Predicting adsorption ability of adsorbents at arbitrary sites for pollutants using deep transfer learning

The study addresses the challenge of quantitatively predicting the adsorption ability of adsorbents toward heavy metal ions (HMIs) at arbitrary surface sites. Traditional experimental characterization cannot easily identify active sites and their activity intensities, and ab initio DFT calculations, while quantitative, are computationally expensive and limited for extensive configurational exploration. Machine learning has accelerated materials prediction but often requires large, task-specific datasets, making accurate prediction difficult when data are scarce. The authors propose using transfer learning (TL) within a deep neural network (DNN) framework to leverage knowledge learned from a large dataset (Pb(II)/g-C3N4) to related systems (Hg(II)/g-C3N4 and Cd(II)/g-C3N4), thereby reducing data requirements and computation time while maintaining high accuracy. The work uses two-dimensional g-C3N4 as a representative adsorbent due to its abundant active sites and large surface area, aiming to provide rapid, accurate, site-resolved adsorption predictions for multiple HMIs.

The introduction surveys: (1) applications of AI/ML in materials discovery and their benefits in accelerating research; (2) environmental urgency related to HMIs and organic pollutants; (3) prior development of high-performance adsorbents; (4) limitations of experimental detection of active sites and the computational expense of first-principles calculations for large configurational spaces; and (5) advances and challenges in ML for materials, including descriptor design and data scarcity leading to overfitting and reduced generalization. The authors highlight transfer learning’s successes in related scientific domains (e.g., materials property prediction and neural network potentials) and motivate its underexplored use in adsorption energy prediction to address small-data regimes while exploiting structural and chemical similarities across related adsorption systems.

Overall approach: Build a deep neural network potential energy surface (Deep Potential-Smooth Edition, DeepPot-SE) to predict single-point adsorption energies (ΔE) of HMIs on g-C3N4 at arbitrary surface positions. Train a source model on a large Pb(II)/g-C3N4 dataset (7000 DFT-calculated ΔE), then apply parameter-based transfer learning to fine-tune for Hg(II)/g-C3N4 and Cd(II)/g-C3N4 using only 700 ΔE per ion. Dataset generation: For Pb(II)/g-C3N4, 7000 single-point adsorption energies were computed by DFT by scanning Pb(II) positions over a parallelogram-shaped single-layer g-C3N4 surface; Pb(II) was placed randomly 100–300 pm above the surface. For Hg(II) and Cd(II), 700 ΔE each were computed similarly, with random placements 200–400 pm above the surface. Randomization used time-seeded C++ code to ensure diverse configurations. ΔE = E_sub+met − E_sub − E_met. DFT details: VASP with PAW potentials; PBE-GGA functional; DFT-D3 dispersion corrections; plane-wave cutoff 500 eV; Monkhorst–Pack k-point mesh 3×3×1; convergence thresholds 1×10−4 eV/atom (energy) and 0.01 eV/Å (forces); 15 Å vacuum for slab separation; isolated species and slab pre-optimized. Descriptors: Local Environment Matrix (LEM) capturing local radial and angular features in a symmetry-preserving local frame. A 10.0 Å neighbor cutoff with smoothing starting at 8.8 Å. LEM ensures translational, rotational, and permutational invariance and scalability. Neural network model and training: DeepPot-SE implemented in Python/C++ with TensorFlow. Architecture: three fully-connected hidden layers with 20 nodes each. Batch size 64; Adam optimizer. Learning rates: 0.002 for training from scratch (FS) and 0.001 for TL fine-tuning. For Pb(II), 6000/1000 train/test split; for Hg(II) and Cd(II), 600/100 train/test split. Loss monitored every 100 iterations. Parameter-based TL: initialize Hg/Cd models with pretrained Pb(II) model parameters, then fine-tune on small target datasets instead of random initialization. Performance assessment: Compare FS vs TL on Hg and Cd with identical small datasets, tracking RMSE over iterations to detect overfitting in FS and generalization improvements in TL. Build expanded Hg and Cd datasets (700 DFT + 6300 TL-predicted ΔE) to enable unbiased statistics comparable to Pb(II)’s 7000-point dataset. Experimental validation: Synthesize g-C3N4 by calcining urea (10 g, 550 °C, 3 h, 5 °C min−1). Characterize morphology (SEM) and structure (XRD with peaks at 13.2° and 27.6°). Measure adsorption from aqueous solutions of Cd(NO3)2, Hg(NO3)2, and Pb(NO3)2 at 100 and 200 mg L−1. Shake 24 h to equilibrium, centrifuge, quantify residual HMIs by ICP-OES (Optima 7300 DV). Compute adsorption amount qe = (Co − Ce)V/(M m).

