Accurate physical simulation is fundamental to science and engineering, yet conventional numerical solvers incur high costs when handling complex geometries, varying boundary and initial conditions, and diverse physical parameters. Recent deep-learning-based methods offer faster solutions, while limited flexibility and generalization on irregular meshes still hinder their practical deployment. Here we show an efficient graph-transformer operator, named PhysGTO, for learning physical dynamics through explicit manifold embeddings in both physical and latent spaces. The method aligns heterogeneous node-level conditions, constructs sparse structure-preserving connections, and integrates lightweight local message passing with global attention to capture multiscale physical dependencies. Its design scales linearly with the number of mesh points, reducing model size and computational cost while enabling efficient inference. On a benchmark of 11 datasets covering irregular meshes, time-dependent flows, and large three-dimensional geometries, PhysGTO achieves state-of-the-art accuracy with substantially lower computational cost, showing strong flexibility, scalability, and generalization across diverse physical systems.
Liu et al. (Wed,) studied this question.