Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real‐world phenomena but the use of deterministic optimization for symbolic regression has been limited...

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Veröffentlicht in:AIChE journal Jg. 68; H. 6
Hauptverfasser: Engle, Marissa R., Sahinidis, Nikolaos V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken, USA John Wiley & Sons, Inc 01.06.2022
American Institute of Chemical Engineers
Schlagworte:
Complexity
cubic equations of state
Equations of state
mixed‐integer nonlinear programming
Nonlinear programming
Optimization
Regression
surrogate modeling
symbolic regression
Thermodynamics
Trees
ISSN:0001-1541, 1547-5905
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Zusammenfassung:Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real‐world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. We present a novel deterministic mixed‐integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics‐based constraints on the first and second derivatives.
Bibliographie:Funding information
U.S. Department of Energy; Office of Fossil Energy
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SourceType-Scholarly Journals-1
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content type line 14
ISSN:0001-1541
1547-5905
DOI:10.1002/aic.17457