# Manifold Learning for Knowledge Discovery and Intelligent Inverse Design of Photonic Nanostructures: Breaking the Geometric Complexity

arXiv: https://arxiv.org/abs/2102.04454 · HTML: https://mlsanity.com/paper/2102.04454/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 58 references that are in the map.
- First posted on arXiv 7 Feb 2021.

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

- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Stochastic AUC Maximization with Deep Neural Networks](https://mlsanity.com/paper/1908.10831/) (2019)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [Benchmarking deep inverse models over time, and the neural-adjoint method](https://mlsanity.com/paper/2009.12919/) (2020)
- [Freeform Diffractive Metagrating Design Based on Generative Adversarial Networks](https://mlsanity.com/paper/1811.12436/) (2018)
- [Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures](https://mlsanity.com/paper/1902.03865/) (2019)
- [A Cyclical Deep Learning Based Framework For Simultaneous Inverse and Forward design of Nanophotonic Metasurfaces](https://mlsanity.com/paper/2005.12796/) (2020)
- [Deep Learning Reveals Underlying Physics of Light-matter Interactions in Nanophotonic Devices](https://mlsanity.com/paper/1905.06889/) (2019)
- [Knowledge Discovery In Nanophotonics Using Geometric Deep Learning](https://mlsanity.com/paper/1909.07330/) (2019)

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

- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Diffusion Probabilistic Model Based Accurate and High-Degree-of-Freedom Metasurface Inverse Design](https://mlsanity.com/paper/2304.13038/) (2023)
- [Inverse Design in Nanophotonics via Representation Learning](https://mlsanity.com/paper/2507.00546/) (2025)
- [Deep learning-based variational autoencoder for classification of quantum and classical states of light](https://mlsanity.com/paper/2405.05243/) (2024)
- [Bayesian Optimization for Function-Valued Responses under Min-Max Criteria](https://mlsanity.com/paper/2512.07868/) (2025)

## Abstract (arXiv)

Here, we present a new approach based on manifold learning for knowledge discovery and inverse design with minimal complexity in photonic nanostructures. Our approach builds on studying sub-manifolds of responses of a class of nanostructures with different design complexities in the latent space to obtain valuable insight about the physics of device operation to guide a more intelligent design. In contrast to the current methods for inverse design of photonic nanostructures, which are limited to pre-selected and usually over-complex structures, we show that our method allows evolution from an initial design towards the simplest structure while solving the inverse problem.