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Data-driven discovery of formulas by symbolic regression

Published online by Cambridge University Press:  12 July 2019

Sheng Sun ,
Runhai Ouyang ,
Bochao Zhang  and
Tong-Yi Zhang
Sheng Sun
Affiliation:
Materials Genome Institute, Shanghai University, China; mgissh@t.shu.edu.cn
Runhai Ouyang
Affiliation:
Materials Genome Institute, Shanghai University, China; rouyang@shu.edu.cn
Bochao Zhang
Affiliation:
Materials Genome Institute, Shanghai University, China; mgizbc@shu.edu.cn
Tong-Yi Zhang
Affiliation:
Materials Genome Institute, Shanghai University, China; zhangty@shu.edu.cn
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Abstract

Discovering knowledge from data is a quantum jump from quantity to quality, which is the characteristic and the spirit of the development of science. Symbolic regression (SR) is playing a greater role in the discovery of knowledge from data, specifically in this era of exponential data growth, because SRs are able to discover mathematical formulas from data. These formulas may provide scientifically meaningful models, especially when combined with domain knowledge. This article provides an overview of SR applications in the field of materials science and engineering. Integrating domain knowledge with SR is the key and a crucial approach, which allows gaining knowledge from data quickly, accurately, and scientifically. In the data-driven paradigm, SR allows for uncovering the underlying mechanisms of materials behavior, properties, and functions, in a wide range of areas from basic academic research to industrial applications, including experiments and computations, by providing explicit interpretable models from data, in comparison with other machine-learning “black-box” models. SR will be a powerful tool for rational and automatic materials development.

Keywords

symbolic regressiongenetic programminggrammar-guided genetic programminggrammatical evolutionmathematic formulas

Information

Type
The Machine Learning Revolution in Materials Research
Information
MRS Bulletin , Volume 44 , Issue 7: The Machine Learning Revolution in Materials Research , July 2019 , pp. 559 - 564
Copyright
Copyright © Materials Research Society 2019 

