Semi-empirical Neural Network Modeling and Digital Twins Development

Semi-empirical Neural Network Modeling presents a new approach on how to quickly construct an accurate, multilayered neural network solution of differential equations. Current neural network methods have significant disadvantages, including a lengthy learning process and single-layered neural networks built on the finite element method (FEM). The strength of the new method presented in this book is the automatic inclusion of task parameters in the final solution formula, which eliminates the need for repeated problem-solving. This is especially important for constructing individual models with unique features. The book illustrates key concepts through a large number of specific problems, both hypothetical models and practical interest. - Offers a new approach to neural networks using a unified simulation model at all stages of design and operation - Illustrates this new approach with numerous concrete examples throughout the book - Presents the methodology in separate and clearly-defined stages

Dmitry Tarkhov, born 14 Jan 1958 in St. Petersburg. In 1981 graduated with honors from the faculty of physics and mechanics of Leningrad Polytechnic Institute, majoring in Applied Mathematics and entered graduate school at the Department 'Highermathematics. After graduation, heworked at the Department as an assistant, then associate Professor and continues to work presently as a Professor. In 1987 he defended the thesis 'the Straightening of the trajectories on the infinite dimensional torus", for which he was awarded the degree of Ph.D. of physical and mathematical Sciences. In 1996, while working as a part-time chief systems analyst at the St. Petersburg Futures exchange he began studying neural networks. He has published more than 200 scientific papers on this topic. In 2006 he defended doctoral thesis 'Mathematical modeling of technical objects on the basis of structural and parametrical adaptation of artificial neural networks", for which he was awarded the degree of doctor of technical Sciences."