Abstraction: Models simplify complex real-world systems by focusing on essential elements and relationships while ignoring less relevant details.
Mathematical Representation: They are expressed using mathematical equations, symbols, or formalism, making them precise and quantifiable.
Purpose-Driven: Models are created for specific purposes, such as prediction, explanation, optimization, or decision-making, and their structure reflects this purpose.
Assumptions: Models are based on assumptions about the behavior of the system being modeled. These assumptions can vary in realism and complexity.
Variables: Models involve variables that represent system components or attributes, and these variables are interconnected through mathematical relationships.
Parameters: Models often include parameters, which are constants or coefficients that influence the behavior of the system and can be adjusted for calibration or scenario analysis.
Validity and Applicability: The accuracy and applicability of a model depend on how well it reflects the real system, and models can be validated through data comparison.
Sensitivity Analysis: Models can be used for sensitivity analysis to understand how changes in input variables or parameters affect the output.
Time Dependency: Depending on the type of model, it may be static (time-independent) or dynamic (incorporating time as a variable).
Generalization: Models can be designed to provide insights beyond the specific case they represent, allowing for general principles and trends to be identified.
Interpretation: They provide a framework for interpreting data, making predictions, and testing hypotheses about the system under study.
Communication: Models facilitate communication and collaboration among experts and stakeholders by providing a common language and framework.
Limitations: Models have limitations due to simplifications and assumptions, and these limitations should be understood and acknowledged.
Solvability: Mathematical models are often solvable, meaning that they allow for analysis and computation to obtain solutions or insights.
Predictive Power: Many models are designed to make predictions about future states or behaviors of a system based on its current or past state.
These characteristics highlight the versatility and utility of mathematical models in various fields for understanding, decision-making, and problem-solving.
Abstraction:
Models simplify complex real-world systems by focusing on essential elements and relationships while ignoring less relevant details.
Mathematical Representation:
They are expressed using mathematical equations, symbols, or formalism, making them precise and quantifiable.
Purpose-Driven:
Models are created for specific purposes, such as prediction, explanation, optimization, or decision-making, and their structure reflects this purpose.
Assumptions:
Models are based on assumptions about the behavior of the system being modeled. These assumptions can vary in realism and complexity.
Variables:
Models involve variables that represent system components or attributes, and these variables are interconnected through mathematical relationships.
Parameters:
Models often include parameters, which are constants or coefficients that influence the behavior of the system and can be adjusted for calibration or scenario analysis.
Validity and Applicability:
The accuracy and applicability of a model depend on how well it reflects the real system, and models can be validated through data comparison.
Sensitivity Analysis:
Models can be used for sensitivity analysis to understand how changes in input variables or parameters affect the output.
Time Dependency:
Depending on the type of model, it may be static (time-independent) or dynamic (incorporating time as a variable).
Generalization:
Models can be designed to provide insights beyond the specific case they represent, allowing for general principles and trends to be identified.
Interpretation:
They provide a framework for interpreting data, making predictions, and testing hypotheses about the system under study.
Communication:
Models facilitate communication and collaboration among experts and stakeholders by providing a common language and framework.
Limitations:
Models have limitations due to simplifications and assumptions, and these limitations should be understood and acknowledged.
Solvability:
Mathematical models are often solvable, meaning that they allow for analysis and computation to obtain solutions or insights.
Predictive Power:
Many models are designed to make predictions about future states or behaviors of a system based on its current or past state.
Yes, you can model for these purposes, but the more complex the situation, the more easily one can be misled.
In regression, if your model is less complex than needed, results tend to be biased. If your regression model is more complex than needed, variance tends to increase. But I have found that the more complex the model needs to be, the less likely that heteroscedasticity is at the level one might expect. This just seems to be another consequence of the fact that the more complex the situation, the less well it can actually be modeled in practice, which is hardly surprising.
Sorry for the delay. I see you've read about mathematical modeling. Of course they can be classified, the text you put on modeling is extensive, but I do not agree with every point of what is said in that text. It must be based on history, yes, although we are talking about mathematics. The history of mathematics is properly the history of what we today call modeling. It all started, apparently, when the objects needed to be counted. Many applications followed until the construction of monumental buildings such as the enormous Renaissance Cathedrals. But what would have happened to those architects if they had not exactly modeled the force systems that would be generated in each wall or dome? Therefore, I do not believe that details should be overlooked when modeling, nor should some be considered more important than others, simply the models, which are all mathematical, are the representation of objective reality in our Brain and mathematics is the language with which this unique organ translates what he captured after a deep abstraction. What are called less influential details are, in most cases, variables that depend on others with a much higher contribution of information; in most cases their influence is reflected in the latter. The others that seem to influence and not strongly, since they do not affect the process that is analyzed. Now, the classification of mathematical models is pure human abstraction to be able to study and solve the models from a perspective. The classification criteria are those established to simplify tasks. But the phenomena and processes of industry and nature do not come in any classification, nor is their nature physical, mathematical or chemical, they are all an amalgamation of situations in different disciplines of knowledge. Therefore, to Model you must have a broad culture of the process that is modeled and of all the disciplines that involve the process or phenomenon. Then we continue talking
I would say you can use it is soft context like understanding what someone is expecting from model. An example can be that I want to create fast working, physics-based, easily interpretable model. This means that I might lose some information in order to achieve speed but mostly model will be based on some physical information. Although, I don't think it would be good to state that each model can be placed to cathegories based on these characteristics as sometimes they can overlap eachother. That is why I said 'soft'. For the record, I agree with two previous comments as they did explain entire idea of classification with examples.
Andrius, por eso es necesario definir el problema, los objetivos, diagnosticar bien el problem a
Exactly they are the rationale, need for mathematical modelling but do not rely most on the application you used to get the answers because it may give you inaccurate answers sometimes
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