document: An algorithm combining neural networks with fundamental parameters An algorithm combining neural networks with the fundamental parameters equations -LRB- NNFP -RRB- is proposed for making corrections for non-linear matrix effects in x-ray fluorescence analysis . In the algorithm , neural networks were applied to relate the concentrations of components to both the measured intensities and the relative theoretical intensities calculated by the fundamental parameter equations . The NNFP algorithm is compared with the classical theoretical correction models , including the fundamental parameters approach , the Lachance-Traill model , a hyperbolic function model and the COLA algorithm . For an alloy system with 15 measured elements , in most cases , the prediction errors of the NNFP algorithm are lower than those of the fundamental parameters approach , the Lachance-Traill model , the hyperbolic function model and the COLA algorithm separately . If there are the serious matrix effects , such as matrix effects among Cr , Fe and Ni , the NNFP algorithm generally decreased predictive errors as compared with the classical models , except for the case of Cr by the fundamental parameters approach . The main reason why the NNFP algorithm has generally a better predictive ability than the classical theoretical correction models might be that neural networks can better calibrate the non-linear matrix effects in a complex multivariate system
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