The analysis and process of not only the current states of information objects, but also the prediction of future states with a certain time interval presents a major significance for adaptive information systems. This allows improving the quality and reliability of these systems functioning, reducing the delay in response to external influences, preparing for operations, and increasing the responsiveness and speed of the system. In order to solve this problem, the article proposes a neural network method for forecasting the state of information objects based on the application of machine learning technologies. A formalized algorithm for its implementation in the notation of set theory is presented. A distinctive characteristic of the designed method is the automatic determination of the optimal structure of the neural network, depending on the type of information object. The method also covers the possibility of using the complex of the previous states of the object to improve the forecast accuracy. Practical researches on approbation of the neural network method showed its efficiency and high accuracy. The following popular datasets were used as input data: Individual household electric power consumption, HAR (Human Activity Recognition) accelerometer, as well as gathered data on human relocation. LSTM (Long Short-Term Memory) neural network was applied to conduct the forecasts. The comparison of the developed method with a similar software solution DEvol (DeepEvolution) showed comparable or better indicators in terms of accuracy and time for the problem solution (1.7 times faster on average).