This article deals with the application of transfer learning methods and domain adaptation in a recurrent neural network based on the long short-term memory architecture (LSTM) to improve the efficiency of management decisions and state economic policy. Review of existing approaches in this area allows us to draw a conclusion about the need to solve a number of practical issues of improving the quality of predictive analytics for preparing forecasts of the development of socio-economic systems. In particular, in the context of applying machine learning algorithms, one of the problems is the limited number of marked data. The authors have implemented training of the original recurrent neural network on synthetic data obtained as a result of simulation, followed by transfer training and domain adaptation. To achieve this goal, a simulation model was developed by combining notations of system dynamics with agent-based modeling in the AnyLogic system, which allows us to investigate the influence of a combination of factors on the key parameters of the efficiency of the socio-economic system. The original LSTM training was realized with the help of TensorFlow, an open source software library for machine learning. The suggested approach makes it possible to expand the possibilities of complex application of simulation methods for building a neural network in order to justify the parameters of the development of the socio-economic system and allows us to get information about its future state.