# Inverse deep learning methods and benchmarks for artificial electromagnetic material design

arXiv: https://arxiv.org/abs/2112.10254 · HTML: https://mlsanity.com/paper/2112.10254/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 66 references that are in the map.
- First posted on arXiv 19 Dec 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [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)
- [A Generative Model for Inverse Design of Metamaterials](https://mlsanity.com/paper/1805.10181/) (2018)
- [Benchmarking Invertible Architectures on Inverse Problems](https://mlsanity.com/paper/2101.10763/) (2021)
- [Designing nanophotonic structures using conditional-deep convolutional generative adversarial networks](https://mlsanity.com/paper/1903.08432/) (2019)
- [Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures](https://mlsanity.com/paper/1902.03865/) (2019)

## Built on by (most cited first, 10 of 10)

- [An Agentic Framework for Autonomous Metamaterial Modeling and Inverse Design](https://mlsanity.com/paper/2506.06935/) (2025)
- [Learning Electromagnetic Metamaterial Physics With ChatGPT](https://mlsanity.com/paper/2404.15458/) (2024)
- [Tackling Multimodal Device Distributions in Inverse Photonic Design using Invertible Neural Networks](https://mlsanity.com/paper/2208.14212/) (2022)
- [Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling](https://mlsanity.com/paper/2211.14366/) (2022)
- [Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates](https://mlsanity.com/paper/2304.13860/) (2023)
- [Aligning Reasoning LLMs for Materials Discovery with Physics-aware Rejection Sampling](https://mlsanity.com/paper/2509.00768/) (2025)
- [IDToolkit: A Toolkit for Benchmarking and Developing Inverse Design Algorithms in Nanophotonics](https://mlsanity.com/paper/2305.18978/) (2023)
- [Interpretable inverse design of optical multilayer thin films based on extended neural adjoint and regression activation mapping](https://mlsanity.com/paper/2507.18644/) (2025)
- [Neural Electromagnetic Fields for High-Resolution Material Parameter Reconstruction](https://mlsanity.com/paper/2603.02582/) (2026)
- [Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments](https://mlsanity.com/paper/2608.29907/) (2026)

## Abstract (arXiv)

Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but to compare, contrast, and evaluate assorted techniques it is critical to clarify the underlying ill-posedness of inverse problems. Here we review state-of-the-art approaches and present a comprehensive survey of deep learning inverse methods and invertible and conditional invertible neural networks to AEM design. We produce easily accessible and rapidly implementable AEM design benchmarks, which offers a methodology to efficiently determine the DL technique best suited to solving different design challenges. Our methodology is guided by constraints on repeated simulation and an easily integrated metric, which we propose expresses the relative ill-posedness of any AEM design problem. We show that as the problem becomes increasingly ill-posed, the neural adjoint with boundary loss (NA) generates better solutions faster, regardless of simulation constraints. On simpler AEM design tasks, direct neural networks (NN) fare better when simulations are limited, while geometries predicted by mixture density networks (MDN) and conditional variational auto-encoders (VAE) can improve with continued sampling and re-simulation.