Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions

Area of Science:

• Computational Materials Science
• Computational Chemistry
• Chemical Engineering

Background:

• Evaluating expensive, rapidly changing functions is crucial for computational materials science and chemistry.
• High dimensionality poses significant challenges for creating accurate surrogate models, increasing computational costs.

Purpose of the Study:

• To develop a novel interpolation method that overcomes the curse of dimensionality for expensive functions.
• To enable faithful function reconstructions from limited data for applications like multiscale simulations.

Main Methods:

• A modified Shepard interpolation method incorporating local metrics to identify directions of rapid change.
• Utilizing local error estimates to weight approximations and prevent oscillations.
• Testing on analytic functions and a kinetic Monte Carlo model for heterogeneous catalysis.

Main Results:

• The novel method successfully reconstructs complex functions even with sparse data.
• It demonstrates superior performance compared to isotropic metric Shepard methods.
• Outperforms state-of-the-art Gaussian process regression in accuracy and efficiency.

Conclusions:

• The proposed method effectively addresses the curse of dimensionality in surrogate modeling.
• It offers a computationally efficient and accurate approach for complex scientific simulations.
• Paves the way for more sophisticated multiscale modeling in materials science and chemistry.