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Likelihood-free parameter inference is a well-known statistical methodology that estimates the posterior distribution of model parameters even in cases where the likelihood function is intractable. The performance of this method is highly correlated with the learning of summary statistics, which capture the key features from the high dimensional data such as time series. To retain sufficient information to infer the parameters, we explore a generative neural networkmodel, autoencoders. Specifically, we use autoencoders to compress the high-dimensional datainto the low-dimensional latent representations and reconstruct the input based on this low-dimensional information. When the reconstructed output is sufficiently similar to the original input, we assume that these summary statistics contain enough representative information to beused for parameter inference. We demonstrate the effectiveness of these approaches through experiments on simulated data from a gene regulatory network. Our work provides a new perspective on the use of autoencoders in statistical inference and demonstrates the potential ofthis approach in addressing the challenges of likelihood-free parameter estimation in complexsystems.