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We investigate the use of machine learning for solving analytic problems intheoretical physics. In particular, symbolic regression is making rapidprogress in recent years as a tool to fit data using functions whose overallform is not known in advance. Assuming that we have a mathematical problem thatis posed analytically, e.g. through equations, but allows easy numericalevaluation of the solution for any given set of input variable values, one cangenerate data numerically and then use symbolic regression to identify theclosed-form function that describes the data, assuming that such a functionexists. In addition to providing a concise way to represent the solution of theproblem, such an obtained function can play a key role in providing insight andallow us to find an intuitive explanation for the studied phenomenon. We use astate-of-the-art symbolic regression package to demonstrate how an exactsolution can be found and make an attempt at solving an unsolved physicsproblem. We use the Landau-Zener problem and a few of its generalizations asexamples to motivate our approach and illustrate how the calculations becomeincreasingly complicated with increasing problem difficulty. Our resultshighlight the capabilities and limitations of the presently available symbolicregression packages, and they point to possible modifications of these packagesto make them better suited for the purpose of finding exact solutions asopposed to good approximations. Our results also demonstrate the potential formachine learning to tackle analytically posed problems in theoretical physics.

Using machine learning to find exact analytic solutions to analytically posed physics problems