# Interpretable inverse design of optical multilayer thin films based on extended neural adjoint and regression activation mapping

arXiv: https://arxiv.org/abs/2507.18644 · HTML: https://mlsanity.com/paper/2507.18644/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 54 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [Benchmarking deep inverse models over time, and the neural-adjoint method](https://mlsanity.com/paper/2009.12919/) (2020)
- [OptoGPT: A Foundation Model for Inverse Design in Optical Multilayer Thin Film Structures](https://mlsanity.com/paper/2304.10294/) (2023)
- [Diabetic Retinopathy Detection via Deep Convolutional Networks for Discriminative Localization and Visual Explanation](https://mlsanity.com/paper/1703.10757/) (2017)
- [Inverse deep learning methods and benchmarks for artificial electromagnetic material design](https://mlsanity.com/paper/2112.10254/) (2021)
- [Multi-objective and categorical global optimization of photonic structures based on ResNet generative neural networks](https://mlsanity.com/paper/2007.12551/) (2020)
- [Migrating Knowledge between Physical Scenarios based on Artificial Neural Networks](https://mlsanity.com/paper/1809.00972/) (2018)
- [TMM-Fast: A Transfer Matrix Computation Package for Multilayer Thin-Film Optimization](https://mlsanity.com/paper/2111.13667/) (2021)
- [OL-Transformer: A Fast and Universal Surrogate Simulator for Optical Multilayer Thin Film Structures](https://mlsanity.com/paper/2305.11984/) (2023)

## Abstract (arXiv)

We propose an extended neural adjoint (ENA) framework, which meets six key criteria for artificial intelligence-assisted inverse design of optical multilayer thin films (OMTs): accuracy, efficiency, diversity, scalability, flexibility, and interpretability. To enhance the scalability of the existing neural adjoint method, we present a novel forward neural network architecture for OMTs and introduce a material loss function into the existing neural adjoint loss function, facilitating the exploration of material configurations of OMTs. Furthermore, we present the detailed formulation of the regression activation mapping for the presented forward neural network architecture (F-RAM), a feature visualization method aimed at improving interpretability. We validated the efficacy of the material loss by conducting an ablation study, where each component of the loss function is systematically removed and evaluated. The results indicated that the inclusion of the material loss significantly improves accuracy and diversity. To substantiate the performance of the ENA-based inverse design, we compared it against the residual network-based global optimization network (Res-GLOnet). The ENA yielded the OMT solutions of an inverse design with higher accuracy and better diversity compared to the Res-GLOnet. To demonstrate the interpretability, we applied F-RAM to diverse OMT structures with similar optical properties, obtained by the proposed ENA method. We showed that distributions of feature importance for various OMT structures exhibiting analogous optical properties are consistent, despite variations in material configurations, layer number, and thicknesses. Furthermore, we demonstrate the flexibility of the ENA method by restricting the initial layer of OMTs to SiO2 and 100 nm.