Deterministic States

Abstract

The deterministic methods discussed in Chap. 1 were presented for problems that require the modeling of observations of one variable (like the total stopping distance of cars, the energy consumption, the atmospheric CO2 concentration, or the global temperature anomaly). However, most real problems are characterized by relations that involve several variables. Such relations have to provide the correct dimension of variables considered (for example, a characteristic time scale of any problem has to be calculated by a relation that provides a time). This constraint implies a reduction of all possible relations between variables, i.e., it reduces the original complexity of problems significantly (for example, it may require that a certain variable cannot be involved in a relation). The technique that provides such a problem reduction will be described in this chapter. This approach is extremely helpful, but it cannot completely solve the problem. The equations obtained in this way still involve unknown parameters that have to be determined by means of observations. Hence, the methods to be described in this chapter usually represent the first step before using the modeling approaches presented in Chap. 1 to determine unknown parameters.