DEVELOPMENT OF A HYBRID MODEL «PHYSICS-INFORMED AUTOENCODER WITH SPECTRAL CONSISTENCY»

Abstract

The subject matter of the article is the application of hybrid neural network models, constrained by physical laws, to inverse spectroscopic problems, particularly for the reconstruction of physicochemical parameters of materials from their spectral characteristics. The paper proposes a novel architecture – Physics-Informed Autoencoder with Spectral Consistency, which combines the capabilities of deep learning with prior physical knowledge, specifically the Bouguer–Lambert–Beer law for modeling absorption. The goal is to enhance the accuracy, robustness, and interpretability of models solving ill-posed inverse spectroscopic problems, especially under limited availability of experimental data and the presence of noise and spectral distortions. The tasks to be solved include: the development of a hybrid architecture that integrates a physical forward model and a neural residual correction block; the generation of synthetic spectra using physical modeling, spectral augmentation, and noise simulation; the implementation of active learning for the optimization of the training set; numerical optimization of the network configuration; and a comparative analysis with other architectures. The methods used are based on mathematical modeling of spectral responses, convolutional neural networks (CNN), autoencoders, weakly-supervised training, active learning, and performance metrics such as MSE and R². A series of numerical experiments were carried out on both synthetic mixtures and real spectral data of CuSO₄·5H₂O films deposited by photochemical laser irradiation. The results show that the proposed model accurately reconstructs component concentrations and film thicknesses even under noisy and non-ideal conditions. Conclusions. The scientific novelty of the results obtained is as follows: 1) for the first time, a hybrid neural network architecture was developed for approximating inverse spectroscopy problems, which combines the advantages of data-driven methods and physically based models in the form of a Physics-Informed Autoencoder, in which the physical forward model is integrated directly into the architecture and supplemented by an adaptive correction neural network; 2) the method for restoring physicochemical parameters of materials from spectral data was improved by combining physical modeling with neural network compensation of residual discrepancies; 3) a systematic comparison of hybrid physics-informed architectures was further developed, as a result of which the advantage of the developed model over other variations of the Physics-Informed Autoencoder, as well as over modern neural network methods based on CNN+LSTM and CNN+Transformer in terms of restoration accuracy and physical consistency of results, was shown; 4) the developed architecture provides high accuracy (R² ≈ 0.987), resistance to noise and overlapping spectral lines, as well as physical interpretability of the latent space, and active learning allowed to reduce the data volume by 40% without loss of accuracy.