Physics-Informed Neural Networks for Digital Twins

My research investigates physics-informed neural networks (PINNs) from the perspective of digital twins (DTs), focusing on several key aspects:

1. Automated Construction of Virtual Space: We explored the meshless nature of PINNs, which is crucial for automated virtual space construction. An adaptive sampling method for collocation points tailored to fluid dynamics was proposed and compared with existing techniques to assess the practicality of PINNs' mesh-free properties.

2. Data-Driven Model Updating: We evaluated the performance of data-driven PINNs (DD-PINNs) for scenarios where datasets are continuously acquired in DTs. Our findings highlight the superiority of DD-PINNs over conventional, data-free PINNs, especially under higher Reynolds number conditions where traditional methods fail. By visualizing the loss landscape, we demonstrated the reasons behind DD-PINN's success in more complex fluid dynamics.

3. Guidelines for DD-PINNs in DTs: A key insight from the study was that random sampling for collocation points outperformed other adaptive sampling techniques in DD-PINNs. This is attributed to the need for uniformly distributed points to offset the local regularization effects of the data-driven loss term.

4. Scalability to Different Physics: We validated the scalability of DD-PINNs by applying them to parametric Navier-Stokes (NS) equations. The results showed that DD-PINNs provide an advantage over both data-free PINNs and data-driven neural networks. This scalability is crucial for DTs that require real-time predictions under various partial differential equation (PDE) parameters.

5. Applicability to Multi-Fidelity/Sparse Datasets: The research extended DD-PINNs to handle heterogeneous data sources, reflecting real-world scenarios where datasets vary in fidelity and sparsity. Our multi-fidelity DD-PINNs outperformed data-free PINNs, standard neural networks, and single-fidelity DD-PINNs, showcasing excellent extrapolation performance even beyond the Reynolds numbers used during training. This flexibility is vital for DTs that combine sparse high-fidelity data from physical space with data from virtual space.

6. Uncertainty Quantification (UQ): Finally, we evaluated the UQ capabilities of multi-fidelity DD-PINNs using an ensemble approach. The results indicated that these models provide reasonable uncertainty estimates across different Reynolds numbers. This quality is promising for DT applications, where reliable predictive uncertainty is crucial for decision-making.

Click for more details