Bridging data and physics: A graph neural network-based hybrid twin framework

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 from measurements, they require large amounts of high-quality data across the entire spatial and temporal domain. In many real-world scenarios, such information is unavailable as physical quantities are measurable only at limited points, making full data-driven modeling unreliable. To overcome this limitation, a hybrid twin approach is required. Instead of simulating phenomena from scratch, here we focus on the modeling of the ignorance component. 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, and even more, obtaining data measuring the same phenomenon for different spatial configurations — system’s domain, external load, etc. — is challenging in practice. Our contribution is to overcome this limitation by using Graph Neural Networks (GNNs) to represent the ignorance model. GNNs inherently handle geometric structures, making them compatible with any approximation technique, for instance, FEM. They 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 assess the performance of the proposed methodology, we evaluate this GNN-based hybrid twin on nonlinear heat transfer problems across different meshes, geometries, and load positions. The results indicate that the GNN captures model discrepancies and generalizes corrections across varying domain geometries and mesh discretizations. This leads to improvements in simulation accuracy and interpretability, while also reducing data requirements