Prediction of equations of state of molecular liquids by an artificial neural network.
Keywords:Artificial Neural Network, Equation of State, Molecular Liquids
In this work an artificial neural network (ANN) was used to determine the pressure and internal energy equations of state of noble gases and some molecular liquids by predicting thermodynamic state variables like density and temperature encoded in the radial distribution function. The ANN is trained to predict the thermodynamic state variables using only the structural data. Then, predicted values are used to compute equations of state of real liquids such as argon, neon, krypton and xenon as well as some molecular liquids like nitrogen, carbon dioxide, methane and ethylene. In order to assess the ANN predictions the relative percentage error with the exact values were determined, showing that its magnitude is less than 1%. Thus, the comparison between equations of state computed with the predicted variables and experimental results exhibits a very good agreement for most of the liquids studied here. Since our ANN implementation only requires the microscopic structure as an input, data incoming from experiments, theoretical frameworks or simulations are suitable to perform predictions of state variables and with that complement the thermodynamic characterisation of liquids through the determination of equations of state. Moreover, further improvements or extensions related with the microscopic structure database can be safely addressed without changing the neural network architecture presented here.
Z. Ge, Z. Song, S. X. Ding, and B. Huang, Data mining and analytics in the process industry: The role of machine learning, IEEE Access 5 (2017) 20590.
G. Carleo et al. Machine learning and the physical sciences, Rev. Mod. Phys. 91 (2019) 045002.
B. Sanchez-Lengeling and A. Aspuru-Guzik, Inverse molecular design using machine learning: Generative models for matter engineering, Science 361 (2018) 360.
K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, Machine learning for molecular and materials science, Nature 559 (2018) 547.
E. E. O. Ishida, Machine learning and the future of supernova cosmology, Nat. Astron. 3 (2019) 680.
A. Peel et al., Distinguishing standard and modified gravity cosmologies with machine learning, Phys. Rev. D 100 (2019) 023508.
E. A. Bedolla-Montiel, L. C. Padierna, and R. Castañeda-Priego, Machine learning for condensed matter physics, J. Phys.: Condes. Matter 33 (2020) 053001.
G. Toth, N. Kiraly, and A. Vrabecz, Pair potentials from diffraction data on liquids: A neural network solution, J. Chem. Phys. 123 (2005) 174109.
M. S. G. Nandagopal, E. Abraham, and N. Selvaraju, Advanced neural network prediction and system identification of liquidliquid flow patterns in circular microchannels with varying angle of confluence, Chem. Engineering J. 309 (2017) 850.
J. P. Allers, J. A. Harvey, F. H. Garzon, and T. M. Alam, Machine learning prediction of self-diffusion in lennard-jones fluids, J. Chem. Phys. 153 (2020) 034102.
Royal chemical society, chemspider. http://www. chemspider.com/accessed:2021-08-10.
U. S. Department of Commerce, National Institute of Standards and Technology (NIST), https://www.nist.gov/accessed: 2021-08-10.
J. P. Hansen and I.R. McDonald, Theory of Simple Liquids 3rd ed. (Academic Press, London, 2006).
F. Donado, J. García-Serrano, G. Torres-Vargas, and C. TapiaIgnacio, Temperature and particle concentration dependent effective potential in a bi-dimensional nonvibrating granular model for a glass-forming liquid, Physica A 524 (2019) 56.
M. J. Sanchez-Miranda, J. L. Carrillo-Estrada, and F. Donado, Crystallization processes in a nonvibrating magnetic granular system with short range repulsive interaction, Scientific Reports 9 (2019) 3531.
R. Rivas-Barbosa et al., Different routes into the glass state for soft thermo-sensitive colloids, Soft Matter 14 (2018) 5008.
Y. Zhao, Z. Wu, and W. Liu, Theoretical and analytical radial distribution function for dense fluids, Physica A 389 (2010) 5007.
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids 1st ed. (Oxford University Press, Oxford, 1987).
