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Solving the 2D Advection-Diffusion Equation using Fixed-Depth Symbolic Regression and Symbolic Differentiation without Expression Trees

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arxiv 2411.00011 v2 pith:ZM53DO3N submitted 2024-10-18 stat.CO cs.LGcs.NAmath.NA

Solving the 2D Advection-Diffusion Equation using Fixed-Depth Symbolic Regression and Symbolic Differentiation without Expression Trees

Edward Finkelstein This is my paper
classification stat.CO cs.LGcs.NAmath.NA
keywords symbolicadvection-diffusionapproximatedifferentiationequationexpressionfixed-depthmethod
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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