Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids

Alam, Todd M.; Allers, Joshua P.; Leverant, Calen J.; Harvey, Jacob A.

doi:10.1063/5.0093658

Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids

Journal Article · Fri Jul 01 00:00:00 EDT 2022 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0093658· OSTI ID:1877160

^[1]; ^[2]; ^[3]; ^[2]

ACC Consulting New Mexico, Cedar Crest, NM (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of Florida, Gainesville, FL (United States)

Symbolic regression (SR) with a multi-gene genetic program has been used to elucidate new empirical equations describing diffusion in Lennard-Jones (LJ) fluids. Some examples include equations to predict self-diffusion in pure LJ fluids and equations describing the finite-size correction for self-diffusion in binary LJ fluids. The performance of the SR-obtained equations was compared to that of both the existing empirical equations in the literature and to the results from artificial neural net (ANN) models recently reported. It is found that the SR equations have improved predictive performance in comparison to the existing empirical equations, even though employing a smaller number of adjustable parameters, but show an overall reduced performance in comparison to more extensive ANNs.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003525

OSTI ID:: 1877160

Alternate ID(s):: OSTI ID: 1874591

Report Number(s):: SAND2022-9282J; 708092

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 1 Vol. 157; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (57)

Modeling Diffusion in Functional Materials: From Density Functional Theory to Artificial Intelligence Elbaz, Yuval; Furman, David; Caspary Toroker, Maytal Advanced Functional Materials https://doi.org/10.1002/adfm.201900778	journal	July 2019
The viscosity of dense fluid mixtures: Mixing rules reexamined using nonequilibrium molecular dynamics Murad, S. AIChE Journal, Vol. 32, Issue 3 https://doi.org/10.1002/aic.690320321	journal	March 1986
Co-evolution of non-linear PLS model components Searson, Dominic; Willis, Mark; Montague, Gary Journal of Chemometrics, Vol. 21, Issue 12 https://doi.org/10.1002/cem.1084	journal	January 2007
GPTIPS 2: An Open-Source Software Platform for Symbolic Data Mining Searson, Dominic P. Handbook of Genetic Programming Applications https://doi.org/10.1007/978-3-319-20883-1_22	book	January 2015
Genetic programming as a means for programming computers by natural selection Koza, JohnR. Statistics and Computing, Vol. 4, Issue 2 https://doi.org/10.1007/bf00175355	journal	June 1994
Diffusion and viscosity equations of state for a Lennard-Jones fluid obtained from molecular dynamics simulations Rowley, R. L.; Painter, M. M. International Journal of Thermophysics, Vol. 18, Issue 5 https://doi.org/10.1007/bf02575252	journal	September 1997
Prediction of Self-Diffusion Coefficients of Fluids Based on Friction and Free Volume Theories Zhong, Qiu; Yang, Liping; Tao, Ye International Journal of Thermophysics, Vol. 36, Issue 7 https://doi.org/10.1007/s10765-015-1906-3	journal	May 2015
Prediction of the mutual diffusivity in binary non-ideal liquid mixtures from the tracer diffusion coefficients Moggridge, G. D. Chemical Engineering Science, Vol. 71 https://doi.org/10.1016/j.ces.2011.12.016	journal	March 2012
Universal correlation of self-diffusion coefficients of model and real fluids based on residual entropy scaling law Vaz, Raquel V.; Magalhães, Ana L.; Fernandes, Daniel L. A. Chemical Engineering Science, Vol. 79 https://doi.org/10.1016/j.ces.2012.05.006	journal	September 2012
Influence of the mass ratio on viscosity in Lennard–Jones mixtures: The one-fluid model revisited using nonequilibrium molecular dynamics Galliéro, Guillaume; Boned, Christian; Baylaucq, Antoine Fluid Phase Equilibria, Vol. 234, Issue 1-2 https://doi.org/10.1016/j.fluid.2005.05.016	journal	July 2005