- Accuracy and speed: The DNN achieved DFT-level accuracy while being millions of times faster per prediction. Transfer learning reduced required training data to one-tenth compared to training from scratch and is about ten times faster in the training stage. - Pb(II)/g-C3N4 (source model): Using 7000 DFT points (6000 train/1000 test), DNN achieved test RMSE 0.051 eV and R2 = 0.99; maximum deviation 0.133 eV. Energy landscape revealed stronger adsorption predominantly at central regions of the g-C3N4 lattice versus edges. - Hg(II)/g-C3N4 and Cd(II)/g-C3N4 (target models, 700 DFT points each): - Training from scratch (FS) with small data suffered overfitting and poor generalization: Hg test RMSE 0.423 eV (R2 = 0.79), Cd test RMSE 0.121 eV (R2 = 0.90); maximum errors >1 eV in FS. - Transfer learning (TL) yielded substantial improvements: Hg test RMSE 0.012 eV and R2 = 0.99; Cd test RMSE 0.043 eV and R2 = 0.99. Maximum deviations reduced to ~0.056 eV (Hg) and ~0.054 eV (Cd). - Comparative adsorption abilities (7000-point distributions; Pb: DFT 7000, Hg/Cd: 700 DFT + 6300 TL): - Energy ranges (ΔE, eV): Pb: −4.144 to −0.070; Hg: −2.136 to −0.139; Cd: −2.048 to −0.051. - Mean adsorption energies (eV): Pb −1.664, Hg −1.695, Cd −1.707. Standard deviations: Pb 0.585, Hg 0.355, Cd 0.318. Overall predicted adsorption ability ordering: Cd(II) > Hg(II) > Pb(II). - Experimental verification: Batch adsorption tests at 100 and 200 mg L−1 confirmed the same order of adsorption amounts (Cd > Hg > Pb) on g-C3N4, consistent with AI predictions. SEM/XRD confirmed porous, layered g-C3N4 structure with characteristic (100) and (002) reflections.

The study demonstrates that transfer learning can accurately predict adsorption energies at arbitrary sites on an adsorbent surface using small target datasets, provided a high-quality source model exists in a related domain. By leveraging structural and chemical similarities among Pb(II), Hg(II), and Cd(II) adsorption on the same g-C3N4 substrate, the TL models generalize well, overcoming overfitting and poor performance seen in small-data training from scratch. The resulting site-resolved energy landscapes enable a more comprehensive assessment of adsorption ability than single optimized adsorption configurations, revealing stronger adsorption in central regions of g-C3N4 and quantifying variability across sites. The combination of DFT-calibrated accuracy, major computational speedups, and drastically reduced data requirements provides a practical route for rapid pre-experimental screening of adsorbent–pollutant systems. The experimentally observed adsorption order validates the model’s predictions and underscores the approach’s reliability and relevance for environmental applications.

This work introduces an AI framework combining a symmetry-preserving deep neural network potential (DeepPot-SE) with transfer learning to predict adsorption energies of HMIs at arbitrary sites on g-C3N4. A source model trained on 7000 DFT-calculated Pb(II) adsorption energies enables highly accurate TL models for Hg(II) and Cd(II) using only 700 DFT points each, achieving RMSEs below 0.1 eV. Statistical analysis across 7000-point energy distributions for each ion indicates adsorption ability ordering Cd(II) > Hg(II) > Pb(II), corroborated by experimental adsorption measurements. The approach attains DFT-level accuracy with million-fold prediction speedups and an order-of-magnitude reduction in training data. The methodology is general and can be extended to other adsorbents and pollutants, and to related domains such as catalysis and batteries. Future work may explore broader adsorbent chemistries, additional contaminant classes (e.g., organics), more complex environments (solvation, competition), active site identification in defective/heterostructured materials, and robust domain adaptation across substrates.

- Transfer learning effectiveness depends on similarity between source and target domains; significant chemical or structural differences may reduce performance and require more target data or alternative adaptation strategies. - The study focuses on a single adsorbent (g-C3N4) and three divalent HMIs; generalization to other adsorbents, ion valences, or mixed-contaminant systems requires validation. - Adsorption energies are computed for single-point configurations on an idealized slab; effects of solvent dynamics, pH, ionic strength, competing species, surface defects/heterogeneity, and temperature are not explicitly modeled. - DFT functional choice (PBE-D3) and computational settings may influence absolute energies; while TL preserves DFT-level trends, systematic errors inherent to the reference method remain. - Experimental validation confirms relative ordering at two concentrations but does not provide site-resolved validation or kinetic/thermodynamic adsorption parameters (isotherms, rates).