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DataTransfer: Neural Network-based Interpolation across Unstructured Meshes

Jiaxiong Hao, Yunqing Huang, Nianyu Yi

TL;DR

DataTransfer reframes mesh-to-mesh data transfer as a global regression problem that maps scattered source-nodal values to arbitrary target locations without using mesh connectivity. It systematically compares three surrogate models—FNN, ELM, and RBF-ELM—finding that RBF-ELM provides the best practical balance of accuracy, robustness to irregular sampling, and computational efficiency on adaptive, unstructured meshes. FNNs struggle with oscillatory and highly refined regions and can converge to suboptimal minima, ELM delivers high accuracy on uniform samples but degrades under nonuniform sampling, while RBF-ELM maintains accuracy (down to $10^{-7}$ in 2D tests) and is less sensitive to sampling patterns. The approach enables fast, mesh-agnostic data transfer suitable for dynamic or multiphysics simulations and suggests future work on systematic hyperparameter analysis and extension to preserve integral quantities across transfers.

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.

DataTransfer: Neural Network-based Interpolation across Unstructured Meshes

TL;DR

DataTransfer reframes mesh-to-mesh data transfer as a global regression problem that maps scattered source-nodal values to arbitrary target locations without using mesh connectivity. It systematically compares three surrogate models—FNN, ELM, and RBF-ELM—finding that RBF-ELM provides the best practical balance of accuracy, robustness to irregular sampling, and computational efficiency on adaptive, unstructured meshes. FNNs struggle with oscillatory and highly refined regions and can converge to suboptimal minima, ELM delivers high accuracy on uniform samples but degrades under nonuniform sampling, while RBF-ELM maintains accuracy (down to in 2D tests) and is less sensitive to sampling patterns. The approach enables fast, mesh-agnostic data transfer suitable for dynamic or multiphysics simulations and suggests future work on systematic hyperparameter analysis and extension to preserve integral quantities across transfers.

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.

Paper Structure

This paper contains 8 sections, 25 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Neural Network-based interpolation
  3. Problem Formulation
  4. Data Transfer via Feedforward Neural Network
  5. Data Transfer via Extreme Learning Machine
  6. Data Transfer via Radial Basis Function-ELM
  7. Application
  8. Conclusions

Figures (15)

  • Figure 1: Schematic architecture of a fully connected feedforward neural network.
  • Figure 2: \ref{['ex1']}, NN interpolation on a quasi-uniform mesh. (A) training mesh containing 2,500 nodes; (B) exact solution used as reference; (C) history of the training loss; (D) test mesh with 10,000 evaluation points; (E) interpolated solution together with the corresponding error distribution.
  • Figure 3: \ref{['ex2']}, NN interpolation on an adaptive mesh. (A) training mesh; (B) reference solution; (C) history of the training loss; (D) test mesh with 10,000 evaluation points; (E) interpolated solution together with the corresponding error distribution.
  • Figure 4: Schematic architecture of an extreme learning machine network.
  • Figure 5: \ref{['ex3']}, ELM interpolation on a quasi-uniform mesh. (A) Test mesh; (B) interpolated solution and error.
  • ...and 10 more figures

Theorems & Definitions (10)

  • Example 2.1
  • Example 2.2
  • Remark 2.3
  • Example 2.4
  • Example 2.5
  • Example 2.6
  • Example 3.1
  • Example 3.2
  • Example 3.3
  • Example 3.4