The van der Waals one-fluid model for viscosity in Lennard–Jones fluids: Influence of size and energy parameters Galliéro, Guillaume; Boned, Christian; Baylaucq, Antoine Fluid Phase Equilibria, Vol. 245, Issue 1 https://doi.org/10.1016/j.fluid.2006.03.006	journal	July 2006
Mass effect on viscosity of mixtures in entropy scaling framework: Application to Lennard-Jones mixtures Viet, Thieu Quang Quoc; Khennache, Samy; Galliero, Guillaume Fluid Phase Equilibria, Vol. 558 https://doi.org/10.1016/j.fluid.2022.113459	journal	July 2022
On elemental and isotopic fractionation of noble gases in geological fluids by molecular diffusion Hoang, Hai; Ho, Khac Hieu; Battani, Anne Geochimica et Cosmochimica Acta, Vol. 315 https://doi.org/10.1016/j.gca.2021.09.002	journal	December 2021
System size and trajectory length dependence of the static structure factor and the diffusion coefficient as calculated from molecular dynamics simulations: The case of SPC/E water Gereben, Orsolya; Pusztai, László Journal of Molecular Liquids, Vol. 161, Issue 1 https://doi.org/10.1016/j.molliq.2011.04.004	journal	June 2011
Unified approach to the self-diffusion coefficients of dense fluids over wide ranges of temperature and pressure—hard-sphere, square-well, Lennard–Jones and real substances Liu, Hongqin; Silva, Carlos M.; Macedo, Eugénia A. Chemical Engineering Science, Vol. 53, Issue 13 https://doi.org/10.1016/s0009-2509(98)00036-0	journal	July 1998
Prediction of diffusion coefficients for gas, liquid and supercritical fluid: application to pure real fluids and infinite dilute binary solutions based on the simulation of Lennard–Jones fluid Zhu, Yu; Lu, Xiaohua; Zhou, Jian Fluid Phase Equilibria, Vol. 194-197 https://doi.org/10.1016/s0378-3812(01)00669-0	journal	March 2002
Self-Diffusion Coefficients from Entropy Scaling Using the PCP-SAFT Equation of State Hopp, Madlen; Mele, Julia; Gross, Joachim Industrial & Engineering Chemistry Research, Vol. 57, Issue 38 https://doi.org/10.1021/acs.iecr.8b02406	journal	August 2018
Generalized Form for Finite-Size Corrections in Mutual Diffusion Coefficients of Multicomponent Mixtures Obtained from Equilibrium Molecular Dynamics Simulation Jamali, Seyed Hossein; Bardow, André; Vlugt, Thijs J. H. Journal of Chemical Theory and Computation, Vol. 16, Issue 6 https://doi.org/10.1021/acs.jctc.0c00268	journal	April 2020
Finite-Size Effects of Binary Mutual Diffusion Coefficients from Molecular Dynamics Jamali, Seyed Hossein; Wolff, Ludger; Becker, Tim M. Journal of Chemical Theory and Computation, Vol. 14, Issue 5 https://doi.org/10.1021/acs.jctc.8b00170	journal	March 2018
Lattice Thermal Conductivity Prediction Using Symbolic Regression and Machine Learning Loftis, Christian; Yuan, Kunpeng; Zhao, Yong The Journal of Physical Chemistry A, Vol. 125, Issue 1 https://doi.org/10.1021/acs.jpca.0c08103	journal	December 2020
Ionic Conductivity, Diffusion Coefficients, and Degree of Dissociation in Lithium Electrolytes, Ionic Liquids, and Hydrogel Polyelectrolytes Garrido, Leoncio; Aranaz, Inmaculada; Gallardo, Alberto The Journal of Physical Chemistry B, Vol. 122, Issue 34 https://doi.org/10.1021/acs.jpcb.8b06424	journal	August 2018
Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid Bell, Ian H.; Messerly, Richard; Thol, Monika The Journal of Physical Chemistry B, Vol. 123, Issue 29 https://doi.org/10.1021/acs.jpcb.9b05808	journal	June 2019
Machine Learning Self-Diffusion Prediction for Lennard-Jones Fluids in Pores Leverant, Calen J.; Harvey, Jacob A.; Alam, Todd M. The Journal of Physical Chemistry C, Vol. 125, Issue 46 https://doi.org/10.1021/acs.jpcc.1c08297	journal	November 2021
Molecular Simulations of CH ₄ and CO ₂ Diffusion in Rigid Nanoporous Amorphous Materials Thyagarajan, Raghuram; Sholl, David S. The Journal of Physical Chemistry C, Vol. 126, Issue 19 https://doi.org/10.1021/acs.jpcc.2c01609	journal	May 2022
