Mathematical modeling can be divided into two main categories: mechanistic and empirical models.
In ideal cases, experimental work may be substituted by using mechanistic models, e.g. following situations:
Profmath has plenty of experience in mechanistic modeling, and assists in all common problems related to mechanistic modeling.
Empirical models are applied in situations where building mechanistic models is not possible. This includes cases such as:
Empirical models can be used for the same purposes as mechanistic models, but the spectrum of applications is wider. Some examples:
There are many cases in which solving a problem requires both empirical and mechanistic models. ProfMath has plenty of experience in such applications, and our researchers have developed new methods in this field.
Empirical models can be built either based on data from designed experiments or from gathered process data. In the former case, we speak about statistical design of experiments (DOE), and in the latter, about data analysis (or machine learning). Generally, models based on DOE are more reliable than models based on arbitrarily gathered data (often called passive data). In empirical modeling, it is always important know the nature of data used, and the limitations of the models used.
Using passive experimental data, or data based intuitively designed experiments, may easily lead to lead to a situation where a lot money as been spent without results that could be used for reliable conclusions.
ProfMath has plenty of experience on DOE and data analysis in various fields of applications. Our special strengths include optimization, also multiresponse optimization, of processes of process units using so-called response surface methodology (RSM).