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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...

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Multi-level data fusion of laser-induced breakdown spectroscopy and X-ray fluorescence for arsenic determination in pelletized Pteris vittata tissues.

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Related Experiment Video

Updated: Jun 1, 2026

Integrated Field Lysimetry and Porewater Sampling for Evaluation of Chemical Mobility in Soils and Established Vegetation
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A multi-view linearly constrained tabular prior-data fitted network (MLC-TabPFN) model for arsenic quantification in

Liuye Cao1, Jing Huang2, Lei Feng1

  • 1State Key Laboratory for Vegetation Structure, Function and Construction (VegLab), College of Biosystems Engineering and Food Science, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, China.

Journal of Hazardous Materials
|February 19, 2026
PubMed
Summary

This study introduces a novel multi-view linearly constrained tabular prior-data fitted network (MLC-TabPFN) for precise arsenic quantification in plants using Laser-Induced Breakdown Spectroscopy (LIBS). The advanced model significantly improves accuracy for phytoremediation evaluation.

Keywords:
ArsenicLaser-induced breakdown spectroscopy (LIBS)Multi-viewPteris vittataTabular prior-data fitted network (TabPFN)

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Area of Science:

  • Analytical Chemistry
  • Environmental Science
  • Biotechnology

Background:

  • Accurate arsenic (As) quantification in hyperaccumulator plants like Pteris vittata is crucial for assessing phytoremediation efficiency.
  • Laser-Induced Breakdown Spectroscopy (LIBS) offers rapid analysis but faces challenges with biological matrix effects and conventional chemometric models.
  • Existing methods struggle to achieve high precision due to complex sample compositions.

Purpose of the Study:

  • To develop a novel, high-precision quantitative model for arsenic detection in Pteris vittata using LIBS.
  • To overcome the limitations of traditional chemometric approaches in complex biological matrices.
  • To integrate data-driven learning with knowledge-driven principles for enhanced analytical performance.

Main Methods:

  • Development and application of the multi-view linearly constrained tabular prior-data fitted network (MLC-TabPFN) model.
  • Integration of a linear constraint (LC) module to incorporate physical priors (positive correlation between spectral intensity and concentration).
  • Implementation of a multi-view fusion module to combine original and derivative spectra (first and second order).

Main Results:

  • The baseline TabPFN model outperformed PLSR with a higher prediction coefficient of determination (R²p = 0.956 vs 0.933).
  • The LC module reduced mean absolute percentage error (MAPEp) from 8.537% to 7.641% (R²p = 0.971).
  • The final MLC-TabPFN model achieved a superior R²p of 0.981, with RMSEp of 40.189 mg/kg and MAPEp of 6.249%.

Conclusions:

  • The proposed MLC-TabPFN framework offers a superior solution for high-precision LIBS analysis of arsenic in complex biological matrices.
  • The synergistic combination of advanced machine learning and physical domain knowledge significantly enhances analytical accuracy.
  • This approach validates the potential for improved phytoremediation efficacy assessment through precise elemental quantification.