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References

Goldstein, E.B., Coco, G., Front. Environ. Sci. 3, 1 (2015).CrossRefGoogle Scholar
Langley, P., “Rediscovering Physics with BACON.3,” Proc. 6th Int. Jt. Conf. Artif. Intell.—Vol. 1 (Morgan Kaufmann Publishers, 1979), pp. 505–507, http://dl.acm.org/citation.cfm?id=1624861.1624976.Google Scholar
Schmidt, M., Lipson, H., Science 324, 81 (2009).CrossRefGoogle Scholar
Schaeffer, H., McCalla, S.G., Phys. Rev. E 96, 023302 (2017).CrossRefGoogle Scholar
Rudy, S.H., Brunton, S.L., Proctor, J.L., Kutz, J.N., Sci. Adv. 3, e1602614 (2017).CrossRefGoogle Scholar
Ghiringhelli, L.M., Vybiral, J., Ahmetcik, E., Ouyang, R., Levchenko, S.V., Draxl, C., Scheffler, M., New J. Phys. 19, 023017 (2017).CrossRefGoogle Scholar
Ouyang, R., Curtarolo, S., Ahmetcik, E., Scheffler, M., Ghiringhelli, L.M., Phys. Rev. Mater. 2, 083802 (2018).CrossRefGoogle Scholar
Ramakrishna, S., Zhang, T.-Y., Lu, W.-C., Qian, Q., Low, J.S.C., Yune, J.H.R., Tan, D.Z.L., Bressan, S., Sanvito, S., Kalidindi, S.R., J. Intell. Manuf. (2018).Google Scholar
Agrawal, A., Choudhary, A., APL Mater . 4, 053208 (2016).CrossRefGoogle Scholar
Wang, Y., Wagner, N., Rondinelli, J.M., “Symbolic Regression in Materials Science,” submitted arXiv:1901.04136 (2019), http://arxiv.org/abs/1901.04136 (accessed March 26, 2019).Google Scholar
Praks, P., Brkić, D., Water 10, 1175 (2018).CrossRefGoogle Scholar
Goldstein, E.B., Coco, G., Murray, A.B., Green, M.O., Earth Surf. Dyn. 2, 67 (2014).CrossRefGoogle Scholar
Hinchliffe, M.P., Willis, M.J., Comput. Chem. Eng. 27, 1841 (2003).CrossRefGoogle Scholar
Ly, D.L., Lipson, H., J. Mach. Learn. Res. 13, 3585 (2012).Google Scholar
Cornforth, T.W., Lipson, H., Genet. Program. Evolvable Mach. 14, 155 (2013).CrossRefGoogle Scholar
Gout, J., Quade, M., Shafi, K., Niven, R.K., Abel, M., Nonlinear Dyn . 91, 1001 (2018).CrossRefGoogle Scholar
Quade, M., Abel, M., Shafi, K., Niven, R.K., Noack, B.R., Phys. Rev. E 94, 012214 (2016).CrossRefGoogle Scholar
De Jong, K.A., Evolutionary Computation: A Unified Approach (MIT Press, Cambridge, MA, 2006).Google Scholar
Koza, J.R., Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, MA, 1992).Google Scholar
McKay, R.I., Hoai, N.X., Whigham, P.A., Shan, Y., O’Neill, M., Genet. Program. Evolvable Mach. 11, 365 (2010).CrossRefGoogle Scholar
Ryan, C., Collins, J.J., Neill, M.O., “Grammatical Evolution: Evolving Programs for an Arbitrary Language,” Eur. Conf. Genet. Program. (Springer, 1998), pp. 83–96.CrossRefGoogle Scholar
Miller, J., Ed., Cartesian Genetic Programming (Springer, Heidelberg, Germany, 2011).CrossRefGoogle Scholar
Poli, R., Langdon, W.B., McPhee, N.F., Koza, J.R., A Field Guide to Genetic Programming (Lulu Press, Morrisville, NC, 2008).Google Scholar
Sette, S., Boullart, L., Eng. Appl. Artif. Intell. 14, 727 (2001).CrossRefGoogle Scholar
Gunaratnam, D.J., Degroff, T., Gero, J.S., Appl. Soft Comput. 2, 283 (2003).CrossRefGoogle Scholar
Jamadar, I.M., Vakharia, D.P., Measurement 94, 177 (2016).CrossRefGoogle Scholar
Angeline, P.J., Kinnear, K.E., “On Using Syntactic Constraints with Genetic Programming,” in Advances in Genetic Programming (MIT Press, Cambridge, MA, 1996), https://ieeexplore.ieee.org/document/6277529 (accessed March 23, 2019).Google Scholar
Ratle, A., Sebag, M., Appl. Soft Comput. 1, 105 (2001).CrossRefGoogle Scholar
Ryan, C., O’Neill, M., Collins, J., Eds., Handbook of Grammatical Evolution (Springer International Publishing, Cham, Switzerland, 2018).CrossRefGoogle Scholar
Gandomi, A.H., Alavi, A.H., Ryan, C., Eds., Handbook of Genetic Programming Applications (Springer International Publishing, Cham, 2015).CrossRefGoogle Scholar
Sastry, K., Johnson, D.D., Goldberg, D.E., Bellon, P., Phys. Rev. B 72, 085438 (2005).CrossRefGoogle Scholar
Sastry, K., Johnson, D.D., Goldberg, D.E., Bellon, P., Int. J. Multiscale Comput. Eng. 2, 239 (2004).CrossRefGoogle Scholar
Padilla, H.A., Harnish, S.F., Gore, B.E., Beaudoin, A.J., Dantzig, J.A., Robertson, I.M., Weiland, H., “High Temperature Deformation and Hot Rolling of AA7055,” Metallurgical Modeling for Aluminum Alloys, Proc. Mater. Solutions Conf. 2001: 1st Int. Symp. Metall. Model. Alum. Alloys, Tiryakioglu, M., Lalli, L.A., Eds. (ASM International, Materials Park, OH, 2003), pp. 1–8.Google Scholar
Behler, J., J. Chem. Phys. 145, 170901 (2016).CrossRefGoogle ScholarPubMed
Li, W., Ando, Y., Minamitani, E., Watanabe, S., J. Chem. Phys. 147, 214106 (2017).CrossRefGoogle Scholar
Natarajan, S.K., Behler, J., Phys. Chem. Chem. Phys. 18, 28704 (2016).CrossRefGoogle Scholar
Wang, P., Shao, Y., Wang, H., Yang, W., Extreme Mech. Lett. 24, 1 (2018).CrossRefGoogle Scholar
Behler, J., Int. J. Quantum Chem. 115, 1032 (2015).CrossRefGoogle Scholar
Dolgirev, P.E., Kruglov, I.A., Oganov, A.R., AIP Adv . 6, 085318 (2016).CrossRefGoogle Scholar
Fracchia, F., Del Frate, G., Mancini, G., Rocchia, W., Barone, V., J. Chem. Theory Comput. 14, 255 (2017).CrossRefGoogle Scholar
Deringer, V.L., Csányi, G., Phys. Rev. B 95, 094203 (2017).CrossRefGoogle Scholar
Glielmo, A., Sollich, P., De Vita, A., Phys. Rev. B 95, 214302 (2017).CrossRefGoogle Scholar
Li, Z., Kermode, J.R., De Vita, A., Phys. Rev. Lett. 114, 096405 (2015).CrossRefGoogle Scholar
Brown, W.M., Thompson, A.P., Schultz, P.A., J. Chem. Phys. 132, 024108 (2010).CrossRefGoogle Scholar
Kenoufi, A., Kholmurodov, K.T., Biol. Chem. Res. 2, 1 (2015).Google Scholar
Makarov, D.E., Metiu, H., J. Chem. Phys. 108, 590 (1998).CrossRefGoogle Scholar
Slepoy, A., Peters, M.D., Thompson, A.P., J. Comput. Chem. 28, 2465 (2007).CrossRefGoogle Scholar
Hernandez, A., Balasubramanian, A., Yuan, F., Mason, S., Mueller, T., “Fast, Accurate, and Transferable Many-Body Interatomic Potentials by Genetic Programming,” submitted arXiv:1904.01095 (2019), http://arxiv.org/abs/1904.01095 (accessed April 10, 2019).Google Scholar
Javadi, A.A., Rezania, M., Adv. Eng. Inform. 23, 442 (2009).CrossRefGoogle Scholar
Faramarzi, A., Alani, A.M., Javadi, A.A., Comput. Struct. 137, 63 (2014).CrossRefGoogle Scholar
Gandomi, A.H., Sajedi, S., Kiani, B., Huang, Q., Autom. Constr. 70, 89 (2016).CrossRefGoogle Scholar
Gandomi, A.H., Alavi, A.H., Neural Comput. Appl. 21, 171 (2012).CrossRefGoogle Scholar
Versino, D., Tonda, A., Bronkhorst, C.A., Comput. Methods Appl. Mech. Eng. 318, 981 (2017).CrossRefGoogle Scholar
Preston, D.L., Tonks, D.L., Wallace, D.C., J. Appl. Phys. 93, 211 (2003).CrossRefGoogle Scholar
Follansbee, P.S., Kocks, U.F., Acta Metall . 36, 81 (1988).CrossRefGoogle Scholar