Transport of Multicomponent Hydrocarbon Mixtures in Shale Organic Matter by Molecular Simulations Collell, Julien; Galliero, Guillaume; Vermorel, Romain The Journal of Physical Chemistry C, Vol. 119, Issue 39 https://doi.org/10.1021/acs.jpcc.5b07242	journal	September 2015
Machine Learning-Based Upscaling of Finite-Size Molecular Dynamics Diffusion Simulations for Binary Fluids Leverant, Calen J.; Harvey, Jacob A.; Alam, Todd M. The Journal of Physical Chemistry Letters, Vol. 11, Issue 24 https://doi.org/10.1021/acs.jpclett.0c03108	journal	November 2020
Free Volume Theory of Hydrocarbon Mixture Transport in Nanoporous Materials Obliger, Amaël; Pellenq, Roland; Ulm, Franz-Josef The Journal of Physical Chemistry Letters, Vol. 7, Issue 19 https://doi.org/10.1021/acs.jpclett.6b01684	journal	September 2016
Ion Diffusion Coefficients in Ion Exchange Membranes: Significance of Counterion Condensation Kamcev, Jovan; Paul, Donald R.; Manning, Gerald S. Macromolecules, Vol. 51, Issue 15 https://doi.org/10.1021/acs.macromol.8b00645	journal	July 2018
Influence of Diffusion Time on the Diffusion Coefficients of Gases in Polymers Determined by Pulsed Gradient Spin Echo NMR Garrido, Leoncio; Guzmán, Julio Macromolecules, Vol. 51, Issue 21 https://doi.org/10.1021/acs.macromol.8b02107	journal	October 2018
Diffusion Behavior of Water Molecules in Hydrogels with Controlled Network Structure Fujiyabu, Takeshi; Li, Xiang; Chung, Ung-il Macromolecules, Vol. 52, Issue 5 https://doi.org/10.1021/acs.macromol.8b02488	journal	February 2019
Enhanced Diffusive Transport in Fluctuating Porous Media Sarfati, Raphaël; Calderon, Christopher P.; Schwartz, Daniel K. ACS Nano, Vol. 15, Issue 4 https://doi.org/10.1021/acsnano.1c00744	journal	April 2021
Predictive Darken Equation for Maxwell-Stefan Diffusivities in Multicomponent Mixtures Liu, Xin; Vlugt, Thijs J. H.; Bardow, André Industrial & Engineering Chemistry Research, Vol. 50, Issue 17 https://doi.org/10.1021/ie201008a	journal	September 2011
Self-Diffusion in Gases and Liquids Ruckenstein, Eli; Liu, Hongqin Industrial & Engineering Chemistry Research, Vol. 36, Issue 9 https://doi.org/10.1021/ie9701332	journal	September 1997
Comparison between Different Explicit Expressions of the Effective Hard Sphere Diameter of Lennard-Jones Fluid: Application to Self-Diffusion Coefficients Silva, Carlos M.; Liu, Hongqin; Macedo, Eugénia A. Industrial & Engineering Chemistry Research, Vol. 37, Issue 1 https://doi.org/10.1021/ie970281s	journal	January 1998
Correlation for the Viscosity of Normal Hydrogen Obtained from Symbolic Regression Muzny, Chris D.; Huber, Marcia L.; Kazakov, Andrei F. Journal of Chemical & Engineering Data, Vol. 58, Issue 4 https://doi.org/10.1021/je301273j	journal	March 2013
System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions Yeh, In-Chul; Hummer, Gerhard The Journal of Physical Chemistry B, Vol. 108, Issue 40 https://doi.org/10.1021/jp0477147	journal	October 2004
A universal scaling law for atomic diffusion in condensed matter Dzugutov, Mikhail Nature, Vol. 381, Issue 6578 https://doi.org/10.1038/381137a0	journal	May 1996
A meeting with Enrico Fermi Dyson, Freeman Nature, Vol. 427, Issue 6972 https://doi.org/10.1038/427297a	journal	January 2004
Self-diffusion and shear viscosity of simple fluids. A molecular-dynamics study Heyes, David M. Journal of the Chemical Society, Faraday Transactions 2, Vol. 79, Issue 12 https://doi.org/10.1039/f29837901741	journal	January 1983
Viscosity and self-diffusion of simple liquids. Hard-sphere treatment of molecular dynamics data Heyes, David M. Journal of the Chemical Society, Faraday Transactions 2, Vol. 83, Issue 11 https://doi.org/10.1039/f29878301985	journal	January 1987
Transport coefficients of the Lennard-Jones model fluid. II Self-diffusion Meier, Karsten; Laesecke, Arno; Kabelac, Stephan The Journal of Chemical Physics, Vol. 121, Issue 19 https://doi.org/10.1063/1.1786579	journal	November 2004
Effect of the computational domain size and shape on the self-diffusion coefficient in a Lennard-Jones liquid Kikugawa, Gota; Ando, Shotaro; Suzuki, Jo The Journal of Chemical Physics, Vol. 142, Issue 2 https://doi.org/10.1063/1.4905545	journal	January 2015
