Graph Learning in Physical-informed Mesh-reduced Space for Real-world Dynamic Systems

Yeping Hu, Bo Lei, Victor M. Castillo

Abstract: Recent machine learning approaches have demonstrated their ability to extract information from data that could be translated into knowledge about the underlying dynamic systems. However, these learning-based models suffer from scalability issues when training on high-dimensional and high-resolution simulation data generated for real-world applications. In this work, we aim to tackle this challenge by deliberately prioritizing certain aspects of dynamic systems, while allocating relatively less attention and computational resources to others. Specifically, we concentrate on improving the predictive accuracy of crucial properties or regions that significantly impact these dynamic systems, while comparatively reducing emphasis on the remaining aspects. By employing graph learning schemes and custom-designed modules, we have developed a two-stage prediction model that incorporates prior knowledge of the systems. This approach enables us to place a heightened emphasis on the region of interest (ROI) during the learning process where the model operates in a reduced-dimensional mesh space, resulting in reduced computational costs while preserving crucial physical properties. To test and evaluate our method, we utilized two simulation datasets: lid-driven cavity and cylinder flow. The results show that even under reduced operational space, our method still achieves desirable performance on accuracy and generalizability of both prediction and physical consistency over region of interest.