READ ME File For 'Dataset for the PhD Thesis "Inverse Design of Structural Colour Devices via Machine Learning"'

Dataset DOI: https://doi.org/10.5258/SOTON/D2870

ReadMe Author: Peng Dai, University of Southampton ORCID ID: 0000-0002-5973-9155

This dataset supports the thesis entitled Inverse Design of Structural Colour Devices via Machine Learning
AWARDED BY: Univeristy of Southampton
DATE OF AWARD: 2023

DESCRIPTION OF THE DATA
The dataset includes the datasets used for the ANNs training, validation and test, and the raw data used to plot the figures in the PhD thesis. These datasets were collected via home developed python code, Lumerical FDTD solutions and experiments. The pkl files can be opened via the python pickle package. The csv and xlsx files can be viewed via Microsoft Excel.

This dataset contains:
1. dataset_chapter_4.7z: including the datasets used in chapter 4 for ANN training, validation and test.
2. dataset_chapter_5.zip: including the datasets used in chapter 5 for ANN training, validation and test.
3. dataset_chapter_6.csv: including the datasets used in chapter 6 for ANN training, validation and test.

4. Spread_sheet.xlsx: including the raw data used in chapters 4 to 6 for plotting figures.
Figure 4.3 Forward neural network training for predicting F-P cavity structural colours. The histogram of the probability and average values of $\Delta E_{2000}$ of the FNNs with different a) hidden layer numbers, b) neuron numbers per layer, and c) the FNN with seven hidden layers and 250 neurons in each hidden layer for different dataset size. d) The training loss curves for defining the loss function in CIE 1931-XYZ and CIELAB colour spaces. e) The probability histogram and average values of $\Delta E_{2000}$ comparisons while the loss function is defined in CIE 1931-XYZ colour space and CIELAB colour space. f) The selected colours in the CIE 1931-xy chromaticity diagram with the boundary of each ellipse representing the colours that have a $\Delta E_{1976}$ of 6 to the selected colour.
Figure 4.4 Inverse neural network for predicting F-P cavity structural colours. a) The tandem architecture with an input layer of $\mathbf{Lab}$ and an output layer of geometric parameter $\mathbf{D}$ and connected to the pretrained forward neural network. b) The schematic of different weights’ initialisation positions. c) The loss landscape schematics of the one-to-many problem (left) and one-to-one mapping (right), respectively. The MSEs after 200 epochs as a function of a random seed, the training loss curves, the histogram of the distribution, and average values of $\Delta E_{2000}$ of the INNs with d)–f) different numbers of hidden layers and g)–i) different numbers of neurons per layer.
Figure 4.6 Transmissive spectra and corresponding CIE 1931-RGB tristimulus values for the designed colours. a) The transmissive spectra (black line) and the contribution from the three stimuli (shades underneath the line) for the (i, ii, iii) blue, (iv, v, vi) green, and (vii, viii, ix) red colour designed by the INN in this work. Within each figure, the middle row figure represents the ANN designs, while the top and bottom figures represent the spectra from a 10 nm thinner layer and a 10 nm thicker dielectric layer. (b) The CIE 1931-RGB tristimulus values as a function of dielectric layer thickness for the blue, green, and red colours, respectively. The CIE 1931-RGB tristimulus values of the targeted colours are also included (dotted lines) for comparison.
Figure 5.5 The training results of the Lab regressor. a) The training and validation loss curves of the Lab regressor. b) The histogram of Lab regressor test $\Delta E$.
Figure 5.6 cGAN training loss curves. a) The training loss curves of the generator (blue) and evaluator (red). b) The curves of evaluator loss components including the real (red) and fake (blue) scores. c) The MSE between $\mathbf{Lab}$s predicted by the generator and ground truth (red), and the generator’s fake score (blue).
Figure 5.7 The distribution comparison between ground truth and prediction. The thickness histograms a-c) of the test set and d-f) predicted by the generator.
Figure 5.8 The tendencies of solution group number and $\Delta E$ as $\mathbf{z}$ sampling number varies. a-b) The solution group number histograms when each $\mathbf{Lab}$ combines 100 (a) and 1,000 $\mathbf{z}$ (b). c) The curve of average test solution group number against $\mathbf{z}$ number, the circle and triangle markers refer to the solution group numbers when each $\mathbf{Lab}$ is assigned with 1,000 and 2,100 $\mathbf{z}$, respectively. d-e) The test $\Delta E$ histograms when each $\mathbf{Lab}$ is assigned with 1 (d) and 1,000 (e) $\mathbf{z}$. f) The curve of average test $\Delta E$ against $\mathbf{z}$ number, in which the insert is the enlarged of the yellow shading region, the circle and triangle markers refer to the $\Delta E$ while each $\mathbf{Lab}$ assigned with the $\mathbf{z}$ number of 15 and 400. 
Figure 5.9 The $\Delta d_2$ histograms between predicted $d_2$ and ground truths in the test set.
Figure 5.10 The test results of cGAN when evaluator disabled. a-c) The test predicted thickness distribution while the evaluator was disabled. d) The corresponding test $\Delta E$ distribution. e) The corresponding predicted colour distribution on the CIE 1931-xy chromaticity diagram.
Figure 5.11 The training and test results that the evaluator has two extra layers of the linear block. a) The loss curves of GAN while evaluator has two extra hidden layers than the network used in the main body of this paper. b) The curves of the evaluator detail loss components, which are real (red) and fake (blue) scores. c) The curves of the generator’s detail loss components, MSE between predicted $\mathbf{Lab}$ and ground truth (red) and fake score (blue). d-f) The generator predicted thickness distributions.
Figure 5.12 The training and test results that the evaluator is missing two layers of the linear block. a) The loss curves of GAN while the evaluator is missing two hidden layers. b) The curves of the evaluator detail loss components, which are real (red) and fake (blue) scores. c) The curves of the generator’s detail loss components, MSE between predicted Lab and ground truth (red), and fake score. d-f) The generator predicted thickness distributions.
Figure 5.13 The multiple solution test results in which the evaluator and generator are imbalanced. a) The solution group number histograms when the evaluator is missing or has two extra layers of linear blocks and 1,000 different $\mathbf{z}$ is sampled for each colour. The $\Delta E$ distributions when the evaluator is missing two b) and has two extra c) layers of linear blocks, in which the $\mathbf{z}$ sampling times is 1,000.
Figure 5.14 The analysis of sRGB colour filter design results. a-c) The MSE curves of the colours with sRGB values of a) ($0.5, 0, 0$ red), b) ($0, 0.5, 0$ green) and c) ($0, 0, 0.5$ blue) when the \ce{SiO2} thickness ($d_2$) was swept from 0 to 1000 nm and Ag thicknesses (\ce{d_1} and \ce{d_3}) were fixed at 30 nm. The DBSCAN clustered predicted $d_2$ histograms for the d) red, e) green and f) blue colours. The dark-coloured bar indicates the lower resonant order, and the light-coloured bar means the higher order.
Figure 5.15 The experimental results of fabricated sRGB colour filters. a-c) The cross-sectional SEM images of the fabricated colour filters with all the scale bars of 100 nm. d-f) The measured spectra (solid line) and corresponding theoretical ones (dash line). g-i) The colour reconstructions, wherein TGT. is the target colour; DSG. is the theoretical colour of the designed colour filter; EXPT. SPT. is the theoretical colour of the measured spectrum and EXPT. PHT. is the photograph of the sample taken by the camera. 
Figure 6.1 a) The schematic of the proposed five-layer structure. b) The reflective spectra of the structure with the thickness of $\mathbf{D}$ (100, 5, 100, 100) nm at 30\degree C (cyan curve) and 85\degree C (red curve), in which the inserts are the corresponding colours. c-d) The CIE 1931-xy chromaticity diagrams of the dataset at 30\degree C (c) and 85\degree C (d), respectively.
Figure 6.2 a) The real parts of the refractive indices of \ce{VO2} at 30\degree C and 85\degree C. b) The imaginary parts of the refractive indices of \ce{VO2} at 30\degree C and 85\degree C. 
Figure 6.3 a) The data flow and the cGAN architecture in this work. b) The loss curves of the discriminator (black curve) and generator (red curve). c) The components of discriminator loss, where the black curve is the fake score and the red curve is the real score. d) The components of generator loss, where the black curve is the fake score, and the red curve is the MSE which is computed between the input $\mathbf{Lab}$ and predicted $\mathbf{Lab}$ in (a).
Figure 6.6 a, b) The test $\Delta E$ histograms when each Lab is assigned with 1 $\mathbf{z}$ (a) and 1,000 $\mathbf{z}$ (b), respectively. c) The test average $\Delta E$ as the function of the number of $\mathbf{z}$, in which the insert is the enlargement of the yellow shading region. d) Eight cGAN inverse design examples, the target colours with 30\degree C are outlined by a blue dash frame (left), and the target colours with 85\degree C are outlined by a red dash frame (right).
Figure 6.9 The spectra of (a) solution 1 and (b) solution 2, where the inserts are the corresponding colours of the spectra. The reproduced campus photo (c) at 30\degree C and (d) at 85\degree C.
Figure 6.10 The spectra of a) solution 3 and b) solution 4, where the inserts are the corresponding colours of the spectra. The reconstructed campus photo at (c) 30\degree C and (d) at 85\degree C.


