DataTransfer: Neural network based interpolation across non-nested meshes

TL;DR

This paper introduces a neural network approach for high-precision function interpolation across non-nested meshes, improving efficiency and robustness over traditional methods.

Contribution

It proposes a neural network model that uses nodal function values for mesh-independent interpolation, with a comparative analysis of different network architectures.

Findings

Radial basis function networks offer the best balance of accuracy and efficiency.

The neural approach outperforms conventional methods in non-nested mesh interpolation.

Numerical experiments confirm the model's effectiveness in function transfer tasks.

Abstract

In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and numerical stability of algorithms. This paper proposes neural network based function mapping model across meshes, wherein the interpolation process is reformulated as a data-driven regression problem over scattered function data. Conventional interpolation and projection-based approaches are highly dependent on mesh connectivity and corresponding geometric properties, which renders such methods computationally costly and sensitive to mismatches between source and target meshes. The proposed method constructs a neural network approximator using nodal function values on the source mesh to obtain a global representation of the function, which can then be interpolated onto any other meshes. To investigate the network architectural impacts on model performance, three representative feedforward network structures are numerically compared in this work: multi-layer perceptrons, extreme learning machines, and network incorporating radial basis function hidden units. The results reveal distinct trade-offs among accuracy, computational efficiency and model robustness, among which the radial basis function-based network achieves the most desirable overall performance balance, enabling fast and precise function calculation. Numerical experiments conducted on non-nested meshes validate the efficacy of the proposed model in both function interpolation and cross-mesh data transmission tasks.