A neural network is an information processing system whose   The structure and operating principle are modeled on that of the human brain. A neural network consists of  three types of layers:

• input, where data is collected,
• hidden layer, in which connections between neurons are sought, so in this layer the so-called “hidden layer” takes place. learning process,
• output, in which the conclusions and results of the analysis are collected.

The first layer receives the raw input data. Often this data is referred to as raw data, but in practice it requires adequate preparation. The next layer receives the data resulting from the processing of the data in the previous layer. In the last layer, the output of the system is generated.

Each layer is made up of neurons. The number of layers in the network and the number of neurons in a layer can be arbitrary, the only limitation being the capacity of the infrastructure to support the network.  Neurons are interconnected allowing signals to flow from inputs to outputs, and each connection has a specific weight. Connections between neurons simultaneously form connections between layers. In  The neurons are used to aggregate the input data, with the  outside or from the previous layer, and their transformation. During the learning process, the network weights are modified, the network itself detects patterns and existing interdependencies using learning data. Each neuron performs its own simple calculations, a  By connecting neurons into a network, the potential for computation is multiplied (which makes it possible to use the analogy of the structure and operation of the brain in describing neural networks – one nerve cell can do little, a structure containing billions of such cells becomes an evolutionarily very advanced organ).

The potential applications of neural networks are many, among the most popular are:

• facial recognition,
• Automatic transcription of speech to text,
• handwriting recognition.

One of the more promising directions for neural networks is time series forecasting. Time   series is a characteristic type of data that are the result of  observations   development of certain phenomena   in   time.  In   time   series  two types of components are distinguished:

• systematic component,   bound by a deterministic process, it is the result of a   interactions   of specified  factors  on   the phenomenon under study,
• the random component, associated with the stochastic process, which, as the name suggests, is the result of actions of a random nature.

The systematic component can be in the form of a trend, an average constant level or a periodic (cyclical or seasonal) component.

The peculiarities of time series force an appropriate approach to the forecasting problem. It is necessary to use methods,  which  include  changes  occuring  over  time  and  can  describe   associated       regularities  Designating  forecasts  of future  values  variable  that has  figure  time  array  benefits  ,  primarly    from   its past   values. For this reason, recurrent neural networks are used to forecast variables evolving over time (Recursive Neural Networks, RNN). While in  the case of a traditional neural network assumes that all inputs (and outputs) are independent of each other, then RNNs perform the same task for each element of the sequence, and the output depends on previous calculations. So, figuratively speaking, we can say that recurrent networks have a “memory” that captures information about what has been computed so far. RNNs, of course, have their disadvantages and limitations, among the most important are the long training time and the gradual fading of the memory of the first inputs (after a certain time, the RNN state contains virtually no traces of the first inputs). The latter problem was solved by using neurons with long-term memory. This concept is implemented by LSTM-type networks(Long Short-Term Memory) and their simplified version , a GRU-type network (Gated Recurrent Unit).

This article was written thanks to the funds from the European Union’s co-financing of the Operational Program Intelligent Development 2014-2020, a project implemented under the competition of the National Center for Research and Development: under the “Fast Track” competition for micro, small and medium-sized entrepreneurs – competition for projects from less developed regions under Measure 1.1: R&D projects of enterprises Sub-measure 1.1.1 Industrial research and development work carried out by enterprises. Project title: “Developing software to improve forecast accuracy and inventory optimization from the perspective of customer and supplier collaborating in the supply chain using fuzzy deep neural networks.