Date of data collection: November 2019 to September 2023

Information about geographic location of data collection: Southampton UK; Changsha China.

Licence: CC BY

Related projects/Funders:
International Exchange Scheme (IEC\NSFC\170193) between Royal Society (UK) and the National Natural Science Foundation of China (China)
EPSRC (EP/N035437/1)

Related publication:
Peng Dai, Kai Sun, Otto L. Muskens, C. H. de Groot, Ruomeng Huang. "Inverse design of a vanadium dioxide based dynamic structural colour via conditional generative adversarial networks". Optical Materials Express, 12(10): 3970-3981, 2022.

Peng Dai, Kai Sun, Xingzhao Yan, Otto L. Muskens, C. H. de Groot, Xupeng Zhu, Yueqiang Hu, Huigao Duan, Ruomeng Huang. "Inverse design of structural colour: finding multiple solutions via conditional generative adversarial networks". Nanophotonics, 11 (13): 3057-3069, 2022.

Peng Dai, YasiWang, Yueqiang Hu, C. H. de Groot, Otto Muskens, Huigao Duan, Ruomeng Huang. "Accurate inverse design of Fabry-Perot-cavity-based colour filters far beyond sRGB via a bidirectional artificial neural network". Photonics Research, 9 (5): B236-B246, 2021.

Date that the file was created: November, 2023