**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31584

##### Estimating Reaction Rate Constants with Neural Networks

**Authors:**
Benedek Kovacs,
Janos Toth

**Abstract:**

Solutions are proposed for the central problem of estimating the reaction rate coefficients in homogeneous kinetics. The first is based upon the fact that the right hand side of a kinetic differential equation is linear in the rate constants, whereas the second one uses the technique of neural networks. This second one is discussed deeply and its advantages, disadvantages and conditions of applicability are analyzed in the mirror of the first one. Numerical analysis carried out on practical models using simulated data, and our programs written in Mathematica.

**Keywords:**
Neural networks,
parameter estimation,
linear regression,
kinetic models,
reaction rate coefficients.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334686

**References:**

[1] J. S. Almeida, E. O. Voit, “Neural-Network-Based Parameter Estimation in S-System Models of Biological Networks". Genome Information. vol. 14, 2003. pp 114-123.

[2] Y. Bard, “Nonlinear Parameter Estimation" New York, Academic Press, 1974.

[3] S.M. Blower and H. Downlatabadi, “Sensitivity and Uncertainity Anlysis of Complex Models of Desease Transmission: an HIV Model, as an Example", International Statistical Review, vol. 62, no. 2, pp 29-243, 1994.

[4] C. Brochot, J. Toth, F. Y. Bois, “Lumping in pharmacokinetics", Journal of pharmokinetics and Pharmodynamics vol. 32 no. 5-6, pp 719-736, Dec. 2005.

[5] F. C. Christo, A. R. Masri, E. M. Nebot, “Utilising artificial neural network and repro-modelling in turbulent combustion", Proceedings of the IEEE International Conference on Neural Networks, Perth, 27th November-1st December 1995, vol. 1, pp 911-916, 1995.

[6] M. Grindal, J. Offutt and S. F. Andler, “Combination Testing Strategies: A Survey", GMU Technical Report ISE-TR-04-05, vol. 15, no. 3, July 2004, pp 167-199.

[7] K. M. Hangos, J. T'oth, “Maximum likelihood estimation of reaction-rate constants", Computers and Chemical Engineering, vol. 12, pp. 135-139, 1998.

[8] K. M. Hanson, “Halftoning and Quasi-Monte Carlo", Los Alamos National Library, pp. 430-442, 2005.

[9] K. Kovacs, B. Vizvari, M. Riedel, J. Toth, “Decomposition of the permanganate/oxalic acid overall reaction to elementary steps based on integer programming theory", Physical Chemistry, Chemical Physics, vol. 6, 1236-1242, 2004.

[10] A. Liaqat, M. Fukuhara, T. Takeda, “Optimal estimation of parameters of dynamical systems by neural network collocation method", Computer Physics Communications, vol. 150, pp 215-234, 2003.

[11] M. T. Manry, S. J. Apollo, Y. Qiang, “Minimum mean square estimation and neural networks", Neurocomputing, vol. 13, pp 59-74, 1996.

[12] I. Nagy, Gy. P'ota, J. T'oth, “Detailed balanced and unbalanced triangle reactions", Journal of Chemical Education, submitted for publication

[13] C. R. Rao, Linear Statistical Inference and Its Applications, John Wiley & Sons, Inc.: New York, London, Sydney, 1965.

[14] T. Smith, Y.-S. Lin, L. Mezzetti, F. Y. Bois, K. Kelsey, J. Ibrahim, “Genetic and dietary factors affecting human metabolism of 1,3-butadiene", Chemico-Biological Interactions, vol. 132, no. 0, pp 407-428, 2001.

[15] A. S. Tomlin, T. Tur'anyi, M. J. Pilling, “Mathematical tools for the construction, investigation and reduction of combustion mechanisms", in Low temperature combustion and autoignition, J. Peters, Ed. Amsterdam: Elsevier, 1997, pp 293-437.

[16] J. B. Witkoskie, D. J. Doren, “Neural Network Models of Potential Energy Surfaces: Prototypical Examples", Journal of Chemical Theory and Computation, vol. 1, pp 14-23, 2005.

[17] http://www.wolfram.com/