The necessity of physics-informed neural networks for adsorption-based water treatment machine learning models: A case study of biochar adsorption.

Authors

Yi Fang, Yuming Wen, Yuming Zhang, Shu Zhang, Siming You, Wangliang Li

Published in

Water research. Volume 309. Issue Pt A. Pages 127101. Oct 13, 2026. Epub Oct 13, 2026.

Abstract

Machine learning (ML) models for adsorption can achieve high accuracy under random train-test splits, but this does not establish physical admissibility or transferability to unseen adsorption systems (held-out chemicals, water matrices, or adsorbent fingerprints). Using 3,756 biochar adsorption data points, we compared three tree-ensemble regressors, Gaussian process regression, FT-Transformer, SoftPINN, and HardPINN. All 7 models were assessed using a leakage-controlled random split, whereas group-wise validation was performed only for RF, XGBoost, CatBoost, and HardPINN using leave-one-chemical-out, leave-one-water-matrix-out, and leave-one-adsorbent-fingerprint-out protocols. CatBoost achieved the highest interpolation accuracy (R²=0.9488), but unconstrained models and SoftPINN produced predictions that violated mass-balance bounds. HardPINN adapted an established constrained-output parameterization to the sample-specific adsorption bound, eliminating prediction-level mass-balance violations while retaining competitive accuracy (R²=0.9286). For the four group-wise evaluated models, transfer was relatively stable across water matrices and partial across chemical identities, whereas all four yielded negative median R² values for held-out adsorbent fingerprints (descriptor combinations excluded from training). These results indicate poor transfer to held-out adsorbent fingerprints for the four tested models, without implying corresponding behavior for GPR, FT-Transformer, or SoftPINN. The observed failure under joint distribution shift was consistent with incomplete, mechanism-relevant material descriptors, although material-level and source-level effects could not be separated. This biochar case study integrates an adsorption-specific, sample-dependent feasible output range with assessments of prediction error, physical admissibility and out-of-distribution transfer. Broader applicability to other adsorbent classes remains a hypothesis requiring class-specific external validation.

PMID:
42913235
Bibliographic data and abstract were imported from PubMed on 24 Oct 2026.

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