Beyond Beer‐Lambert Linear Regression: Multi‐Layer Modeling for Wide‐Range Concentration Quantification Using Ultraviolet‐visible Spectroscopy

ABSTRACT Ultraviolet–visible (UV‐Vis) spectroscopy is widely used for chemical quantification due to its simplicity and low cost; however, accurate concentration prediction becomes challenging when target concentrations span wide ranges, where the global linearity assumption of the Beer‐Lambert law often breaks down. To address this limitation, we propose a multi‐layer modeling framework that exploits local linearity rather than relying on a single global model. Two approaches, dynamical‐layer regression and classified‐layer regression, are both integrated with principal component regression and partial least squares. The framework is evaluated using UV‐Vis spectra of nickel sulfate and cobalt sulfate solutions across concentrations ranging from 10 − 6 to 0.9 mol L − 1 , as well as mixed‐solution scenarios. The proposed methods consistently outperform conventional single‐layer linear models and global nonlinear models, achieving up to a 50% reduction in root mean squared error and R 2 values exceeding 0.99 for single‐solute datasets. These results demonstrate that the proposed framework provides a robust and effective solution for wide‐range concentration prediction in spectroscopic analysis.