An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theorem

The objective in this work is to propose a novel approach for solving inverse problems from the output space to the input space using automatic differentiation coupled with the implicit function theorem and a path integration scheme. A common way of solving inverse problems in process systems engine...

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Vydáno v:AIChE journal Ročník 69; číslo 9
Hlavní autoři: Alves, Victor, Kitchin, John R., Lima, Fernando V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken, USA John Wiley & Sons, Inc 01.09.2023
American Institute of Chemical Engineers
Témata:
automatic differentiation
Complexity
Computational efficiency
Computer applications
Computing time
Continuously stirred tank reactors
Differential equations
Differentiation
implicit function theorem
inverse mapping
Inverse problems
Mapping
Membrane reactors
Natural gas
Nonlinear programming
process systems engineering
Reactors
Robustness (mathematics)
Systems engineering
Theorems
ISSN:0001-1541, 1547-5905
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Shrnutí:The objective in this work is to propose a novel approach for solving inverse problems from the output space to the input space using automatic differentiation coupled with the implicit function theorem and a path integration scheme. A common way of solving inverse problems in process systems engineering (PSE) and in science, technology, engineering and mathematics (STEM) in general is using nonlinear programming (NLP) tools, which may become computationally expensive when both the underlying process model complexity and dimensionality increase. The proposed approach takes advantage of recent advances in robust automatic differentiation packages to calculate the input space region by integration of governing differential equations of a given process. Such calculations are performed based on an initial starting point from the output space and are capable of maintaining accuracy and reducing computational time when compared to using NLP‐based approaches to obtain the inverse mapping. Two nonlinear case studies, namely a continuous stirred tank reactor (CSTR) and a membrane reactor for conversion of natural gas to value‐added chemicals are addressed using the proposed approach and compared against: (i) extensive (brute‐force) search for forward mapping and (ii) using NLP solvers for obtaining the inverse mapping. The obtained results show that the novel approach is in agreement with the typical approaches, while computational time and complexity are considerably reduced, indicating that a new direction for solving inverse problems is developed in this work.
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ISSN:0001-1541
1547-5905
DOI:10.1002/aic.18119