Mathematics versus Physics (Part 2):
Combining the Best of Both Worlds
in Industrial AI Practice.

Emeli Dral
Chief Data Scientist, Mechanica AI
Introducing data-based techniques into the domain of traditional industrial process modeling often raises the question, Are these approaches friends of foes? Our Chief Data Scientist Emeli Dral explores the differences and practical implications for performing process optimization tasks.

You can read the first blog post on this topic here.
Despite the fact that machine learning technologies and the classical approach to modeling are often conflicting, these technologies can also be complementary. In fact, each of them is a tool that can suit certain tasks better than others—or even be combined to ensure optimal results. Let us explore how in more detail.
Machine Learning–First Approach
In the most intuitive approach, one can take a process that is already described by a classical model, for example a thermodynamic model, and try to use machine learning instead. Then one can compare results in terms of quality, speed, and effort required to support the model, and decide which one to use. In this scenario, machine learning can replace first-principle models if the technology performs better on a given set of tasks.

It is well known that machine learning models, unlike classical models, work well in situations where a large number of data sources is available for analysis, even if each of these sources is of relatively low value and quality—if, for example, it contains "noise" and gaps. In the case of such raw data, it makes sense to test an approach based on machine learning, which is likely to produce a more accurate result.
We can— and should!—also use machine learning when the classical process models are very hard to create, or where routine decisions are made based on rules, heuristics, or human expertise.
Mathematics Plus Physics
Machine learning and classical approaches can be combined in different ways. For example, we can correct the output of a classical model using a machine learning model. Alternatively, we can process the raw data with the help of machine learning algorithms to "clean" and normalize it so that it can later be used as suitable input for a first-principle model.
We can choose one of these two approaches or build a complex hybrid solution that includes multiple models.
In the first approach, machine learning technology works on top of a classical model in order to correct its output based on weak factors and dependencies that classical models cannot take into account. This makes the hybrid solution even more attractive in terms of practical usage: it is still partially interpretable and predictable, and it is robust because it is based on physical principles; moreover, unlike classical models alone, it can react to minor changes in the process that are reflected by a large number of factors, and therefore work much more accurately.

Another way to combine classical and machine learning-based models is to preprocess data using machine learning algorithms so that the resulting data can be used as input to classical models.
Classical models have no mechanisms for protection against outliers, gaps, accumulated errors, or simply inaccurate measurements.
Often, their application in industrial practice is limited precisely because the source data is "dirty" and not suitable for use. In such cases, machine learning algorithms can help. They can be used to fill the gaps, filter outliers, and correct measurement errors so that the data can become usable in classical models. You can think of them as a set of virtual—or inferential—sensors that measure the parameters to fill in the formulas that the classical models contain.
We at Mechanica AI successfully implement all these strategies in our applications. Interested to know how AI can make your production processes more efficient on top of classical approaches? Come and talk to us!
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