The article discusses building hybrid models relating classical numerical methods for solving ordinary and partial differential equations and the universal neural network approach being developed by D Tarkhov and A Vasilyev. The different ways of constructing multilayer neural network structures based on grid methods are considered. The technique of building a continuous approximation using one simple modification of classical schemes is presented. Introduction non-linear relationships into the classic models with and without posterior learning are investigated. The numerical experiments are conducted.

The article deals with the problem of predicting of the temporal elongation law of the sample under dynamic loading. The determination of tensile behavior of samples under uniaxial loading is performed by a standard tensile method. The neural network approach is applied to construct an approximate elongation-force dependence using measurement data and posterior model of the dependence of rupture conditions on the neural network parameters. The considered approach can be used in the building industry.

The article considers industrial applications of digital twins and their contribution to decision-making and prevention of failures in manufacturing. Virtual laboratories are described as an example of using digital twins not only in industry but also for educational purposes. The article is also focused on the value of physical and virtual investigations through the prism of content and language integrated learning approach (CLIL) and it offers recommendations for combining the two to strengthen science inquiry learning and job-relevant learning. Students conduct online investigations resulting in interdisciplinary team interaction and knowledge integration. Adopting the CLIL approach changes engineering students’ attitudes to learning a foreign language, drums up their academic interest, and strengthens their motivation. In addition, the article describes how neural networks are applied for the simulation of physical processes in a virtual laboratory. The advantages of using virtual laboratories for professional-oriented training include linking observable and unobservable phenomena, pointing out essential information, and providing online, adaptive guidance. To evaluate the efficiency of the virtual laboratory environment, we conducted an experiment to assess the effectiveness of an integrated learning course with the elements of a virtual laboratory. The sample was 48 students (23 of them were enrolled on the course based on integrated learning with elements of virtual environment; 25 students studied professional discipline and professional English separately). To collect the data two online testing on English were conducted. The professional discipline was evaluated once at the end of the semester. In addition, we conducted an online survey on motivation for students of both groups to reveal the influence of educational process organization on this indicator. The results of the experiment allowed us to ascertain that the CLIL approach in the virtual laboratory environment resulted in better outcomes and helped the students adopt a more positive attitude to learning English.

The level of PM10 and PM2.5 concentrations in the air on seven roads in St. Petersburg, Russia, were investigated using gravimetry and nephelometry measurement techniques in 2013-2015. The effects of meteorological conditions (temperature, relative humidity, wind direction, and speed) and the intensity of traffic flows on the results of the measurements were also evaluated. On the base of the measurements, there was developed a neural network modelling approach that allowed to quantify exhaust / non-exhaust PM10 and PM 2.5 emissions and carry out numerical investigations of air pollution by transport related PM2.5 and PM10 on street and urban level in St. Petersburg.