## 2 Related Works
[29] proposed an LSTM-RNN model that was trained on multivariate TS data using MAD-GAN architecture, and an innovative discrimination and reconstruction anomaly score was created to employ the discriminator and generator to find anomalies (DR-Score). Authors in the paper [30] proposed a model to create synthetic three-component waveforms of realistic seismic waveforms with numerous labels that sample either earthquake or non-earthquake classes using a conditional GAN on a dataset taken from an earthquake center in Oklahoma. The major drawback of GAN is that it fails to capture the temporal dynamics of the TS data. Hence, to resolve this issue, [PERSON] et al. [8] introduced TimeGAN. [PERSON] et al. 's [8] framework TimeGAN combines the adaptability of the unsupervised GAN technique with the control provided by supervised learning to produce multivariate time-series. TS data are defined as a sequence of vectors dependent on time \((t)\) for both discrete-time and continuous/real-time and can be presented as follows:  
\[x_{t}=x_{1},x_{2},x_{3.....},x_{n} \tag{1}\]  
Depending on the number of values recorded, the values in the TS can also be univariate or multivariate. The time-series data typically accept either a real number or an integer value. [PERSON] et al. [8] tested their model on several time-series types and demonstrated that it outperformed previous GAN architectures. The architecture of the TimeGAN as shown in Figure 2 implements the collaborations of a GAN and different components, where G is the generator and D is the discriminator. The GAN is applied with an additional supervised loss on the latent space that was retrieved from the random vectors. They provided a step-wise supervised loss utilizing the original data as supervision in addition to the conventional unsupervised adversarial loss on both real and synthetic data, which aids in learning from the transition dynamics in genuine sequences. Finally, following the training, the false samples are produced using the generator and the classification component. There are three losses [33] defined in TimeGAN [8] that are as follows:  
\[L_{R}=\sum s,x_{1}:T\sim p[||s-\widehat{s}||^{2}+\sum_{t}||x_{t}-\widehat{x_{ t}}||^{2}] \tag{2}\]  
\[L_{US}=E_{s},x_{1}:T\sim p[log(y_{s})+\sum_{t}log(y_{t})]+\]  
\[E_{s},x_{1}:T\sim p[(log(1-\widehat{y_{s}})+\sum_{t}(log(1-\widehat{y_{t}})] \tag{3}\]\[L_{S}=E_{s},x_{1}:T\sim p[\sum_{t}||h_{t}-g_{x}(h_{s},h_{t}-1,z_{t})||^{2}] \tag{4}\]  
where \(L_{R}\) is loss of reconstruction, \(L_{US}\) is unsupervised loss, \(L_{S}\) is supervised loss and \(p\) is the true distribution. Through back-propagation, the weights of the recovery and embedding functions are updated using the reconstruction loss \(L_{R}\), \(\widehat{p}\) is the distribution of the model, \(x\) represents the real data, \(\widehat{x}\) is the data after reconstruction, and \(T\) is the timestamp. Comparison chart for the related works [8; 24; 25; 26; 27; 28; 29; 30] performed in the line of implementing GAN using time-series data is given in Table 1. Table 1 contrasts the related works [8; 24; 25; 26; 27; 28; 29; 30] considering the techniques, datasets and evaluation methods used. The reflections of the above papers are discussed in the following Section 3, which explains the challenges faced in dealing with time-series data and the problem statement of the research.