Data-driven Physics-Informed Neural Networks (PINNs)

My research aims to enhance digital twins through physics-informed neural networks (PINNs), exploring how these models can create more robust and adaptable virtual representations of complex physical systems. A key area of focus has been the development of adaptive sampling methods to enable mesh-free modeling within PINNs. This advancement allows the automated construction of virtual models, eliminating the need for tedious and time-consuming manual mesh generation, thereby making digital twin construction significantly more efficient and scalable.

Beyond traditional PINNs, I investigated data-driven PINNs (DD-PINNs), which leverage real-world datasets to enhance predictive capabilities. Integrating datasets directly into the physics-informed framework not only enriches the model's accuracy but also has a profound impact on its optimization process. Specifically, embedding data into the loss function makes the loss landscape of the PINNs much more convex and smoother. This characteristic simplifies the optimization process, enabling faster convergence and improved stability in scenarios where data-free models struggle. As a result, DD-PINNs exhibit remarkable adaptability, handling complex physics such as varying Reynolds numbers in fluid dynamics, while remaining up-to-date with real-time changes in their physical counterparts without requiring retraining for each scenario.

I also explored the integration of datasets with varying levels of fidelity, addressing a common challenge in real-world engineering applications. The multi-fidelity DD-PINNs I developed were capable of incorporating both high-fidelity, sparse datasets and lower-fidelity, more abundant data sources, resulting in substantial improvements in prediction accuracy. Impressively, these models demonstrated strong extrapolation capabilities, providing reliable predictions even under conditions beyond the original training data. This flexibility is vital for building digital twins that can operate across a diverse range of scenarios, making the models highly applicable to engineering tasks that require dynamic adaptability.

Furthermore, I incorporated advanced uncertainty quantification methods into the multi-fidelity DD-PINNs to provide accurate and reliable confidence measures. This is crucial for decision-making processes in engineering, where knowing the limits and reliability of predictions can help avoid costly errors. By combining real-time data integration, adaptive modeling, and enhanced uncertainty quantification, my work significantly pushes the boundaries of digital twin technology, paving the way for a more seamless integration of physical systems and their virtual counterparts.

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