Accelerating the simulation of turbulence to stationarity is a critical challenge in various engineering applications. This study presents an innovative equation-free multiscale approach combined with a machine learning technique to address this challenge in the context of the one-dimensional stochastic Burgers' equation, a widely used toy model for turbulence. We employ an encoder-decoder recurrent neural network to perform super-resolution reconstruction of the velocity field from lower-dimensional energy spectrum data, enabling seamless transitions between fine and coarse levels of description. The proposed multiscale-machine learning framework significantly accelerates the computation of the statistically stationary turbulent Burgers' velocity field, achieving up to 442 times faster wall clock time compared to direct numerical simulation, while maintaining three-digit accuracy in the velocity field. Our findings demonstrate the potential of integrating equation-free multiscale methods with machine learning methods to efficiently simulate stochastic partial differential equations and highlight the possibility of using this approach to simulate stochastic systems in other engineering domains. / Master of Science / In many practical engineering problems, simulating turbulence can be computationally expensive and time-consuming. This research explores an innovative method to accelerate these simulations using a combination of equation-free multiscale techniques and deep learning. Multiscale methods allow researchers to simulate the behavior of a system at a coarser scale, even when the specific equations describing its evolution are only available for a finer scale. This can be particularly helpful when there is a notable difference in the time scales between the coarser and finer scales of a system. The ``equation-free approach multiscale method coarse projective integration" can then be used to speed up the simulations of the system's evolution. Turbulence is an ideal candidate for this approach since it can be argued that it evolves to a statistically steady state on two different time scales. Over the course of evolution, the shape of the energy spectrum (the coarse scale) changes slowly, while the velocity field (the fine scale) fluctuates rapidly. However, applying this multiscale framework to turbulence simulations has been challenging due to the lack of a method for reconstructing the velocity field from the lower-dimensional energy spectrum data. This is necessary for moving between the two levels of description in the multiscale simulation framework. In this study, we tackled this challenge by employing a deep neural network model called an encoder-decoder sequence-to-sequence architecture. The model was used to capture and learn the conversions between the structure of the velocity field and the energy spectrum for the one-dimensional stochastic Burgers' equation, a simplified model of turbulence. By combining multiscale techniques with deep learning, we were able to achieve a much faster and more efficient simulation of the turbulent Burgers' velocity field. The findings of this study demonstrated that this novel approach could recover the final steady-state turbulent Burgers' velocity field up to 442 times faster than the traditional direct numerical simulations, while maintaining a high level of accuracy. This breakthrough has the potential to significantly improve the efficiency of turbulence simulations in a variety of engineering applications, making it easier to study and understand these complex phenomena.