AMS-GNO: An Aggregation-based MultiScale Graph Neural Operator for Large Scale PDEs

Neural operators provide efficient surrogates for repeated numerical simulation by learning mappings from PDE parameters, geometries, and boundary conditions to solution fields. Scaling neural operators to large unstructured meshes and point clouds, however, remains challenging: purely local operators require many hops to capture long-range dependencies, whereas global attention or dense soft-assignment mechanisms introduce non-negligible computational and memory overhead by coupling every node to every latent token.Motivated by the inherently local structure of PDEs, we propose AMS-GNO, an Aggregation-based Multiscale Graph Neural Operator that performs long-range interaction on a coarsened graph while preserving sparse, topology-aware communication across scales. AMS-GNO first partitions the original mesh or point cloud into balanced local aggregates using geometric and topological priors, preserving physical connectivity while controlling aggregation size. Local smoothing then expands these hard assignments into a sparse overlapping cross-scale graph, allowing nodes near aggregate boundaries to interact with multiple neighboring coarse nodes. Restricted to this sparse support, attention-based operators separately learn downsampling and upsampling, adaptively determining which fine-scale information should be retained at coarse scales and how coarse representations should be reconstructed. The resulting architecture integrates fine-scale local processing, overlapping cross-scale transfer, and coarse-scale long-range interaction within a unified multiscale framework.Across multiple PDE benchmarks involving complex geometries, AMS-GNO achieves competitive or superior performance relative to state-of-the-art baselines while retaining favorable computational efficiency. Scalability experiments further show approximately linear growth in training time and memory consumption with the number of nodes, and demonstrate applicability to industrial-scale datasets containing millions of nodes. These results suggest that AMS-GNO provides an effective route toward scalable neural operators for high-resolution simulation on complex unstructured domains.