Modeling the quantitative relationship between target components and measured spectral information is an essential part of laser-induced breakdown spectroscopy (LIBS) analysis. However, many traditional multivariate analysis algorithms must reduce the spectral dimension or extract the characteristic spectral lines in advance, which may result in information loss and reduced accuracy. Indeed, improving the precision and interpretability of LIBS quantitative analysis is a critical challenge in Mars exploration. To solve this problem, this paper proposes an end-to-end lightweight quantitative modeling framework based on ensemble convolutional neural networks (ECNNs). This method eliminates the need for dimensionality reduction of the raw spectrum along with other pre-processing operations. We used the ChemCam calibration dataset as an example to verify the effectiveness of the proposed approach. Compared with partial least squares regression (a linear method) and extreme learning machine (a nonlinear method), our proposed method resulted in a lower root-mean-square error for major element prediction (54% and 73% lower, respectively) and was more stable. We also delved into the internal learning mechanism of the deep CNN model to understand how it hierarchically extracts spectral information features. The experimental results demonstrate that the easy-to-use ECNN-based regression model achieves excellent prediction performance while maintaining interpretability.

With the increase in the number of types of spectrometers in use, calibration models cannot be shared among different instruments; however, this problem can be solved via calibration transfer (CT). In this study, a variety of modern process analysis technology (PAT) data are taken as the research object. After preprocessing the spectra data using principal component analysis (PCA) and cubic spline interpolation, the TrAdaBoost algorithm in transfer learning combined with extreme learning machine (ELM), i.e., TrAdaBoost-ELM, is used to transfer the master model to slave instruments and to make comparisons with the transfer via an extreme learning machine auto-encoder method (TEAM) and the semisupervised parameter-free framework for calibration enhancement (SS-PFCE) method. After the master model is transferred by the TrAdaBoost-ELM algorithm for the prediction dataset of slave instruments, the mean coefficient of determination of prediction ( $R_{\mathrm {p}}^{2}$ ) increases from 0.7843 to 0.8707, and the mean root-mean-square error of prediction (RMSEP) decreases from 2.7508 to 2.3112. Furthermore, variable combination population analysis (VCPA) in combination with a genetic algorithm (VCPA-IGA) was used to select characteristic wavelengths in molecular and atomic spectra, respectively. For the same type of laser-induced breakdown spectroscopy (LIBS) instruments K1 and K2, after processing by the VCPA-IGA algorithm, the LIBS calibration model established on K1 was transferred successfully to K2, and for the major elements, the mean $R_{\mathrm {p}}^{2}$ = 0.9563 and the mean RMSEP = 1.3796. After processing by the VCPA algorithm, the near-infrared (NIR) model for instrument L was transferred to a different instrument J, and the prediction results were $R_{\mathrm {p}}^{2}$ = 0.9110 and RMSEP = 0.4044 °Brix. The results demonstrated that an appropriate variable selection method combined with the TrAdaBoost-ELM algorithm can be effectively used for CT for spectrometers of the same and different types, thus achieving model sharing between different spectrometers.

Laser-induced breakdown spectroscopy (LIBS) is a useful tool for the in situ detection of material components on Mars. This technique can directly acquire key information, such as the types and abundance of elements in the surface rocks and soil of Mars, with submillimeter spatial precision. Because the LIBS signal is prone to interference from the sample matrix and self-absorption effects, as well as other factors, the accuracy of its qualitative and quantitative analyses can be diminished without proper treatment. High-resolution LIBS generates hundreds or thousands of variables, causing low efficiency or high probability of overfitting in wavelength selection algorithms. Chemometric methods can be used to overcome the effects of these factors, extract useful information from the complex spectral data, and establish more robust analytical models. In this paper, model population analysis (MPA) combined with a range of variable selection methods is used to analyze the standard ground samples of the ChemCam team quantitatively. The analytical performance of LIBS is improved by optimizing and improving the algorithms. The results show that the two-step hybrid modeling method based on MPA has excellent prediction performance. Compared with other single or hybrid models, our method enables extensive use of the strengths of the models used and compensates for their weaknesses when handling high-dimensional datasets. The model established in this paper may contribute to the quantitative analysis of LIBS spectral data in future Mars exploration missions.