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Data-driven discovery of formulas by symbolic regression

  • Sheng Sun (a1), Runhai Ouyang (a2), Bochao Zhang (a3) and Tong-Yi Zhang (a4)


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.



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1.Goldstein, E.B., Coco, G., Front. Environ. Sci. 3, 1 (2015).
2.Langley, P., “Rediscovering Physics with BACON.3,” Proc. 6th Int. Jt. Conf. Artif. Intell.—Vol. 1 (Morgan Kaufmann Publishers, 1979), pp. 505507,
3.Schmidt, M., Lipson, H., Science 324, 81 (2009).
4.Schaeffer, H., McCalla, S.G., Phys. Rev. E 96, 023302 (2017).
5.Rudy, S.H., Brunton, S.L., Proctor, J.L., Kutz, J.N., Sci. Adv. 3, e1602614 (2017).
6.Ghiringhelli, L.M., Vybiral, J., Ahmetcik, E., Ouyang, R., Levchenko, S.V., Draxl, C., Scheffler, M., New J. Phys. 19, 023017 (2017).
7.Ouyang, R., Curtarolo, S., Ahmetcik, E., Scheffler, M., Ghiringhelli, L.M., Phys. Rev. Mater. 2, 083802 (2018).
8.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).
9.Agrawal, A., Choudhary, A., APL Mater . 4, 053208 (2016).
10.Wang, Y., Wagner, N., Rondinelli, J.M., “Symbolic Regression in Materials Science,” submitted arXiv:1901.04136 (2019), (accessed March 26, 2019).
11.Praks, P., Brkić, D., Water 10, 1175 (2018).
12.Goldstein, E.B., Coco, G., Murray, A.B., Green, M.O., Earth Surf. Dyn. 2, 67 (2014).
13.Hinchliffe, M.P., Willis, M.J., Comput. Chem. Eng. 27, 1841 (2003).
14.Ly, D.L., Lipson, H., J. Mach. Learn. Res. 13, 3585 (2012).
15.Cornforth, T.W., Lipson, H., Genet. Program. Evolvable Mach. 14, 155 (2013).
16.Gout, J., Quade, M., Shafi, K., Niven, R.K., Abel, M., Nonlinear Dyn . 91, 1001 (2018).
17.Quade, M., Abel, M., Shafi, K., Niven, R.K., Noack, B.R., Phys. Rev. E 94, 012214 (2016).
18.De Jong, K.A., Evolutionary Computation: A Unified Approach (MIT Press, Cambridge, MA, 2006).
19.Koza, J.R., Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, MA, 1992).
20.McKay, R.I., Hoai, N.X., Whigham, P.A., Shan, Y., O’Neill, M., Genet. Program. Evolvable Mach. 11, 365 (2010).
21.Ryan, C., Collins, J.J., Neill, M.O., “Grammatical Evolution: Evolving Programs for an Arbitrary Language,” Eur. Conf. Genet. Program. (Springer, 1998), pp. 8396.
22.Miller, J., Ed., Cartesian Genetic Programming (Springer, Heidelberg, Germany, 2011).
23.Poli, R., Langdon, W.B., McPhee, N.F., Koza, J.R., A Field Guide to Genetic Programming (Lulu Press, Morrisville, NC, 2008).
24.Sette, S., Boullart, L., Eng. Appl. Artif. Intell. 14, 727 (2001).
25.Gunaratnam, D.J., Degroff, T., Gero, J.S., Appl. Soft Comput. 2, 283 (2003).
26.Jamadar, I.M., Vakharia, D.P., Measurement 94, 177 (2016).
27.Angeline, P.J., Kinnear, K.E., “On Using Syntactic Constraints with Genetic Programming,” in Advances in Genetic Programming (MIT Press, Cambridge, MA, 1996), (accessed March 23, 2019).
28.Ratle, A., Sebag, M., Appl. Soft Comput. 1, 105 (2001).
29.Ryan, C., O’Neill, M., Collins, J., Eds., Handbook of Grammatical Evolution (Springer International Publishing, Cham, Switzerland, 2018).
30.Gandomi, A.H., Alavi, A.H., Ryan, C., Eds., Handbook of Genetic Programming Applications (Springer International Publishing, Cham, 2015).
31.Sastry, K., Johnson, D.D., Goldberg, D.E., Bellon, P., Phys. Rev. B 72, 085438 (2005).
32.Sastry, K., Johnson, D.D., Goldberg, D.E., Bellon, P., Int. J. Multiscale Comput. Eng. 2, 239 (2004).
33.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. 18.
34.Behler, J., J. Chem. Phys. 145, 170901 (2016).
35.Li, W., Ando, Y., Minamitani, E., Watanabe, S., J. Chem. Phys. 147, 214106 (2017).
36.Natarajan, S.K., Behler, J., Phys. Chem. Chem. Phys. 18, 28704 (2016).
37.Wang, P., Shao, Y., Wang, H., Yang, W., Extreme Mech. Lett. 24, 1 (2018).
38.Behler, J., Int. J. Quantum Chem. 115, 1032 (2015).
39.Dolgirev, P.E., Kruglov, I.A., Oganov, A.R., AIP Adv . 6, 085318 (2016).
40.Fracchia, F., Del Frate, G., Mancini, G., Rocchia, W., Barone, V., J. Chem. Theory Comput. 14, 255 (2017).
41.Deringer, V.L., Csányi, G., Phys. Rev. B 95, 094203 (2017).
42.Glielmo, A., Sollich, P., De Vita, A., Phys. Rev. B 95, 214302 (2017).
43.Li, Z., Kermode, J.R., De Vita, A., Phys. Rev. Lett. 114, 096405 (2015).
44.Brown, W.M., Thompson, A.P., Schultz, P.A., J. Chem. Phys. 132, 024108 (2010).
45.Kenoufi, A., Kholmurodov, K.T., Biol. Chem. Res. 2, 1 (2015).
46.Makarov, D.E., Metiu, H., J. Chem. Phys. 108, 590 (1998).
47.Slepoy, A., Peters, M.D., Thompson, A.P., J. Comput. Chem. 28, 2465 (2007).
48.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), (accessed April 10, 2019).
49.Javadi, A.A., Rezania, M., Adv. Eng. Inform. 23, 442 (2009).
50.Faramarzi, A., Alani, A.M., Javadi, A.A., Comput. Struct. 137, 63 (2014).
51.Gandomi, A.H., Sajedi, S., Kiani, B., Huang, Q., Autom. Constr. 70, 89 (2016).
52.Gandomi, A.H., Alavi, A.H., Neural Comput. Appl. 21, 171 (2012).
53.Versino, D., Tonda, A., Bronkhorst, C.A., Comput. Methods Appl. Mech. Eng. 318, 981 (2017).
54.Preston, D.L., Tonks, D.L., Wallace, D.C., J. Appl. Phys. 93, 211 (2003).
55.Follansbee, P.S., Kocks, U.F., Acta Metall . 36, 81 (1988).



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