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PreprintCC BYChemRxiv

Small-data pH-resolved kernel modelling of flotation collectors

  • Linfeng Xu1,2,3
  • Jiaxin Nie4,5
  • Yuxin Li1,2
  • Yuting Chen1,2
  • Jianyong He1,2,3,6
  • Li Wang7,8
  • Yijun Cao3,2,4,5
8 affiliations
  1. 1State Key Laboratory of Critical Metals Beneficiation, Metallurgy and Purification
  2. 2Zhengzhou University
  3. 3School of Chemical Engineering
  4. 4School of Materials Science and Engineering
  5. 5Zhongyuan Critical Metals Laboratory, Zhengzhou University
  6. 6Zhongyuan Purification Manufacturing Process Laboratory
  7. 7School of Minerals Processing and Bioengineering
  8. 8Central South University
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Abstract

Small, heterogeneous datasets are common in chemometrics, yet their predictive ceiling is rarely quantified. We assembled 19 flotation collectors from 15 literature sources (116 pH-resolved recovery points) and asked how much of the label, curve maximum and full pH curve can be predicted from molecular descriptors. The model combines DFT, Mordred and local descriptors in an additive molecule/pH kernel with a target branch for the label and maximum and a shape branch for the normalized curve. Whole-molecule leave-one-out gave label R2=0.821 (RMSE 7.79 pp), maximum R2=0.801 (8.07 pp) and full-curve R2=0.635 (19.59 pp). The pooled curve value is misleading: the per-molecule median R2 was 0.138 and the minimum −114.9, and correcting the M04/M13 structures did not rescue these failures. A post hoc source-group test (pooled R2=0.549) and six held-out congeners (R2=0.110; MAE 26.7 pp) further limited the claim. The model can rank training-like collectors, but it cannot certify a new molecule, a new source or a full curve. The study shows why pooled R2 and random splits are insufficient for small chemometric datasets, and provides a benchmark and validation protocol for more honest claims.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026smalldata,
  title = {{Small-data pH-resolved kernel modelling of flotation collectors}},
  author = {Linfeng Xu and Jiaxin Nie and Yuxin Li and Yuting Chen and Jianyong He and Li Wang and Yijun Cao},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15011157/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15011157/v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Small-data pH-resolved kernel modelling of flotation collectors
AU  - Linfeng Xu
AU  - Jiaxin Nie
AU  - Yuxin Li
AU  - Yuting Chen
AU  - Jianyong He
AU  - Li Wang
AU  - Yijun Cao
PY  - 2026
DA  - 2026/10/27
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15011157/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15011157/v1
AB  - Small, heterogeneous datasets are common in chemometrics, yet their predictive ceiling is rarely quantified. We assembled 19 flotation collectors from 15 literature sources (116 pH-resolved recovery points) and asked how much of the label, curve maximum and full pH curve can be predicted from molecular descriptors. The model combines DFT, Mordred and local descriptors in an additive molecule/pH kernel with a target branch for the label and maximum and a shape branch for the normalized curve. Whole-molecule leave-one-out gave label R2=0.821 (RMSE 7.79 pp), maximum R2=0.801 (8.07 pp) and full-curve R2=0.635 (19.59 pp). The pooled curve value is misleading: the per-molecule median R2 was 0.138 and the minimum −114.9, and correcting the M04/M13 structures did not rescue these failures. A post hoc source-group test (pooled R2=0.549) and six held-out congeners (R2=0.110; MAE 26.7 pp) further limited the claim. The model can rank training-like collectors, but it cannot certify a new molecule, a new source or a full curve. The study shows why pooled R2 and random splits are insufficient for small chemometric datasets, and provides a benchmark and validation protocol for more honest claims.
ER  -