The present study aimed to use artificial intelligence to obtain a mathematical model to approximate the exact solution for linear and nonlinear ordinary differential equations with initial conditions arising in physics and engineering. To this end, genetic programming has been implemented, along with its combination with the Runge–Kutta fourth order method (RK4). Regarding formulation, the produced mathematical models by this new hybrid method (GPN) are flexible (in terms of functions used in the model structure and the number of them) and have acceptable accuracy compared to other existing traditional powerful methods now in use. Numerical experiments have been adequately conducted to indicate the sufficient accuracy and productive power of GPN to generate human-competitive results.

本研究旨在利用人工智能获得数学模型，以逼近物理和工程中出现的具有初始条件的线性和非线性常微分方程的精确解。为此，已经实施了遗传编程，以及它与 Runge-Kutta 四阶方法 (RK4) 的结合。在公式方面，与目前使用的其他现有传统强大方法相比，这种新的混合方法 (GPN) 生成的数学模型是灵活的（在模型结构中使用的函数和它们的数量方面）并且具有可接受的精度。已经充分进行了数值实验，表明 GPN 具有足够的准确性和生产能力，可以产生具有人类竞争力的结果。