and uncertainty-aware surrogates capable of handling varying physics and data sources.

Abstract

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.

Figures (17)

• Figure 1: Ecosystem of the digital twins. This image is generated largely based on the report by National Academies national2023foundational, while some parts have been modified. The background image is generated with the assistance of DALL$\cdot$E 2, an AI model developed by OpenAI.
• Figure 2: Overall architectures of PINN. The data-free PINN does not include data-driven loss term whereas data-driven PINN does.
• Figure 3: Newly added adaptive points according to each criterion for different $k$ values. Note that all figures are the results of the last iteration in the RGV-111 model.
• Figure 4: Comparison of velocity components between DNS with $160\times160$ grid and PINN: (a) x-velocity, (b) y-velocity. The flow fields of PINNs are obtained from the best model among the four trained RGV-111 models.
• Figure 5: Prediction of y-velocity flow fields using data-free PINNs: (a) Re=1000, (b) Re=3200. Streamlines are also shown to highlight their failure.