<p>The chlorine dioxide–iodine–malonic acid (CDIMA) reaction governed by the Lengyel–Epstein equations is a canonical reaction–diffusion system known for generating rich Turing patterns and oscillatory behavior. This study implements RBFNNs to analyze and predict the spatiotemporal dynamics of the CDIMA reaction. The coupled nonlinear partial differential equations describe the evolution between iodide <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\left( {I^{ - } } \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <msup> <mi>I</mi> <mo>-</mo> </msup> </mfenced> </math></EquationSource> </InlineEquation> and chlorite ion <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\left( {ClO_{2}^{ - } } \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mrow> <mi>C</mi> <mi>l</mi> <msubsup> <mi>O</mi> <mrow> <mn>2</mn> </mrow> <mo>-</mo> </msubsup> </mrow> </mfenced> </math></EquationSource> </InlineEquation> concentrations whose interactions drive the emergence of spatial patterns. Radial basis function neural networks (RBFNNs) are employed to approximate these complex nonlinear processes which offers a data-driven approach to modeling both reaction kinetics and diffusion. RBFNN successfully learns to reproduce concentration profiles and capture pattern formation under varying reaction rates and diffusion coefficients. This method reduces computational cost while providing insights into parameter settings where analytical solutions are intractable. The accuracy of network is assessed through regression analysis across training, validation, testing, and overall datasets with the correlation coefficient R measuring agreement between predicted and true values. <i>R</i>-value of 1 represents a perfect correlation between predictions and targets demonstrating the ideal performance of the model. This study highlights the potential of RBFNN as a powerful tool for studying complex chemical systems bridging the gap between theoretical models and experimental observations in nonlinear dynamics.</p>

Computational analysis of the Lengyel–Epstein system for the chlorite–iodide–malonic acid reaction using radial basis function neural network

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发表日期：

2026年2月14日

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Nek Muhammad Katbar,
Shengjun Liu,
Hongjuan Liu,
Maher Alwuthaynani

摘要

The chlorine dioxide–iodine–malonic acid (CDIMA) reaction governed by the Lengyel–Epstein equations is a canonical reaction–diffusion system known for generating rich Turing patterns and oscillatory behavior. This study implements RBFNNs to analyze and predict the spatiotemporal dynamics of the CDIMA reaction. The coupled nonlinear partial differential equations describe the evolution between iodide $\left( {I^{ - } } \right)$ $(I^{-})$ and chlorite ion $\left( {ClO_{2}^{ - } } \right)$ $(C l O_{2}^{-})$ concentrations whose interactions drive the emergence of spatial patterns. Radial basis function neural networks (RBFNNs) are employed to approximate these complex nonlinear processes which offers a data-driven approach to modeling both reaction kinetics and diffusion. RBFNN successfully learns to reproduce concentration profiles and capture pattern formation under varying reaction rates and diffusion coefficients. This method reduces computational cost while providing insights into parameter settings where analytical solutions are intractable. The accuracy of network is assessed through regression analysis across training, validation, testing, and overall datasets with the correlation coefficient R measuring agreement between predicted and true values. R-value of 1 represents a perfect correlation between predictions and targets demonstrating the ideal performance of the model. This study highlights the potential of RBFNN as a powerful tool for studying complex chemical systems bridging the gap between theoretical models and experimental observations in nonlinear dynamics.