Learning to Generate Structured Meshes with In-Context: Toward Generalization in Mesh Generation

Abstract Structured mesh generation serves as a crucial preprocessing step in numerical simulations and can be formulated as a mapping problem from geometry to structured mesh. Existing approaches typically establish an isolated mapping for each geometry. This geometry-specific paradigm fails to capture and leverage commonalities across geometries, inevitably requiring recomputation or costly retraining for new geometries. To overcome this limitation, we propose ICL-Mesh, a meta-learning framework based on in-context learning (ICL) for structured mesh generation. It treats learning one mapping as one task and trains a single neural network to extract commonalities across tasks and learn from in-context examples within each task, enabling rapid generalization to unseen tasks without parameter updates. Experimental results demonstrate that ICL-Mesh effectively generalizes to diverse geometries with only a few context examples, and even without examples. It also exhibits robustness to in-context example order sensitivity and can be extended to various mesh generation scenarios, including mesh refinement and coarsening.