用固定深度符号回归求解二维对流扩散方程，无需表达式树。
Solving the 2D Advection-Diffusion Equation using Fixed-Depth Symbolic Regression and Symbolic Differentiation without Expression Trees
- 固定深度符号回归结合符号微分，不依赖表达式树。
- 在两种不同初始/边界条件下均高效获得近似解。
- 适合需要快速求解微分方程的科研与工程场景。
本文提出一种新方法，通过固定深度符号回归与无表达式树的符号微分求解二维对流扩散方程。该方法应用于两个具有不同初始条件和边界条件的案例，验证了其在准确性与求解效率方面的优势。该框架为寻找微分方程的近似解提供了有前景且可扩展的解决方案，未来有望在计算性能和处理更复杂向量目标系统方面进一步提升。
原文摘要 · Abstract (English)
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.
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