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：本文提出一种基于固定深度符号回归与无表达式树符号微分的二维对流-扩散方程求解新方法。该方法应用于具有不同初始条件与边界条件的两种案例，验证了其精确性及高效获得近似解的能力。该框架为微分方程近似求解提供了具有前景的可扩展方案，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应用方面具有改进潜力。