# Research data supporting "A machine learning approach to drawing phase diagrams of topological lasing modes"

To classify the topological states of lasing modes, one needs to solve rate equations and then can analyze the time-dependent data using different machine learning approaches: 1) fixed library, 2) top-down adaptive library, and 3) bottom-up datative library. In this paper, we consider a coupled resonator arrays, so called SSH lattice, with 21 sites. To build libraries, we used 2000 samples implying we considered 2000 different set of gain and linear loss coefficients that forms a 2D parameter space presented in the paper. In this paper, all the coefficients are normalised so that no units are required when solving the equations and presenting the results.

First, the data file "dataset_params.txt" contains the parameters used for the time evolution of the system, and the initial conditions, for each samples generated. It contains 24 columns where the first three columns are the sample index, gain (g_A) and linar loss coefficients (g_AB) for A sites and A and B sites, respectively. Note that we have 2000 samples that is equal to the number of points in graphs in the paper and the sample index was not sorted in ascending/desceding order because the order is not important. The remaining 21 columns are the intial values of site amplitude, x(t=0), that were used when solving the rate equations Eq. (2) and Eq. (3) using the 4th-order Runge-Kutta method. Here, we used 0.01 commonly for all the sites (N=21) and all the different samples (2000).

Second, the data file "dataset_time_series.txt" contains time evolution of the system for each samples generated. The first column is the sample index, the remaining 42 columns are the complex amplitudes of the mode corresponding to Re(a(x=1,t=t0)), Im(a(x=1,t0)), Re(a(x=2,t=t0)), Im(a(x=2,t=t0)), ...., Re(a(x=1,t=t1)), ... .

Third, there are 8 data files that correspond to phase diagrams calculated using the methods describe in the manuscript. All of them have the same structure and contains derived phase diagram, i.e., the first and second columns are the linear loss coefficeints (g_AB) and the gain coefficient (g_A) and the third column is the index for different phases.

filenames:

ahdmd?tab_class_ij.txt

ahdmd?tab_class_ij_bis2.txt

xc_tab_class_red_i_5.txt

xc_tab_class_red_i_1.txt

xc_tab_class_red_i_-2.txt

xc_tab_class_red_ij_0_3.txt

xc_tab_class_red_ij_0_7.txt

xc_tab_class_red_ij_3_7.txt

The datafiles are used in figures as described below

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Files used in figures

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Figure 1:

dataset_params.txt

dataset_time_series.txt

Figure 2:

panel a: ahdmd?tab_class_ij.txt

panel b: ahdmd?tab_class_ij_bis2.txt

Figure 3:

xc_tab_class_red_i_5.txt

Figure 4:

panel a: method is applied for each hyper-parameter value on times series in dataset_time_series, then the number of classes is counted

panel b: xc_tab_class_red_i_1.txt

panel c: xc_tab_class_red_i_-2.txt

Figure 5:

xc_tab_class_red_ij_0_3.txt

Figure 6:

panel a: method is applied for each hyper-parameter value on times series in dataset_time_series, then the number of classes is counted

panel b: xc_tab_class_red_ij_0_7.txt

panel c: xc_tab_class_red_ij_3_7.txt

Figure S1-S3:

use sample in dataset_time_series.txt corresponding to parameters gamma_AB, g_a of panel d-e of figure 1

Figure S4:

Apply described method on each decomposition methods on times series in dataset_time_series.txt

Figure S5:

Apply described method on times series in dataset_time_series.txt

Figure S6:

Apply described method on times series in dataset_time_series.txt

Research results based upon these data are published at https://doi.org/10.1038/s42005-023-01230-z

## Funding

### Supercomputing Wales (2015-07-01 - 2022-12-31); Whitaker, Roger. Funder: Welsh European Funding Office:80898 and 80900

### Photonic topological insulator semiconductor laser and one-way photonics (2017-12-01 - 2023-03-31); Oh, Sang Soon. Funder: Welsh European Funding Office

## History

## Language(s) in dataset

- English-Great Britain (EN-GB)