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

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.