Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The main advantage of asymptotic approach involves the robust approximation to the sought for solution bringing a clear idea of the effect of problem parameters. However, the analytic derivation of the asymptotic series is often highly nontrivial especially, when the exact solution is not available. In this paper, we adapt SR methodology to discover asymptotic series. As an illustration we consider three problem in mechanics, including two-mass collision, viscoelastic behavior of a Kelvin-Voigt solid and propagation of Rayleigh-Lamb waves. The training data is generated from the explicit exact solutions of these problems. The obtained SR results are compared to the benchmark asymptotic expansions of the above mentioned exact solutions. Both convergent and divergent asymptotic series are considered. A good agreement between SR expansions and analytical results is observed. It is demonstrated that the proposed approach can be used to identify material parameters, e.g. Poisson's ratio, and has high prospects for utilizing experimental and numerical data.

翻译：最近，符号回归（SR）已展现出其在发现物理系统基本控制关系方面的有效性。通过将符号回归与渐近方法相结合，可望产生重大影响。渐近方法的主要优势在于对所求解进行稳健逼近，从而清晰揭示问题参数的影响。然而，当精确解不可用时，渐近级数的解析推导往往极具挑战性。本文采用符号回归方法学来发现渐近级数。为验证这一方法，我们考虑了力学中的三个问题，包括双质量碰撞、开尔文-沃伊特固体的粘弹性行为以及瑞利-兰姆波的传播。训练数据由这些问题的显式精确解生成。将符号回归所得结果与上述精确解的基准渐近展开进行比较，其中考虑了收敛和发散两种渐近级数。观察到符号回归展开与解析结果具有良好一致性。研究表明，该方法可用于识别材料参数（如泊松比），并在利用实验和数值数据方面具有广阔前景。