MeshONet: A generalizable and efficient operator learning method for structured mesh generation.

Area of Science:

• Scientific Computing
• Computational Science
• Artificial Intelligence in Engineering

Background:

• Traditional mesh generation methods (TFI, PDE-based) face challenges balancing efficiency and quality.
• Physics-informed intelligent methods improve efficiency but lack generalizability to new geometries, requiring retraining.
• Generalizable and efficient structured mesh generation is critical for scientific computing.

Purpose of the Study:

• Introduce MeshONet, the first generalizable intelligent method for structured mesh generation.
• Address the limitations of existing methods in terms of efficiency, quality, and adaptability to diverse geometries.
• Transform mesh generation into an operator learning problem solvable by a novel neural network architecture.

Main Methods:

• Mesh generation is framed as an operator learning problem with multiple input/solution functions.
• A dual-branch, shared-trunk neural network architecture is proposed to handle function space mappings.
• The method learns from input-output pairs to approximate the complex mapping for mesh generation.

Main Results:

• MeshONet achieves up to a four-order-of-magnitude speedup compared to traditional methods.
• The method demonstrates generalization capabilities, adapting to unseen geometries without retraining.
• High mesh quality is maintained alongside significant efficiency gains.

Conclusions:

• MeshONet represents a breakthrough in generalizable intelligent structured mesh generation.
• The proposed operator learning approach and network architecture effectively address prior limitations.
• This advancement significantly enhances the practicality and applicability of AI in scientific computing mesh generation.