## 2 Engineering Design Meta-Model for Interface Design
### Engineering Design Models  
Two cross-referencing modeling levels with four domains are proposed: (1) _Conceptual models_ and (2) _Concrete models_. Concrete models give a fine and acute description of knowledge for interface modeling. Quite systematically, they use a formal description with a codified and specific language. We can distinguish three subclasses of such models: (a) _mathematical models_, (b) _computational models_, and (c) _experimental models_. **A conceptual model** refers to design models that are represented by concepts or related concepts for interface modeling. A conceptual model is an abstract representation that describes the essential components, concepts, and relationships of an interface. A conceptual model can be used to clarify ideas, identify problems, and develop solutions. It is a simplified representation of an interface that allows people to understand, analyze, and communicate about that interface. A conceptual model is an important tool for visualizing and communicating ideas in a way that is easy to understand and analyze. In interface design, a conceptual model is a representation of the designer's understanding of how users will interact with the interface. It is a high-level abstraction that captures the essential features of the interface and its functionality. An example of a conceptual model in the context of user interfaces is a proposal for an interaction method or a set of specifications that an interaction method must follow. The conceptual model can be represented using different forms such as written descriptions, diagrams, and sketches. The purpose of the conceptual model is to provide a shared understanding among designers, developers, and stakeholders about the design of the interface. This shared understanding can then be used as a basis for building more detailed models. **A mathematical model** represents empirical objects, phenomena, and physical processes encountered during interface modeling in a mathematical or logical way. Mathematical models are often used in interface modeling to provide a more precise and quantitative representation of the system being analyzed. They can be used to simulate the behavior of the interface under different conditions and to make predictions about how the interface will behave in the future. Mathematical models can also be used to optimize the design of the interface by identifying the most efficient or effective parameters and configurations. The choice of mathematical model depends on the specific problem being analyzed as well as the available data and resources. These make it possible to carry out computing and measurements to study the interface in its context. An example of a mathematical model in the context of user interfaces is a model representing the contrast between two elements in a graphic interface. Defining the contrast mathematically enables its validation according to a set of standards. **A computational model** is a representation of an interface that is implemented in a computational way, typically using computer simulation. While some computational models are based on mathematical models, others are derived from empirical data or observations. In interface design, analytical solutions are often not available, making computational models a useful tool for simulating and analyzing the behavior of the interface. An example of a computational model in the context of user interfaces is the virtual prototype of a user interface. Designers can experiment with different design parameters by adjusting inputs in the computer and observing the resulting outputs. While some computational models are treated as \"black boxes\", meaning that the internal workings are not necessarily understood, others can be transparent or interpretable, allowing for a deeper understanding of the underlying mechanisms. Computational models are not only used for simulation purposes but also for optimization, prediction, and data analysis during interface design.