A machine learning method for the discovery of analytic solutions to differential equations is assessed. The method utilizes an inherently interpretable machine learning algorithm, genetic programming-based symbolic regression. An advantage of its interpretability is the output of symbolic expressions that can be used to assess error in algebraic terms, as opposed to purely numerical quantities. Therefore, models output by the developed method are verified by assessing its ability to recover known analytic solutions for two differential equations, as opposed to assessing numerical error. To demonstrate its improvement, the developed method is compared to a conventional, purely data-driven genetic programming-based symbolic regression algorithm. The reliability of successful evolution of the true solution, or an algebraic equivalent, is demonstrated.

评估了一种用于发现微分方程解析解的机器学习方法。该方法利用本质上可解释的机器学习算法，即基于遗传编程的符号回归。其可解释性的一个优点是输出符号表达式，可用于评估代数项中的错误，而不是纯粹的数值量。因此，通过评估其恢复两个微分方程的已知解析解的能力来验证所开发的方法输出的模型，而不是评估数值误差。为了证明其改进，将所开发的方法与传统的、纯粹数据驱动的基于遗传编程的符号回归算法进行了比较。证明了真实解或代数等价物成功演化的可靠性。