B. A. Klumov, On the behavior of indicators of melting: Lennard-jones system in the vicinity of the phase transition, JETP Lett. 98 (2013) 259.
P. L. Fehder, anomalies in the radial distribution functions for simple liquids, J. Chem. Phys. 52 (1970) 791.
Y. Vasseghian, A. Bahadori, A. Khataee, E. N. Dragoi, and M. Moradi, Modeling the interfacial tension of water-based binary and ternary systems at high pressures using a neuro-evolutive technique, ACS Omega 5 (2020) 781.
L. H. Hall and C. T. Story, Boiling point and critical temperature of a heterogeneous data set, J. Chem. Inf. Comput. Sci. 36 (1996) 1004.
A. Azari, S. Atashrouz, and H. Mirshekar, Boiling point and critical temperature of a heterogeneous data set: QSAR with atom type electrotopological state indices using artificial neural network, ISRN Chemical Engineering 36 (2013) 1.
K. Golzar, S. Amjad-Iranagh, and H. Modarress, Prediction of thermophysical properties for binary mixtures of common ionic liquids with water or alcohol at several temperatures and atmospheric pressure by means of artificial neural network, Ind. Eng. Chem. Res. 53 (2014) 7247.
Kenji Suzuki, Artificial Neural Networks: Architectures and Applications (InTech, Croatia, 2013).
D. Livingstone, D. Manallack, and I. Tetko, Data modelling with neural networks: Advantages and limitations, J. Comput. Aided Mol. Des. 11 (1997) 135.
J. Bourquin, H. Schmidli, P. van Hoogevest, and H. Leuenberger, Advantages of artificial neural networks (anns) as alternative modelling technique for data sets showing non-linear relationships using data from a galenical study on a solid dosage form, European Journal of Pharmaceutical Sciences 7 (1998) 5.
J. Sola and J. Sevilla, Importance of input data normalization for the application of neural networks to complex industrial problems, IEEE Transactions on Nuclear Science 44 (1997) 1464-1468.
J. A. Snyman and D. N. Wilke, Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms (Springer, Switzerland, 2018).
C. C. Aggarwal, Neural Networks and Deep Learning (Springer, Switzerland, 2018).
D. P. Kingma and J. Ba, Adam: A method for stochastic optimization (2015), arXiv:1412.6980.
I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT Press, Cambridge, 2016).
K. Eckle and J. Schmidt-Hieber, A comparison of deep networks with relu activation function and linear spline-type methods, Neural Networks 110 (2019) 232.
U. Que-Salinas, P. E. Ramírez-González, and A. Torres-Carbajal, Determination of thermodynamic state variables of liquids from their microscopic structures using an artificial neural network, Soft Matter 17 (2021) 1975.
A. Morsali, E. K. Goharshadi, G. A. Mansoori, and M. Abbaspour, An accurate expression for radial distribution function of the lennard-jones fluid, Chem. Phys. 310 (2005) 11.
G. Rutkai, M. Thol, R. Span, and J. Vrabec, How well does the lennard-jones potential represent the thermodynamic properties of noble gases? Mol. Phys. 115 (2017) 1104.
L. S. Tee, S. Gotoh, and W. E. Stewart, Molecular parameters for normal fluids. lennard-jones 12-6 potential, Ind. Eng. Chem. Fundamen. 5 (1996) 356.
S.-K. Oh, Modified lennard-jones potentials with a reduced temperature-correction parameter for calculating thermodynamic and transport properties: Noble gases and their mixtures (he, ne, ar, kr, and xe), Journal of Thermodynamics 2013 (2013) 828620.
A. Rahman, Correlations in the motion of atoms in liquid argon, Phys. Rev. 136 (1994) A405.
I. R. McDonald and K. Singer, Calculation of thermodynamic properties of liquid argon from lennard-jones parameters by a monte carlo method, Discuss. Faraday Soc. 43 (1967) 40.
J. A. Barker, R. A. Fisher, and R. O. Watts, Liquid argon: Monte carlo and molecular dynamics calculations, Mol. Phys. 21 (1971) 657
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