Some Aspects of Combining Data and Models in Process Engineering

Abstract

Observing phenomena under defined conditions and building mathematical models to make further predictions are essential ingredients of natural and engineering sciences. Recent technological and methodical advances make large and highdimensional simulation data accessible to model building and therefore to optimization. In this article, selected machine learning methods are highlighted and applied to example data from simple flow sheet simulations. Furthermore, the essential outcomes of the workshop dealing with combination of data and models during the Tutzing Symposium 2019 are summarized.

Compensating Data Shortages in Manufacturing with Monotonicity Knowledge

“…With regard to the practical implementation, it is also important to observe that the objective functions x → g j (w k , x) of the lower-level problems (12) are non-convex polynomials and therefore in general have several local minima. Consequently, (12) needs to be solved numerically with a global optimization solver.…”

“…In [3], expert knowledge was used in the form of a specific algebraic relation between input and output to solve a parameter estimation problem with artificial neural networks. Such informed machine learning [4] techniques beneficially combine expert knowledge and data to build hybrid or gray-box models [5][6][7][8][9][10][11][12], which predict the responses more accurately than purely data-based models. In other words, by using informed machine learning techniques, one can compensate data insufficiencies with expert knowledge.…”

Compensating data shortages in manufacturing with monotonicity knowledge

“…With regard to the practical implementation, it is also important to observe that the objective functions x → g j (w k , x) of the lower-level problems ( 12) are non-convex polynomials and therefore in general have several local minima. So, (12) needs to be solved numerically with a global optimization solver.…”

“…3. Solve the (k, j)th lower-level problem (12) for every j ∈ J to obtain global minimizers x k+1,j ∈ X. Add those of the points x k+1,j , for which substantial monotonicity violations occur, i.e., for which g j (w, x k+1,j ) < −ε j , to the current discretization X k and go to Step 2 with k = k + 1.…”

“…It can solve quadratic programs with hundreds of variables and thousands of constraints in just a few seconds because it efficiently exploits the simple structure of the problem. Since on the other hand the lower-level problems (12) are global optimization problems with possibly several local minima, a suitable global optimization solver is required. We decided to use the solver scipy.optimize.shgo [44], which employs a simplicial homology strategy and which, in our applications, turned out to be a good compromise between speed and reliability.…”