On November, 23, ITMO University will host a lecture by Sergey Dolenko, head of the laboratory of data processing adaptive methods of the Skobeltsyn research Institute of nuclear physics of Moscow state University named after M. V. Lomonosov «"Small" neural networks: examples of practical application for solving problems of forecasting, classification and inverse problems», within the framework of scientific school-workshop of young scientists and specialists «Machine learning and cognitive technologies: Finance, society, cities». The sensational success of artificial neural networks over the past five to seven years are mainly associated with the use of convolutional and deep neural networks for processing multimedia information-speech, images and video. Unfortunately, in many practical science and technology tasks, obtaining the amount of data needed to train deep networks is either inaccessible or unacceptably expensive. The lecture discusses three examples of various problems (forecasting, classification, inverse problems) from the field of applied physics, that are successfully solved by "small" neural networks. Special attention is paid to the methodology and special methods of working with data of real world problems.