System-size corrections for self-diffusion coefficients calculated from molecular dynamics simulations: The case of CO2, n-alkanes, and poly(ethylene glycol) dimethyl ethers Moultos, Othonas A.; Zhang, Yong; Tsimpanogiannis, Ioannis N. The Journal of Chemical Physics, Vol. 145, Issue 7 https://doi.org/10.1063/1.4960776	journal	August 2016
Machine learning prediction of self-diffusion in Lennard-Jones fluids Allers, Joshua P.; Harvey, Jacob A.; Garzon, Fernando H. The Journal of Chemical Physics, Vol. 153, Issue 3 https://doi.org/10.1063/5.0011512	journal	July 2020
Machine learning symbolic equations for diffusion with physics-based descriptions Papastamatiou, Konstantinos; Sofos, Filippos; Karakasidis, Theodoros E. AIP Advances, Vol. 12, Issue 2 https://doi.org/10.1063/5.0082147	journal	February 2022
Diffusion in the hard sphere fluid Speedy, Robin J. Molecular Physics, Vol. 62, Issue 2 https://doi.org/10.1080/00268978700102371	journal	October 1987
Diffusion in simple fluids Speedy, R. J.; Prielmeier, F. X.; Vardag, T. Molecular Physics, Vol. 66, Issue 3 https://doi.org/10.1080/00268978900100341	journal	February 1989
Information theory applied to the transport coefficients of Lennard-Jones fluids Heyes, D. M.; Powles, J. G. Molecular Physics, Vol. 71, Issue 4 https://doi.org/10.1080/00268979000102111	journal	November 1990
Information theory applied to the transport coefficients of Lennard-Jones fluids II Heyes, D. M.; Powles, J. G.; Gil Montero, J. C. Molecular Physics, Vol. 78, Issue 1 https://doi.org/10.1080/00268979300100191	journal	January 1993
Finite-size effects of diffusion coefficients computed from molecular dynamics: a review of what we have learned so far Celebi, Alper T.; Jamali, Seyed Hossein; Bardow, André Molecular Simulation, Vol. 47, Issue 10-11 https://doi.org/10.1080/08927022.2020.1810685	journal	September 2020
Computer Simulation of Liquids Allen, Michael P.; Tildesley, Dominic J. https://doi.org/10.1093/oso/9780198803195.001.0001	book	June 2017
Generalized Rosenfeld scalings for tracer diffusivities in not-so-simple fluids: Mixtures and soft particles Krekelberg, William P.; Pond, Mark J.; Goel, Gaurav Physical Review E, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevE.80.061205	journal	December 2009
Relation between the transport coefficients and the internal entropy of simple systems Rosenfeld, Yaakov Physical Review A, Vol. 15, Issue 6 https://doi.org/10.1103/physreva.15.2545	journal	June 1977
Self-diffusion coefficient for the hard-sphere fluid Erpenbeck, Jerome J.; Wood, William W. Physical Review A, Vol. 43, Issue 8 https://doi.org/10.1103/physreva.43.4254	journal	April 1991
Transport coefficients of Lennard-Jones fluids: A molecular-dynamics and effective-hard-sphere treatment Heyes, David M. Physical Review B, Vol. 37, Issue 10 https://doi.org/10.1103/physrevb.37.5677	journal	April 1988
Symbolic regression in materials science Wang, Yiqun; Wagner, Nicholas; Rondinelli, James M. MRS Communications, Vol. 9, Issue 3 https://doi.org/10.1557/mrc.2019.85	journal	June 2019
Current Trends in Fluid Research in the Era of Artificial Intelligence: A Review Sofos, Filippos; Stavrogiannis, Christos; Exarchou-Kouveli, Kalliopi K. Fluids, Vol. 7, Issue 3 https://doi.org/10.3390/fluids7030116	journal	March 2022

Similar Records

Machine learning prediction of self-diffusion in Lennard-Jones fluids

Journal Article · Wed Jul 15 00:00:00 EDT 2020 · Journal of Chemical Physics · OSTI ID:1670740

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Lennard-Jones fluid
artificial neural networks
chemical properties
computer simulation
kinetic theory
machine learning
mass diffusivity
molecular dynamics
regression analysis
symbolic computation

Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids

Citation Formats

References (57)

Similar Records

Related Subjects