cs.NEMar 10, 2026

GPU-Accelerated Genetic Programming for Symbolic Regression with Beagle Framework

Authors: Nathan Haut, Ilya Basin, Marzieh Kianinejad, Ruchika Gupta, Elijah Smith, Zachary Perrico, Wolfgang Banzhaf

Organizations: Michigan State University East Lansing, Michigan, USA · Noblis, Inc. Virginia, USA

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Abstract

Beagle is a new software framework that enables execution of Genetic Programming tasks on the GPU. Currently available for symbolic regression, it processes individuals of the population and fitness cases for training in a way that maximizes throughput on extant GPU platforms. In this contribution, we report on the benchmarking of Beagle on the Feynman Symbolic Regression dataset and compare its performance with a fast CPU system called StackGP and the widely available PySR system under the same wall clock budget. We also report on the use of two different fitness functions, one a point-to-point error function, the other a correlation fitness function. The results demonstrate that the Beagle's GPU-aided Symbolic Regression significantly outperforms leading CPU-based frameworks.

Figures & tables

ParameterSetting
Pt-Pt Pop Size5 mil. (gen <20) 1 mil. (gen >= 20)
Corr Pop Size5 mil. (gen < 5) 3 mil (gen < 10) 1 mil (gen < 15) 500k (gen < 20) 250k (gen >=20)
Operators+,−,∗,/,x2,x,1/x+,-,*,/,x^{2},\sqrt{x},1/x , cos,sin,tan,arccos,arcsincos,sin,tan,arccos,arcsin , arctanarctan , tanh,log,exptanh,log,exp
Selection StrategyMonte-Carlo-Inspired Rank Selection
Table 1. Listed are all the non-default parameters set for Beagle in this work.
ParameterSetting
Pop Size300
Tournament Size5
Elitism Rate10
Operators+,−,∗,/,x2,x,1/x+,-,*,/,x^{2},\sqrt{x},1/x , cos,sin,tan,arccos,arcsincos,sin,tan,arccos,arcsin , arctanarctan , tanh,log,exptanh,log,exp
Selection StrategyPareto Tournament
Table 2. Listed are all the non-default parameters set for StackGP in this work.
ParameterSetting
Model Selection"best"
Parallelism"multithreading"
Elitism Rate10
Operators+,−,∗,/,x2,x,1/x+,-,*,/,x^{2},\sqrt{x},1/x , cos,sin,tan,arccos,arcsincos,sin,tan,arccos,arcsin , arctanarctan , tanh,log,exptanh,log,exp
Table 3. Listed are all the non-default parameters set for PySR in this work.
SetupBeagle (pt-pt)Beagle (corr)StackGPPySR
Typical66826564
Best77898278
Table 4. Performance result of each setup in 10 minute runs. Total of typical and best performance reported for each setup across 10 runs. Numbers indicate the number of problems (out of 100) that were typically solved (typical) and solved at least once (best).
Figure 1. The 10 minute benchmarking performance of the different symbolic regression methods. The darker shaded regions indicate the typical performance ( >=50%>=50\% solved), whereas the lighter region indicates the number of problems solved at least once.
SetupBeagle (pt-pt)Beagle (corr)StackGPPySR
Typical74847072
Best80918386
Table 5. Performance result of each setup in 30 minute runs. Total of typical and best performance reported for each setup across 10 runs. Numbers indicate the number of problems (out of 100) that were typically solved (typical) and solved at least once (best).
Figure 2. The 30 minute benchmarking performance of the different symbolic regression methods. The darker shaded regions indicate the typical performance ( >=50%>=50\% solved), whereas the lighter region indicates the number of problems solved at least once.
EQ #Beagle (pt-pt)Beagle (Corr)StackGPPySR
1101091
201020
301000
401040
50000
610797
Table 6. The validation results of models developed in the 10 minute runs using each symbolic regression system. The numbers indicate the number of validated runs out of 10, except problem 7 where we increased to 20 runs to determine if typical performance was statistically significant.
EQ #Beagle (pt-pt)Beagle (Corr)StackGPPySR
11010103
201021
301001
4110101
50100
6107109
Table 7. The validation results of models developed in the 30 minute runs using each symbolic regression system. The numbers indicate the number of validated runs out of 10.

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