## 1 Introduction  
Gene regulatory networks (GRNs) describe the collective connections among genes, and they regulate their expressions. It is essential to clarify GRNs to understand the function of and disease in organisms. Thus, the inference of GRNs has been an important research topic [1], and many diverse methodologies, which are usually classified into model-free and model-based methods, have been developed. In model-free approaches, gene interactions can be identified by various statistical and machine learning techniques, including mutual information [2, 3, 4], random forests [5, 6, 7], or network deconvolution [8, 9]. In model-based methodologies, a quantitative dynamical model is employed to represent the system's dynamics, such as a Boolean network [10, 11], an ordinary differential equation (ODE) [12, 13, 14, 15], the regression method [16, 17, 18], or a dynamic Bayesian network (DBN) [19, 20, 21]. In the model-based inference methods, it is necessary to optimize the model parameters by using gene expression data. It is obvious that the data from longer observation times would help infer GRNs more accurately. However, time-series gene expression data is not always easily obtained [22]. In some cases, it may be difficult to ensure that observations are made under identical conditions throughout the observation period. Data augmentation has been considered as one of the effective approaches to resolve this data shortage problem. It has been frequently used in various domains such as image processing [23, 24, 25, 26] and time-series prediction [27, 28, 29]. In the field of time-series gene expression, several strategies have also been proposed to generate artificial data, in particular, through the Dialogue on Reverse Engineering Assessment and Methods (DREAM) challenge [30, 31]. Several previous investigations on this matter are accessible [32, 33, 34, 35, 36]. These studies can generate simulated biological datasets that closely mimic real-world data and provide researchers with tools to analyze and investigate genes. The artificial gene network (AGN) model is proposed to simulate temporal expression data for the identification of gene networks [37]. This model uses a feature selection technique where a specific gene remains constant, and the expression profiles of all other genes are observed. The goal is to identify a significant subset of predictors for the target gene. These studies proposed methods to produce synthetic data that closely resemble the real data. However, they have a limitation in producing a variety of data because they did not learn complex generation functions using data but tried to build simple rules. In particular, rule-based or manually designed simulations may fail to capture nonlinear or context-specific regulatory dynamics that naturally occur in biological systems. Additionally, these approaches often lack adaptability and may not generalize diverse datasets or unseen biological conditions. In this study, we propose a network inference approach involving an autoencoder-based data generation model. For our problem, it is noteworthy that the autoencoder has some advantages over the generative adversarial network (GAN) [38]. The autoencoder provides a simple yet effective framework with a lightweight architecture that enables stable training by optimizing a single objective. On the other hand, the GAN requires simultaneous training of two competing networks, which causes mode collapse, sensitivity to hyperparameters, and instability during training [39; 40]. Thus, the autoencoder is more suitable for gene expression problems, where available datasets are typically small and heterogeneous. Several studies have shown that autoencoders perform well in low-data regimes and can effectively extract meaningful representations in biological applications [41; 42]. In addition, the performance of autoencoders is less dependent on the underlying distribution of gene expression values, allowing for better adaptability to biological variation.