Machine learning, as a tool to learn and model complicated (non)linear relationships between input and output data sets, has shown preliminary success in some HPC problems. Using machine learning, scientists are able to augment existing simulations by improving accuracy and significantly reducing latencies. Our ongoing research work is to create a general framework to apply neural network-based models to HPC applications. In particular, we want to use the neural network to approximate and replace code regions within the HPC application to improve performance (i.e., reducing the execution time) of the HPC application. In this paper, we present our preliminary study and results. Using two applications (the Newton-Raphson method and the Lennard-Jones (LJ) potential in LAMMP) for our case study, we achieve up to 2.7x and 2.46x speedup, respectively.