CBE Interdisciplinary Glossary

Computer Modeling

CALIBRATION An adjustment (often determined by statistical estimation techniques such as least square regression) of parameter values so that the model output estimates are close to the measured system output values. The calibrated model is technically valid only for a particular scenario and data base. Also called model tuning.

COMPUTER MODEL A numerical model converted to computer code so that the input and parameter values are entered into a computer and the program determines the associated output values.

CONCEPTUAL MODELThe expert's view of the process being modeled. Often conveyed as a schematic; for example, as interconnected compartments, each compartment having inflow, outflow, and reactions among compartment constituents.
 

Example of a conceptual model.

DESCRIPTIVE MODEL A model that approximately reproduces input/output responses for the available experimental data. It could be empirical or mechanistic.

DETERMINISTIC MODEL A mathematical model which contains no random (stochastic) components; consequently, each component and input is determined exactly by mathematical equations. In principle, for any specified input scenario, the corresponding model output variables are exactly determined. (Contrast with a stochastic model).

EMPIRICAL (or STATISTICAL) MODEL A model determined by statistically fitting equations to data; in contrast to a mechanistic model.

EVALUATION Comparison of the model's output to real data, either from the laboratory or the field. Successful evaluation is necessary for model validation. A spectrum of successful evaluations is sometimes called confirmation.

Table of Contents

Terms & Concepts by Discipline

Index

MATHEMATICAL MODEL A set of equations that describe the conceptual model in mathematical terms. In biofilm engineering, the mathematical model will often be a set of coupled, nonlinear, partial (or ordinary) differential equations. The mathematical model can be either deterministic or stochastic.

MECHANISTIC (or PHENOMENOLOGICAL) MODEL A representation of the physical, biological, or mechanistic theory governing the system; in contrast to an empirical model.

NUMERICAL MODEL A discretized version of the set of differential equations that make up the complicated mathematical model; the numerical model is devised to be converted into computer code.

PHENOMENOLOGICAL MODEL See Mechanistic Model.

SENSITIVITY ANALYSIS Determination of the extent to which model behavior (output) varies as model parameters are varied.

GLOBAL SENSITIVITY Variation of model behavior due to large perturbations of the parameters; often determined using computer experiments.

LOCAL SENSITIVITY Variation of model behavior due to small perturbations of the parameters; often determined by taking derivatives of the mathematical model with respect to the parameters.

STATISTICAL MODEL See Empirical Model.

STOCHASTIC MODEL A mathematical model which contains random (stochastic) components or inputs; consequently, for any specified input scenario, the corresponding model output variables are known only in terms of probability distributions. In contrast to a deterministic model.

VALIDATION Determination of the extent to which a model is well-founded and fulfills the purpose for which it was constructed. Validation denotes the establishment of legitimacy. It requires verification and successful evaluation.

VERIFICATION Determination that the numerical model or computer model is a faithful representation of the mathematical model, and that the mathematical model is a faithful representation of the conceptual model. Verification, which denotes establishment of truth, is possible only for the mathematical steps. Contributes to model validation.