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 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Hoboken, USA
John Wiley & Sons, Inc
01.06.2022
American Institute of Chemical Engineers |
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| ISSN: | 0001-1541, 1547-5905 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Sahinidis, Nikolaos V. Engle, Marissa R. |
| Author_xml | – sequence: 1 givenname: Marissa R. surname: Engle fullname: Engle, Marissa R. organization: Carnegie Mellon University – sequence: 2 givenname: Nikolaos V. orcidid: 0000-0003-2087-9131 surname: Sahinidis fullname: Sahinidis, Nikolaos V. email: nikos@gatech.edu organization: H. Milton Stewart School of Industrial and Systems Engineering, School of Chemical and Biomolecular Engineering, Georgia Institute of Technology |
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| Cites_doi | 10.1007/s10107-018-1289-x 10.1021/i200022a008 10.1039/f29848001019 10.1016/j.supflu.2016.05.012 10.1016/j.compchemeng.2018.10.007 10.1002/aic.14741 10.1007/s10957-018-1396-0 10.1145/2576768.2598264 10.1016/j.cryogenics.2017.04.001 10.1007/s10710-010-9124-z 10.1002/cjce.5450640224 10.1016/0378-3812(83)80084-3 10.1007/s10710-019-09371-3 10.1016/j.compchemeng.2017.06.023 10.1016/j.fluid.2017.04.015 10.1016/j.molliq.2019.111971 10.1126/sciadv.aay2631 10.1016/j.asoc.2020.106432 10.1016/j.ins.2017.11.041 10.1016/0009-2509(84)80034-2 10.1016/S0098-1354(96)00329-8 10.1023/B:IJOT.0000022331.46865.2f 10.1016/j.cej.2019.123412 10.1016/j.compchemeng.2020.107051 10.1080/10556788.2017.1350178 10.1016/j.fluid.2017.05.007 10.1016/j.fluid.2016.12.015 10.1016/0009-2509(72)80096-4 10.1023/A:1021039126272 10.1109/LA-CCI47412.2019.9036755 10.1016/j.engappai.2017.10.021 10.1016/j.fluid.2016.07.026 10.1016/j.compchemeng.2014.05.013 |
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| Title | Deterministic symbolic regression with derivative information: General methodology and application to equations of state |
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