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Optimization Criteria for Mathematical Models Used in Sedimentology
Optimization principles play a key role in mathematical sedimentology in at least three ways.
The data-gathering process is optimized so as either to maximize the amount of information to be obtained with limited cost of sampling and measurement or to minimize the cost of obtaining at least a certain known amount of information.
Many commonly used data-analysis models have been formulated using optimization criteria. Examples include: regression by minimizing the sum of squares; principal component analysis by maximizing the amount of variation associated with each successive component axis, subject to constraints; discriminant-function analysis by placing decision surfaces so as to maximize the separation of predefined groups; cluster analysis by maximizing the compactness of groups; and several others.
Simulation modeling may involve optimization. First, principles of least work or similar optimization criteria may provide keys to the mathematical formulation of a model. This follows as a consequence of the optimization inherent in nature. Second, a basic goal in simulation is to adjust the parameters so as to minimize the difference between the model’s output and the real-world response. Furthermore, the process of exploring the sensitivity of a simulation model to systematic changes in parameters is a natural extension of optimization.
An appreciation of basic optimization principles leads to a clearer understanding as to how mathematics can help to solve sedimentological problems.Optimization Criteria for Mathematical Models Used in Sedimentology
Optimization principles play a key role in mathematical sedimentology in at least three ways.
The data-gathering process is optimized so as either to maximize the amount of information to be obtained with limited cost of sampling and measurement or to minimize the cost of obtaining at least a certain known amount of information.
Many commonly used data-analysis models have been formulated using optimization criteria. Examples include: regression by minimizing the sum of squares; principal component analysis by maximizing the amount of variation associated with each successive component axis, subject to constraints; discriminant-function analysis by placing decision surfaces so as to maximize the separation of predefined groups; cluster analysis by maximizing the compactness of groups; and several others.
Simulation modeling may involve optimization. First, principles of least work or similar optimization criteria may provide keys to the mathematical formulation of a model. This follows as a consequence of the optimization inherent in nature. Second, a basic goal in simulation is to adjust the parameters so as to minimize the difference between the model’s output and the real-world response. Furthermore, the process of exploring the sensitivity of a simulation model to systematic changes in parameters is a natural extension of optimization.
An appreciation of basic optimization principles leads to a clearer understanding as to how mathematics can help to solve sedimentological problems.Optimization Criteria for Mathematical Models Used in Sedimentology
Merriam, Daniel F. (editor) / Bonham-Carter, Graeme (author)
1972-01-01
25 pages
Article/Chapter (Book)
Electronic Resource
English
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