Adaptive Neural Stabilization of Ill-Posed Spectral Problems

The article develops a mathematical model of adaptive neural regularization and creates an algorithmic method for its implementation with a neural network for dynamic determination of the regularization parameter. The developed ANR model combines classical variational stabilization methods with neural network prediction of the regularization parameter and eliminates the key limitation of traditional Tikhonov regularization, associated with the need to manually select the smoothing coefficient, which makes the solution unstable in the case of variable noise conditions and spectral correlation. The ANR neural network subsystem analyzes the statistical features of the spectrum and adaptively selects the optimal α, ensuring a natural balance between reconstruction accuracy and solution smoothness. Numerical experiments demonstrate that adaptive neural-guided regularization provides a reduction in the root mean square error of reconstruction. For a baseline noise level of 2%, RMSE=0.11 mM, while at a noise level of 10%, it increased to 0.32 mM. It is shown that the use of neural-guided regularization allows reducing the reconstruction error by 20–40% compared to the classical Tikhonov regularization. The model retains its versatility and can be integrated into a wide range of spectroscopic methods, from analytical spectrophotometry to optical materials diagnostics. The work outlines prospects for further development, in particular, the extension of ANR to multichannel and hyperspectral systems and the application of physically informed neural networks to solve more complex inverse problems.