# Neural-field design of broadband Rayleigh-wave carpet cloaks under microstructure realisability constraints

> A neural-field and differentiable-FEM framework for designing broadband Rayleigh-wave carpet cloaks within realizable Cauchy materials and mapping the optimized fields to explicit manufacturable microstructures.

## Publication record

- **Title:** Neural-field design of broadband Rayleigh-wave carpet cloaks under microstructure realisability constraints
- **Authors:** David Aznaurov, Davit Piliposyan, Danila Rukhovich, Sébastien Guenneau
- **Year:** 2026
- **Status:** Preprint published on arXiv
- **Venue:** arXiv preprint
- **Research area:** Physics-Driven Machine Learning and Metamaterials
- **First arXiv submission:** 2026-09-04

## Abstract / summary

The paper formulates two-dimensional Rayleigh-wave carpet-cloak design as a PDE-constrained optimization problem within physically realizable Cauchy elasticity. A coordinate-based neural field and differentiable finite element solver optimize symmetric stiffness and density fields for single-frequency and broadband performance. The optimized fields are then mapped to explicit microstructures using homogenization, conditional diffusion, neural-field inverse design, and nearest-neighbor selection.

## Methodology

- PDE-constrained optimization of a two-dimensional Rayleigh-wave carpet cloak
- Coordinate-based neural field coupled to a differentiable finite element solver
- Single-frequency and broadband optimization of symmetric Cauchy stiffness and density fields
- Microstructure-constrained realization using homogenization, conditional diffusion, neural-field inverse design, and nearest-neighbor selection
- Validation with homogenized and fully resolved finite element simulations

## Datasets and benchmarks

- Database of homogenized microstructures

## Principal results

- The optimized Cauchy design approaches the ideal transformation-based cloak in finite element simulations.
- After projection to explicit microstructures, the homogenized model recovers approximately 97% of the defect-free reference surface-displacement magnitude.
- Direct simulation of the fully resolved microstructured geometry recovers approximately 76% at the design frequency.

## Technologies and methods

- Neural fields
- Differentiable finite element methods
- PDE-constrained optimization
- Conditional diffusion
- Homogenization
- Finite element simulation

## Related M:3L research

- [Physics-Driven Machine Learning](https://m3l.am/research/physics-driven-ml.md)
- [Differentiable Finite-Element Methods](https://m3l.am/research/differentiable-fem.md)
- [Metamaterials and Wave Control](https://m3l.am/research/metamaterials.md)

## External resources

- [arXiv record](https://arxiv.org/abs/2609.05163)
- [DOI](https://doi.org/10.48550/arXiv.2609.05163)

## Evidence boundary

Benchmark claims and numerical values above are attributed to the associated paper and its stated protocol. Potential applications are not evidence of completed deployments.

## About M:3L

M:3L is the Mathematical Modeling & Machine Learning Laboratory, a research and engineering laboratory in Yerevan, Armenia, established at the Institute of Mechanics of the National Academy of Sciences of the Republic of Armenia.

## Authoritative URLs

- [Canonical publication page](https://m3l.am/publications/neural-field-rayleigh-wave-cloaks)
- [All M:3L publications](https://m3l.am/publications.md)
- [M:3L research](https://m3l.am/research.md)