Symbolic Regression

A method of systematically generating algebraic equations from data, with potential applications in discovering equations and even laws. The result, so far, has been quite promising, but no "laws" have been discovered, as yet.

Timeline of papers

Genetic algorithm paper by Koza (1994)

Schmidt and Lipson (2009). Note this paper has been criticized for not citing the literature (Crutchfield et al. 1987 and 1998).

SISSO (Luca's group) and subsequent applications in material science.

AI Feynmann from Tegmark.

Recommended

Crutchfield, J. P. (1987). Equations of Motion from a Data Series. Complex Systems, 1, 417–452.

Crutchfield, J. P., & Young, K. (1989). Inferring statistical complexity. Physical Review Letters, 63(2), 105–108.

Koza, J. R. (1994). Genetic programming as a means for programming computers by natural selection. Statistics and Computing, 4(2), 87–112.

Schmidt, M., & Lipson, H. (2009). Distilling Free-Form Natural Laws from Experimental Data. Science, 324(5923), 81–85.

Ouyang, R., Curtarolo, S., Ahmetcik, E., Scheffler, M., & Ghiringhelli, L. M. (2018). SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates. Physical Review Materials, 2(8), 083802.

Ouyang, R., Ahmetcik, E., Carbogno, C., Scheffler, M., & Ghiringhelli, L. M. (2019). Simultaneous learning of several materials properties from incomplete databases with multi-task SISSO. Journal of Physics: Materials, 2(2), 024002.

Udrescu, S.-M., & Tegmark, M. (2020). AI Feynman: A Physics-Inspired Method for Symbolic Regression arXiv:1905.11481.

Dutta, A., Vreeken, J., Ghiringhelli, L. M., & Bereau, T. (2021). Data-driven equation for drug–membrane permeability across drugs and membranes. The Journal of Chemical Physics, 154(24), 244114. https://doi.org/10.1063/5.0053931

Yes, that's me. :P

Purcell, T. A. R., Scheffler, M., Carbogno, C., & Ghiringhelli, L. M. (2022). SISSO++: A C++ Implementation of the Sure-Independence Screening and Sparsifying Operator Approach. Journal of Open Source Software, 7(71), 3960.