Addressing the challenge that traditional isotherm models struggle to reliably describe the competitive adsorption of Cu(II)/Pb(II) mixed ions in formed composite adsorbents,this study constructs a batch adsorption experimental matrix for sodium alginate–biochar composite materials and proposes a Physically Constrained Competitive Adsorption Graph Attention Network (PI-CGAT) to predict and interpret the adsorption capacity, removal efficiency, equilibrium concentration, and Pb(II)/Cu(II) selectivity coefficient in the Cu(II)/Pb(II) binary system.The experimental matrix covers pH 3.0–6.0, contact times of 5–360 min, temperatures of 288–318 K, initial metal ion concentrations of 20–200 mg/L, adsorbent dosages of 0.5–2.0 g/L, and SA/BC mass ratios of 1:1–3:1.PI-CGAT adsorbed Cu(II), Pb(II),carboxyl, hydroxyl, and C–O sites; Ca-crosslinked sodium alginate sites; the mesoporous region of biochar; the aromatic carbon region; mineral ash sites; and pH-regulated surface charge as heterogeneous graph nodes, and represented complexation, ion exchange, pore-associated adsorption, mineral binding, and Cu/Pb competition as edge relationships.At pH 5.5, C₀,Cu = C₀,Pb = 100 mg/L,a dosage of 1.0 g/L, and a contact time of 240 min, the equilibrium adsorption capacities of SA–BC 2:1 for Cu(II) and Pb(II) were 58.27 ± 1.61 mg/g and 88.76 ± 2.22 mg/g, respectively, corresponding to removal efficiencies of 58.27% and 88.76%.In the stoichiometric binary system, the Pb(II)/Cu(II) selectivity coefficient reached 5.63.Model testing results show that the PI-CGAT model has prediction R² values of 0.947 and 0.958 for q_Cu and q_Pb, respectively, with RMSEs of 4.86 mg/g and 5.54 mg/g. Ablation results indicate that removing competing edges increases the overall RMSE by 45.29%, while removing physical constraints increases the overall RMSE by 22.79%.Attention weights show that at pH 5.5, the weights of Pb(II) for the –COOH and Ca-crosslinked sites were 0.36 and 0.22, respectively, while the weight of Cu(II) for the mesopore domain rose to 0.20.The results indicate that PI-CGAT can characterize Cu(II)/Pb(II) site competition while maintaining the physical boundaries of adsorption, providing an interpretable simulation tool for the structural design of composite adsorbents and the optimization of treatment conditions for mixed heavy metal wastewater.
