UDC 519.688:535.3:517.958

Y.Y. Bilak
State University “Uzhhorod National University,” Uzhhorod, Ukraine,
 yuriy.bilak@uzhnu.edu.ua

A.M. Reblian
State University “Uzhhorod National University,” Uzhhorod, Ukraine,
 antonina.reblian@uzhnu.edu.ua

PARAMETRIC SYNTHESIS IN SPECTROSCOPY BASED
ON SPECTRAL SENSITIVITY ANALYSIS

Анотація. The relevance of this study is determined by the fundamental role of inverse problems in parametric synthesis within spectroscopy, which are widely applied in optics, materials science, laser diagnostics, and related fields for reconstructing the physical parameters of media based on their spectral characteristics. In practice, such problems are often ill-posed or weakly identifiable due to limited spectral range, parameter correlations, and non-uniform spectral sensitivity, which leads to instability in classical error-minimization methods and degradation of estimation accuracy. Therefore, the development of methods that combine physics-based modeling with machine learning techniques while accounting for the informational structure of spectral data is highly relevant. The aim of this work is to develop and numerically validate a concept of parametric synthesis in inverse spectroscopic problems based on physics-enhanced neural networks, explicitly accounting for the spectral identifiability of parameters. The study employs mathematical modeling of spectral characteristics, sensitivity analysis, linear algebra, estimation theory (Fisher information matrix, Cramr–Rao bound), and physics-informed neural network architectures. Parametric synthesis is formulated as a learning problem projected onto a parameter subspace for which the information matrix is non-degenerate, ensuring consistency of the neural network solution with the physical structure of the forward problem. Numerical experiments demonstrate that the loss of spectral parameter identifiability is clearly manifested in spectral sensitivity functions, the eigenvalue spectrum of the Fisher information matrix, and the variance of parameter estimates. It is shown that using a constrained or regularized parametric space in physics-enhanced neural networks eliminates learning instability in degenerate cases and improves the physical interpretability of the obtained estimates. The practical significance of this work lies in providing a foundation for developing robust neural network methods for solving inverse spectroscopic problems, oriented toward the actual informational structure of spectral data.

Keywords: spectral sensitivity, parametric synthesis, spectral identifiability, inverse spectral problems, Fisher matrix, information estimability, ill-posed problems, neural network parameter synthesis.

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