Bridging Data and Physics: A Graph Neural Network-Based Hybrid Twin Framework

Abstract

Simulating complex unsteady physical phenomena relies on detailed mathematical models, simulated for instance by using the Finite Element Method (FEM). However, these models often exhibit discrepancies from the reality due to unmodeled effects or simplifying assumptions. We refer to this gap as the ignorance model. While purely data-driven approaches attempt to learn full system behavior, they require large amounts of high-quality data across the entire spatial and temporal domain. In real-world scenarios, such information is unavailable, making full data-driven modeling unreliable. To overcome this limitation, we model of the ignorance component using a hybrid twin approach, instead of simulating phenomena from scratch. Since physics-based models approximate the overall behavior of the phenomena, the remaining ignorance is typically lower in complexity than the full physical response, therefore, it can be learned with significantly fewer data. A key difficulty, however, is that spatial measurements are sparse, also obtaining data measuring the same phenomenon for different spatial configurations is challenging in practice. Our contribution is to overcome this limitation by using Graph Neural Networks (GNNs) to represent the ignorance model. GNNs learn the spatial pattern of the missing physics even when the number of measurement locations is limited. This allows us to enrich the physics-based model with data-driven corrections without requiring dense spatial, temporal and parametric data. To showcase the performance of the proposed method, we evaluate this GNN-based hybrid twin on nonlinear heat transfer problems across different meshes, geometries, and load positions. Results show that the GNN successfully captures the ignorance and generalizes corrections across spatial configurations, improving simulation accuracy and interpretability, while minimizing data requirements.