DataTransfer: Neural Network-based Interpolation across Unstructured Meshes

Abstract: This paper presents a neural network-based interpolation framework for transferring numerical approximations on different unstructured meshes. Traditional projection or interpolation techniques often depend on mesh connectivity, explicit element mappings, or local reconstruction procedures, which can be computationally demanding and sensitive to mesh misalignment. Instead, we formulate the problem as a data-driven regression task that predicts function values at arbitrary target locations from scattered nodal data on the source mesh. By systematically exploring and comparing several neural network architectures, we identify a configuration that balances accuracy and efficiency and that performs reliably across a range of mesh resolutions and topologies. The resulting model enables fast and accurate evaluation without requiring access to mesh connectivity or element-wise information. Numerical experiments on adaptive meshes suggest that the framework is effective for field reconstruction and data transfer tasks. The code used in this paper is publicly available on GitHub.