MetaNOR: A Meta-Learnt Nonlocal Operator Regression Approach for Metamaterial Modeling

TL;DR

MetaNOR is a meta-learning approach that efficiently creates surrogate models for new metamaterials by transferring knowledge from previous tasks, significantly reducing data requirements for modeling wave propagation.

Contribution

The paper introduces MetaNOR, a novel meta-learning framework for nonlocal operator regression that enables rapid transfer learning for diverse metamaterial microstructures.

Findings

Substantial improvements in sampling efficiency for new materials.

Effective transfer of learned kernels to unseen metamaterial tasks.

Reduced data requirements for accurate wave propagation modeling.

Abstract

We propose MetaNOR, a meta-learnt approach for transfer-learning operators based on the nonlocal operator regression. The overall goal is to efficiently provide surrogate models for new and unknown material-learning tasks with different microstructures. The algorithm consists of two phases: (1) learning a common nonlocal kernel representation from existing tasks; (2) transferring the learned knowledge and rapidly learning surrogate operators for unseen tasks with a different material, where only a few test samples are required. We apply MetaNOR to model the wave propagation within 1D metamaterials, showing substantial improvements on the sampling efficiency for new materials.