THEORY → MODEL
A theory provides a conceptual framework. A model converts selected concepts into a structured representation that can be calculated, simulated, compared and revised.
This transition is not itself evidence that the theory is correct. It is a formalization step that makes assumptions explicit and exposes them to testing.
MODEL PURPOSE
FORMALIZE
Convert qualitative concepts into explicit mathematical or computational relationships.
SIMULATE
Generate model outputs under defined initial conditions and parameter values.
TEST
Produce outputs that can be compared with observations or independently generated data.
VARIABLES / PARAMETERS
STATE VARIABLES
Quantities representing the current state of the modeled system.
PARAMETERS
Fixed or externally selected quantities controlling the behavior of the model.
OBSERVABLES
Quantities that can, in principle, be connected to measurable observations.
STARTING STATE
Every deterministic model requires a defined starting configuration. Initial conditions determine the state from which the model begins its evolution.
Different initial conditions can produce different outputs. Therefore, the initial state must be documented and kept separate from the resulting model behavior.
TIME DEPENDENCE
The model describes how the selected state variables evolve as a function of the model's time parameter.
Here, S₀ represents the initial state, P represents the selected parameters, and t represents model time.
MODEL ≠ OBSERVATION
A model generates an output. An observation is obtained from an empirical measurement or an independently defined data source. The two must remain conceptually separate.
OUTPUT
QUANTITY
Agreement between a model output and an observation is a comparison result. It should not be described as proof without considering measurement uncertainty, alternative explanations and the assumptions built into the model.
DETERMINISTIC
In a deterministic formulation, once the model equations, parameters and initial conditions are fixed, the model produces a defined trajectory or output.
This property concerns the mathematical structure of the model. It does not establish that the modeled system itself is deterministic in nature.
TESTABLE OUTPUT
A useful model must allow at least some outputs to be translated into observations that could potentially disagree with the model.
REPEATABILITY
A deterministic computational model should produce the same output when the same equations, parameters, initial conditions and computational procedure are used.
Reproducibility of a simulation does not by itself establish empirical validity. It establishes that the defined computational procedure can be repeated.
MODEL BOUNDARY
ASSUMPTIONS
Every model depends on assumptions. Changing an assumption can change the resulting behavior.
PARAMETER SPACE
Conclusions may depend on the parameter range that has actually been explored.
EMPIRICAL LIMIT
A model output becomes scientifically informative only through comparison with relevant observations and competing explanations.
OPEN TO REVISION
The model is treated as a working formalization rather than a final description of reality. New observations, contradictions, parameter sensitivities or better alternative formulations may require modification.
MODEL LAB 4
The computational layer provides an environment for examining the model behavior under defined inputs and parameters.
OPEN MODEL LAB v4 →TEST IT.