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 operationIllustrates this new approach with numerous concrete examples throughout the bookPresents the methodology in separate and clearly-defined stages

1. Examples of problem statements and functionals 2. The choice of the functional basis (set of bases) 3. Methods for the selection of parameters and structure of the neura network model  4. Results of computational experiments 5. Methods for constructing multilayer semi-empirical models