# Design Technology and AI-Based Decision Making Model for Digital Twin Engineering
## 2 Literature Review  
There are three groups of approaches and methods used for DT designs:  
* modeling methods based on the mathematical modeling of physical processes (structural models) (Simulation-Based DT) [1; 2; 3; 4; 5];
* modeling methods based on data (Data-based DT) [6; 7];
* hybrid methods (Hybrid DT) [8; 9; 10; 11]. Features of the above methods are given in Table 1, which summarizes modeling approaches by certain characteristics. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Feature**} & \multicolumn{3}{c}{**Modeling Approach**} \\ \cline{2-4}  & **Mathematical Modeling** & **Data-Based Modeling** & **Hybrid Modeling** \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Object \\ (system) \\ \end{tabular} } & Describes the laws of functioning of & It is built on the basis of available & It is built on the basis of available \\  & an object (process) and its connection & empirical data using machine & the functioning \\  & with the external environment. & learning tools. The modeling & regularities and is \\  & The system behavior is modeled, & problem is reduced to model & adjusted with empirical \\  & causal relationships and patterns & parameters selection and & data \\  & are identified. & some function composition & data \\  & & White box model, & Black box model, \\  & principle & cause-and-effect modeling & correlation modeling & The gray box model \\ Simulation and design & & Top down & Bottom up & Top down, bottom up \\  & & Information uncertainty is controlled & \\ Description & by input data and accuracy of & Probabilistic description & Deterministic, \\  & of & modeling. & of information based on data \\  & & Description—deterministic, & distributions in training samples & stochastic \\  & & stochastic & Statistical methods, \\  & & & extrapolation methods, machine \\  & & learning methods, big data & Interdisciplinary models \\  & & analytics methods & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative analysis of the models for DTs of organizational and technical system designs. A generalized modeling method is the mathematical modeling of the physics (functioning principles) of an object/process. The physical model provides for the computer modeling of physical processes as well as a description of their functioning and relationships with the external environment. The construction of such models in practice is associated with the mathematical programming methods (operations research) [12], and simulation modeling based on its various paradigms and approaches--system-dynamic, discrete-event or agent-based modeling [13]. Mathematical modeling is a key component of the digital transformation. To create models that are used to create system models, the DT can use the results of detailed three-dimensional numerical calculations performed using interdisciplinary CAE solvers. Depending on the purpose, mathematical models can be descriptive or optimizing. The purpose of descriptive models is to establish the laws of change in model parameters. The optimization model provides a search for the function's extreme value under restrictions using numerical methods. Depending on the certainty of the initial information degree and taking into account the time factor, linear, non-linear, stochastic programming, game-theoretic and fuzzy logic methods can be used. Simulation models as a subclass of mathematical models are divided into static and dynamic; deterministic and stochastic; discrete and continuous. In continuous simulation models the variables change continuously, the state of the simulated system changes as a continuous function of time, and as a rule, this change is described by systems of differential equations. In discrete simulation models, variables change discretely at certain moments in simulation time. The dynamics of discrete models are a process of transitioning from the moment of the next event to the moment of the next event. Data-driven modeling includes data mining, artificial intelligence, big data and advanced analytic methods.