--- title: "Modeling process" source: "https://systems-analysis.info/eng/Modeling_process" wiki: "systems-analysis.info/eng" article: "Modeling_process" language: "en" categories: - "Category:English" - "Category:Mathematical modeling" - "Category:Modeling" - "Category:Operations research" - "Category:Science" - "Category:Systems analysis" - "Category:Systems approach" revision_id: 258 wiki_created_at: 2026-09-06T22:19:38Z wiki_modified_at: 2026-09-06T22:19:38Z downloaded_at: 2026-09-07T22:22:15Z --- # Modeling process The process of modeling can be viewed as a transition from models of one class to another. Three major classes of models are conventionally distinguished: cognitive, substantive, and formal models. They constitute three interconnected levels of modeling that cannot be considered in isolation from one another. The mutual influence of these modeling levels is related to the potentiality of models. The creation of any model is associated with the emergence of new knowledge about the object under study, which leads to the reassessment and refinement of concepts and views on the modeling object at different levels. This, in turn, leads to the revision of the corresponding substantive and cognitive models, ensuring a spiral development across all levels of modeling for the object under study. ## Cognitive and Substantive Models When observing an original object, a certain mental image of the object forms in the researcher's mind—its ideal model, which is commonly referred to in scientific literature as a cognitive model (mental, contributing to cognition). When forming such a model, the researcher usually aims to answer specific questions, so everything unnecessary is cut away from the infinitely complex structure of the object to obtain a more compact and concise description. The representation of a cognitive model in natural language is called a substantive model. Cognitive models are subjective, as they are formed speculatively by the researcher based on all their prior knowledge and experience. One can only get an idea of a cognitive model by describing it in a symbolic form. It cannot be asserted that cognitive and substantive models are equivalent, as the former may contain elements that the researcher is unable or unwilling to formulate. At the same time, if a substantive model is formulated by someone else or is the product of collective creativity, its interpretation, level of understanding, and degree of trust can vary significantly depending on the interpreter. A substantive model is often called a technical problem statement. Based on their function and purpose, substantive models are subdivided into descriptive, explanatory, and predictive models: - A descriptive model can be any description of an object. - An explanatory model allows one to answer the question of why something happens. - A predictive model must describe the future behavior of the object. It is worth noting that a predictive model does not necessarily have to include an explanatory one. ## Conceptual Models A conceptual model is commonly defined as a substantive model formulated using the concepts and representations of the knowledge domains involved in studying the modeling object. In a broader sense, a conceptual model is understood as a substantive model based on a specific concept or point of view. Three types of conceptual models are distinguished: logico-semantic, structural-functional, and cause-and-effect. - A logico-semantic model is a description of the object in the terms and definitions of the relevant knowledge domains, including all known, logically consistent statements and facts. Analysis of such models is carried out using logic, drawing upon the knowledge accumulated in the respective subject areas. - When building a structural-functional model, the object is usually viewed as an integral system, which is broken down into individual elements or subsystems. The parts of the system are linked by structural relationships that describe subordination and the logical and temporal sequence for solving individual tasks. Various kinds of schematics, maps, and diagrams are convenient for representing such models. - A cause-and-effect model is often used to explain and predict the behavior of an object. These models are primarily focused on the following: 1) identifying the main interconnections between the constituent elements of the object under study; 2) determining how changes in some factors affect the state of the model's components; 3) understanding how the model will function as a whole and whether it will adequately describe the dynamics of the parameters of interest to the researcher. ## Formal Models A formal model is a representation of a conceptual model using one or more formal languages (for example, the languages of mathematical theories, special-purpose modeling languages, or algorithmic languages). In the humanities, the modeling process often concludes with the creation of a conceptual model of the object. In the natural sciences, it is usually possible to construct a formal model. While the importance of substantive and formal models for the process of cognition is more or less recognized by researchers, the role of cognitive models is often underestimated. This is due to the subjectivity of such models and the hidden nature of the thought process. However, there are objects and processes for which the role of cognitive models is particularly significant. For example, an operator or a decision-maker manages an object or process primarily based on their own cognitive models. The role of this type of model is also significant in the social sciences. Mathematical modeling is an ideal, scientific, symbolic, formal modeling where the object is described in the language of mathematics, and the model is studied using various mathematical methods. Any mathematical model intended for scientific research allows one to find the values of parameters of interest for the modeled object or phenomenon based on given input data. Therefore, it can be assumed that the essence of any such model lies in mapping a certain given set of input parameter values to a set of output parameter values. This allows a mathematical model to be viewed as a kind of mathematical operator. The concept of an operator can be interpreted quite broadly. It can be a function that links input and output values, or a mapping representing a symbolic notation of a system of algebraic, differential, integro-differential, or integral equations. It can also be an algorithm, a set of rules, or tables that ensure the finding (or determination) of output parameters from given initial values. Defining a mathematical model through the concept of an operator is more constructive from the perspective of classifying such models, as it encompasses the entire diversity of currently existing mathematical models. Advantages of mathematical modeling compared to physical experiments: - Cost-effectiveness (in particular, conservation of the real system's resources); - The ability to model hypothetical objects, i.e., those not realized in nature; - The ability to implement modes that are dangerous or difficult to reproduce in reality; - The ability to change the time scale; - The simplicity of multi-aspect analysis; - Greater predictive power due to the ability to identify general patterns; - The versatility of the technical and software tools used (programming systems and general-purpose application packages). An information model is a model of an object, represented as information that describes the parameters and variables of the object relevant to the given context, the relationships between them, the object's inputs and outputs, and which allows for the modeling of possible states of the object by feeding information about changes in input values to the model. ## External links - Scientific modelling — Wikipedia ## See also - [Modeling (scientific)](https://systems-analysis.info/eng/Modeling_(scientific) "Modeling (scientific)") - [Black box](https://systems-analysis.info/eng/Black_box "Black box") - [Formalization of system models](https://systems-analysis.info/eng/Formalization_of_system_models "Formalization of system models") - [Model](https://systems-analysis.info/eng/Model "Model") - [Core concepts of systems analysis](https://systems-analysis.info/eng/Core_concepts_of_systems_analysis "Core concepts of systems analysis")