Abstract

I became interested in attempting to predict temperatures in the state of Georgia way back in the day, i.e., the date was November 1 – 4, 2009. I found a neat website for the temperatures from January 1895 to December 2001. Unfortunately, the website no longer exists online, however, I saved the data to an extinct PC of mine and a USB solid state drive. I used two methods to attempt predictions of the annual temperatures from January 2002 to December 2025. The first algorithm is polynomial least squares curve fitting [1]. The second method is a radial basis function neural network [2] [3] that is trained by an evolutionary hill-climber of my design and implementation [4] [5]. The applications were written in one of my favorite computer programming languages, namely, C# [6].

Methodologies

I created a polynomial least squares dynamic-link library (DLL) using Gaussian elimination with pivoting and an inverse matrix calculation utilizing an upper-triangular matrix [7]. At first the driver application was capable of fitting a 1-degree to 100-degrees polynomial. I found that my algorithm was only valid for a 1-degree to 76-degrees fitting polynomial. I used degrees: 1, 4, 8, 16, 32, 64, and 76.

Predicted Statewide Georgia Annual Average Temperatures in Degrees Fahrenheit
Poly Degree	1	4	8	16	32	64	76	Model
Year	T (F)	T (F)	T (F)	T (F)	T (F)	T (F)	T (F)	Average
2002	64.2	63.1	63.8	63.6	62.4	63.0	62.9	63.3
2003	64.2	63.2	63.6	63.4	64.1	63.7	63.7	63.7
2004	64.2	63.3	63.4	63.4	64.5	63.9	64.0	63.8
2005	64.2	63.3	63.4	63.5	64.2	63.9	64.0	63.8
2006	64.2	63.4	63.4	63.6	63.8	63.7	63.8	63.7
2007	64.2	63.5	63.4	63.7	63.3	63.6	63.6	63.6
2008	64.2	63.6	63.4	63.7	63.0	63.4	63.4	63.5
2009	64.2	63.6	63.4	63.7	62.9	63.3	63.3	63.5
2010	64.1	63.7	63.5	63.7	62.9	63.3	63.2	63.5
2011	64.1	63.8	63.6	63.6	63.1	63.3	63.2	63.5
2012	64.1	63.8	63.7	63.6	63.3	63.4	63.3	63.6
2013	64.1	63.9	63.7	63.6	63.6	63.5	63.5	63.7
2014	64.1	63.9	63.8	63.6	63.9	63.6	63.6	63.8
2015	64.1	64.0	63.9	63.6	64.1	63.8	63.8	63.9
2016	64.1	64.0	63.9	63.6	64.3	63.9	63.9	64.0
2017	64.1	64.1	64.0	63.7	64.4	64.0	64.1	64.1
2018	64.1	64.1	64.1	63.7	64.4	64.1	64.2	64.1
2019	64.1	64.2	64.1	63.9	64.4	64.2	64.2	64.2
2020	64.1	64.2	64.2	64.0	64.3	64.3	64.3	64.2
2021	64.1	64.3	64.2	64.1	64.2	64.3	64.3	64.2
2022	64.1	64.3	64.2	64.2	64.2	64.3	64.3	64.2
2023	64.1	64.3	64.3	64.3	64.1	64.3	64.3	64.2
2024	64.0	64.4	64.3	64.5	64.0	64.3	64.3	64.3
2025	64.0	64.4	64.3	64.6	64.0	64.3	64.3	64.3

The second method was a radial basis function neural network that was trained by an evolutionary hill-climber of my design and implementation. I used 8, 16, 32, 64 basis functions. The population of the hill-climber was 16 and generations 262,144.

Predicted Statewide Georgia Annual Average Temperatures in Degrees Fahrenheit
Basis	8	16	32	64	Model
Year	T (F)	T (F)	T (F)	T (F)	Average
2002	65.4	64.2	65.4	65.2	65.1
2003	65.5	64.2	65.4	65.2	65.1
2004	65.5	64.2	65.5	65.3	65.1
2005	65.5	64.2	65.5	65.3	65.1
2006	65.6	64.2	65.5	65.3	65.2
2007	65.6	64.2	65.6	65.3	65.2
2008	65.6	64.2	65.6	65.4	65.2
2009	65.7	64.2	65.6	65.4	65.2
2010	65.7	64.2	65.6	65.4	65.2
2011	65.7	64.2	65.7	65.4	65.3
2012	65.7	64.2	65.7	65.5	65.3
2013	65.8	64.2	65.7	65.5	65.3
2014	65.8	64.2	65.8	65.5	65.3
2015	65.8	64.3	65.8	65.5	65.4
2016	65.9	64.3	65.8	65.6	65.4
2017	65.9	64.3	65.8	65.6	65.4
2018	65.9	64.3	65.9	65.6	65.4
2019	66.0	64.3	65.9	65.6	65.5
2020	66.0	64.3	65.9	65.7	65.5
2021	66.0	64.3	66.0	65.7	65.5
2022	66.0	64.3	66.0	65.7	65.5
2023	66.1	64.3	66.0	65.7	65.5
2024	66.1	64.3	66.1	65.8	65.6
2025	66.1	64.3	66.1	65.8	65.6

I trust the polynomial fitting results more than the radial basis function neural network values. The polynomial fitting had mean square errors < 1 whereas the radial basis function neural network had mean square errors between 1 and 9. The general trends were increasing temperatures which are in line with the theorized global warming.

References

[1]	H. T. Lau, A Numerical Library in C for Scientists and Engineers, Boca Raton: CRC Press, 1995.
[2]	T. M. Mitchell, Machine Learning, Boston: WCB McGraw-Hill, 1997.
[3]	A. P. Engelbrecht, Computational Intelligence An Introduction, Hoboken: John Wiley and Sons, 2002.
[4]	Z. Michalewicz, Genetic Algorithms + Data Structures = Evolutionary Programs 3rd Edition, Berlin: Springer, 1999.
[5]	D. B. Fogel, Evolutionary Computation Toward a New Philosophy of Machine Intelligence, Piscataway: IEEE Press, 2000.
[6]	C. Petzold, Programming Windows with C#, Redmond: Microsoft Press, 2002.
[7]	S. D. Conte and C. d. Boor, Elementary Numerical An Algorithmic Approach, New York: McGraw-Hill Book Company, 1980.