To curb the energy consumption of buildings and their related CO₂ emissions, Oak Ridge National Laboratory (ORNL) developed the thermally anisotropic building envelope (TABE) - a multi-layer design comprising insulation materials and metal foils connected to thermal loops. This study developed a machine learning-assisted framework to control the TABE in residential buildings to reduce the computation load for future optimal rule-based control and application. First, a 2D finite element model was established in COMSOL to calculate the hourly heat flux through exterior walls installed with the TABE. Then, TABE wall heat fluxes were simulated for various indoor and outdoor boundary conditions, thermal loops fluid temperatures and flow rates. Since the finite element simulations are computationally expensive, an artificial neural network (ANN) was then trained to use as a proxy of the finite element (COMSOL) modeling. Finally, the trained ANN model was coupled with the EnergyPlus model to predict the energy consumption of a US Department of Energy prototype single-family house installed with the TABE. An optimal simple rule-based control was determined from predefined rules for a case study. The results demonstrate that the developed machine learning-assisted framework can reduce 99.9% of the computation time while efficiently managing residential building energy for installed TABE walls.