Prediction of supercritical CO2 solubility with a thermodynamics-conditioned equivariant graph neural network model

Supercritical CO 2 (scCO 2 ) is a green alternative to organic solvents and the working fluid of supercritical fluid extraction (SFE), used in analytical sample preparation and natural-product isolation. Its wider adoption is limited by the difficulty of predicting analyte solubility: experimental determination at supercritical conditions is tedious, requires specialized equipment, and yields values that vary by up to two orders of magnitude across laboratories. Existing predictive models either rely on substance-specific fitted parameters or trade mechanistic transparency for accuracy. We present an interpretable graph-neural-network framework that couples the equivariant Polarizable Atom Interaction Neural Network (PaiNN) with Feature-wise Linear Modulation (FiLM), integrating global thermodynamic descriptors (temperature, pressure, density, evaporation enthalpy, critical point) into a three-dimensional structure-aware model. It was trained on 27,461 solubility measurements across 958 organic molecules curated from Makarov et al., 2025. Five-fold cross-validation gave a coefficient of determination of 0.767 and a median absolute error of 0.36 in log₁₀-solubility (nested 10-fold cross-validation: R² = 0.770, 0.332). The final predictor averages the outputs of the five fold models. To examine whether the model’s reasoning is chemically plausible, we adapted a walk-based GNN layer-wise relevance propagation explainer to the FiLM architecture and added structural ablation. Atom-rank consistency across folds (ρ = 0.72), plausible element rankings (O, N > C, H), and trends with molecular weight, polar surface area and acetylation show that predictions are consistent with physically meaningful patterns. The ready-to-use model enables in silico SFE screening and reduces organic-solvent use in sample preparation.