A NEAT Approach to Evolving Neural-Network-based Optimization of Chiral Photonic Metasurfaces: Application of a Neuro-Evolution Pipeline

TL;DR

This work addresses the challenge of designing chiral metasurfaces with nonlinear geometry–response mappings by integrating NEAT neuroevolution into an existing deep-learning optimization pipeline. The authors evaluate 9,600 GaP unit-cell geometries, evolving both network topology and weights to predict chiroptical outputs such as $\Delta R_{CD}$ and $R_{pref}$, while examining input dimensionality, feature scaling, and multi-output configurations. Key findings show that NEAT with standardized features and a compact input set generalizes well, and that two-output NEAT models achieve notably lower final validation errors ($\text{MSE} \approx 0.07$) than single-output ones, enabling design of GaP/Air metasurfaces with $\Delta R_{CD}$ up to $0.0095$ and $R_{pref}$ around $0.016$ for $t=\lambda_0/3$, comparable to or better than fixed-topology networks. The results illustrate a scalable path toward fully automated, self-configuring photonic design pipelines, with potential for transfer learning to experimental data and integration into agentic AI-assisted fabrication workflows, advancing autonomous metasurface design.

Abstract

The design of chiral metasurfaces with tailored optical properties remains a central challenge in nanophotonics due to the highly nonlinear relationship between geometry and chiroptical response. Machine-learning-assisted optimization pipelines have recently emerged as efficient tools to accelerate this process, yet their performance strongly depends on the choice of neural-network (NN) architecture. In this work, we integrate the NeuroEvolution of Augmenting Topologies (NEAT) algorithm into an established deep-learning optimization framework for dielectric chiral metasurfaces. NEAT autonomously evolves both network topology and connection weights, enabling task-specific architectures without manual tuning, whereas the reinforcement-learning strategy in our framework evolves knowledge of the solution space and fine-tunes a model's weights in parallel. Using a pipeline-produced dataset of 9,600 simulated GaP metasurface geometries, we evaluate NEAT under varying input dimensionalities, feature-scaling methods, and data sizes. With standardized feature scaling yielding the most consistent performance for both examined output dimensionalities, the relatively compact NEAT-evolved NN models, when integrated into the full optimization pipeline, achieve similar or improved predictive accuracy and generalization compared to initially employed dense few-layer perceptrons. Accordingly, these resource-efficient models successfully perform inference of metasurfaces exhibiting strong circular dichroism in the visible spectrum, allowing for transfer learning between simulated and experimental data. This approach demonstrates a scalable path toward adaptive, self-configuring machine-learning frameworks for automated photonic design both standalone and as building block for agentic artificial intelligence (AI).

Figures (7)

• Figure 1: Schematic diagram of the NEAT-enhanced neural-network optimization pipeline. It delivers stochastically a practical data pool (dataset evolution) through iterative inference and simulation steps, evolves structures with the help of the previously reported reinforcement strategy in the deep-learning pipeline (training and shape evolution) and improves the neural network model with the neuroevolution algorithm NEAT (model evolution). As sketched, a few-layer perceptron can act as the initial pipeline model. Green boxes represent the model training part and the acquired labelled data pool for it gradually growing with each pipeline iteration. Example shapes delivered by the pipeline after different iteration steps, here first (greenish) and last (blueish), are indicated centrally. Evolved neural networks via NEAT with six input features (yellow), hidden neurons (white) and two output values (blue nodes) are sketched in the right panel, with an example of a winner model deployed into the prediction pipeline for finetuning indicated.
• Figure 2: Overview of the NEAT algorithm results obtained for 2 output neurons, with 24 and 6 input neurons used in the model (top and bottom, respectively). a) and d) show the averaged training losses for every train-test split of the dataset in a comparison of normalized (dark colored) and standardized (light colored) data. Error bars obtained from averaging over 5 repetitions are provided for each value. b) and e) similarly show the respective averaged test losses. c) and f) summarize the re-scaled results of the tests, that is, undoing the "scaler". The direct comparison displays lower MSE values in the case of less input features and standardization for sufficiently sized training data.
• Figure 3: Analysis of the connectivity from input neurons to other neurons in terms of usage frequency, average weights, and total number of connections. The connectivity profiles for 24 and 6 input neurons are summarized for normalized data in (a) and (c), and for standardized data in (b) and (d), respectively, enabling a direct comparison between cases of different input sizes and scaling methods. For each specific configuration, the weights and usage frequencies are averaged across 15 independent runs characterized by identical input--output counts and the same feature scaling protocol. Furthermore, the values for total connections are obtained by summing together the active links developed by the input neurons throughout those 15 runs.
• Figure 4: (a), (b) Score assigned to each neuron for the two and one output neuron models, respectively. (c), (d) show corresponding averaged values of the neurons across equivalent coordinates in the four quadrants for these two compared cases. Indices 0 and 1, 2 and 3, and 4 and 5 correspond to the first, second and third coordinate, respectively.
• Figure 5: Evolution of validation losses and training durations for each iteration of the NEAT-incorporated optimization pipeline with the one and two output NN models (top and bottom, respectively). MSE average validation losses (8 runs for K-fold cross validation) are displayed alongside the average number of training epochs required for convergence for both cases. Insets: corresponding neuroevolved network architectures utilized as the deep-learning building block for this case.