Solving the 2D Advection-Diffusion Equation using Fixed-Depth Symbolic Regression and Symbolic Differentiation without Expression Trees
arXiv:2411.00011
Abstract
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.
12 pages, 22 equations. Improved results added. Figures removed for brevity. Typos corrected. The text was made more concise and up-to-date in some areas