Genetic Programming Based Symbolic Regression for Analytical Solutions
to Differential Equations
- URL: http://arxiv.org/abs/2302.03175v1
- Date: Tue, 7 Feb 2023 00:23:07 GMT
- Title: Genetic Programming Based Symbolic Regression for Analytical Solutions
to Differential Equations
- Authors: Hongsup Oh, Roman Amici, Geoffrey Bomarito, Shandian Zhe, Robert
Kirby, Jacob Hochhalter
- Abstract summary: We present a machine learning method for the discovery of analytic solutions to differential equations.
We demonstrate the ability to recover true analytic solutions, as opposed to a numerical approximation.
- Score: 8.669375104787806
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we present a machine learning method for the discovery of
analytic solutions to differential equations. The method utilizes an inherently
interpretable algorithm, genetic programming based symbolic regression. Unlike
conventional accuracy measures in machine learning we demonstrate the ability
to recover true analytic solutions, as opposed to a numerical approximation.
The method is verified by assessing its ability to recover known analytic
solutions for two separate differential equations. The developed method is
compared to a conventional, purely data-driven genetic programming based
symbolic regression algorithm. The reliability of successful evolution of the
true solution, or an algebraic equivalent, is demonstrated.
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