This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and boundary conditions, demonstrating its accuracy and ability to find approximate solutions efficiently. This framework offers a promising, scalable solution for finding approximate solutions to differential equations, with the potential for future improvements in computational performance and applicability to more complex systems involving vector-valued objectives.

翻译：本文提出了一种利用固定深度符号回归和无表达式树符号微分求解二维对流扩散方程的新方法。该方法应用于两种具有不同初始条件和边界条件的案例，验证了其精确性与高效获取近似解的能力。该框架为微分方程近似求解提供了一种具有前景且可扩展的解决方案，未来在计算性能提升及面向涉及向量值目标的更复杂系统适用性方面具有改进潜力。