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

arXiv: https://arxiv.org/abs/2206.02040 · HTML: https://mlsanity.com/paper/2206.02040/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 4 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Meta-learning for Few-shot Natural Language Processing: A Survey](https://mlsanity.com/paper/2007.09604/) (2020)
- [Reliable and Explainable Machine Learning Methods for Accelerated Material Discovery](https://mlsanity.com/paper/1901.02717/) (2019)
- [A data-driven peridynamic continuum model for upscaling molecular dynamics](https://mlsanity.com/paper/2108.04883/) (2021)
- [Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws](https://mlsanity.com/paper/2012.04157/) (2020)
- [MetaDelta: A Meta-Learning System for Few-shot Image Classification](https://mlsanity.com/paper/2102.10744/) (2021)
- [Data-driven learning of robust nonlocal physics from high-fidelity synthetic data](https://mlsanity.com/paper/2005.10076/) (2020)

## Built on by (most cited first, 6 of 6)

- [Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses](https://mlsanity.com/paper/2401.06070/) (2024)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics](https://mlsanity.com/paper/2301.12095/) (2023)
- [Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification](https://mlsanity.com/paper/2211.01330/) (2022)
- [Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures](https://mlsanity.com/paper/2301.04540/) (2023)
- [Embedded Nonlocal Operator Regression (ENOR): Quantifying model error in learning nonlocal operators](https://mlsanity.com/paper/2410.20331/) (2024)

## Abstract (arXiv)

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.