Neural networks have learnt to predict the behavior of stochastic systems more precisely
Scientists suggested approaches of "strong" and "weak" prediction in order to prognose the behavior of stochastic, that means random systems, with the help of neural networks. Authors defined when it was possible to calculate future values of a certain parameter of a system precisely, and which conditions make such prediction impossible, but you can make a "weak" prediction – forecast the probability of this or that system's behavior. Method of weak prediction with the use of neural networks can be used for such stochastic systems as neuronal nets, that is important for design of interfaces "brain-computer", and also for forecasting of financial markets and climate changes. Results of the research supported by the grant of Russian Science Foundation (RSF) are published in the magazine Chaos.
Some systems that we find in real life (financial markets, geophysical and climate systems, control systems and other) are permanently influenced by uncontrollable noise. That means that they function practically unpredictably. For example, neurons of brain as well as lasers are influenced also by random fluctuations (vibrations). The behavior of such stochastic – randomly functioning – systems can't be calculated mathematically, but you can try to predict it with the help of gathering large volume of data about noise sources and frequency of their appearance. Nowadays for this purpose algorithms of artificial intelligence are used. The best method is to use recurrent neural networks – models that are adjusted to processing of sequences. However, they haven't been able by now to predict how the stochastic system will behave due to the fact that it is very difficult to register outer random inputs.
Scientists from Immanuel Kant Baltic Federal University (Kaliningrad) and Madrid Polytechnic University (Spain) singled out two categories of prediction – strong and weak. Strong prediction is making of precise trajectory on which model or system will move. For example, with the help of strong forecast it is possible to count the intensity of erbium laser in a certain moment. This information is important for calculation of specific values of its power after a certain period of time by means of exposure of random signal.
Weak prediction enables to calculate not the behavior of the system, but probability that it will behave some way or other. For example, how strong is the probability that next three minutes of laser's work its intensity will be higher than a certain given quantity. To make a strong prediction you need to collect all data concerning noise source, that is not always possible. In the case of weak prediction, you don't have to know all information about noise, but only its statistic characteristics, in order to calculate the probability of obtaining this or that result.
Authors gave into recurrent neural net information about job characteristics of erbium laser and outer noise source. Fulfilling reservoir computing with the help neural networks, they checked modes of strong and weak prediction of laser's intensity after several seconds. It turned out that precise forecast could be achieved only in a small diapason of noise intensity, whereas weak prediction could be carried out practically within the whole studied diapason of magnitudes. It turned out that with the use of weak prediction zone of prognosing increased in 2,5 times. Scientists repeated the experiment on biological neurons that were under the outer random influence and confirmed the result.
Thus, researchers proved that models of weak prediction can be more efficient than "strong" ones. It will be useful, for example, in financial analytics for forecasting stock prices and other financial instruments, subjected to a great amount of random influences; for prediction of activity of neural networks that is important for elaboration of interfaces "brain-computer", and also in forecasting climate events.
"Our results present a powerful base for solution of real problems in neuroscience, laser physics, intelligence systems for self-contained units and other fields. With their help it is possible to elaborate more efficient control systems and raise the preciseness of prediction. For example, strong or weak prediction of brain activity will enable to find out different irregularities in its work and diseases, and also will be useful for creation of interfaces brain-computer. In particular, weak prediction can help to prognose noise characteristics in signals of brain activity and to distinguish one pattern of brain activity from another more precisely", – tells the participant of the project, supported by the grant of RSF, Nikita Kulagin, student, laboratory assistant of Baltic Center of Neurotechnologies and Artificial Intelligence of Immanuel Kant Baltic Federal University.
In future authors are going to research the application of the suggested approach for wider class of complex systems, in order to create digital twins of stochastic systems.
More information:
doi.org/10.1063/5.0252908
Provided by Immanuel Kant Baltic Federal University