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

TL;DR

This paper introduces a new approach combining fixed-depth symbolic regression and symbolic differentiation, avoiding expression trees, to efficiently approximate solutions to the 2D advection-diffusion equation with promising accuracy and scalability.

Contribution

It proposes a novel method that eliminates the need for expression trees in symbolic regression for solving PDEs, enhancing scalability and efficiency.

Findings

Accurately solves 2D advection-diffusion equations with different conditions

Demonstrates efficiency and scalability of the method

Potential for application to more complex systems

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.