MADField: Multi-fidelity Amortized Density Field for Adsorption in Nanoporous Materials

High-throughput computational screening of nanoporous materials for gas storage and separation requires fast and accurate characterization of adsorption equilibrium. Particle-based grand canonical Monte Carlo (GCMC) and density-based classical density functional theory (cDFT) provide simulation-based estimates of gas uptake and adsorbate density fields, but their accuracy--speed tradeoff remains insufficient for large-scale screening. In this work, we address this gap with Multi-fidelity Amortized Density Field (MADField) that reframes adsorption prediction as equilibrium density-field estimation. MADField exploits density supervision from complementary fidelity levels: cDFT provides broad, scalable density supervision, while particle-sampling GCMC provides higher-fidelity density labels after coarse graining. To enable this, we generate and release a large-scale cDFT adsorption dataset spanning thousands of MOF frameworks and nine adsorbates. We first train a density predictor on cDFT labels, use its predictions to initialize previously failed cDFT calculations and expand the cDFT label set, and then fine-tune the model on GCMC-derived density fields. Across a comprehensive benchmark spanning multiple adsorbates and material classes, MADField improves uptake accuracy over the strongest baselines by 6.0$\times$ and 15.4$\times$ for cDFT and GCMC approximation, respectively. Its predicted density fields also accelerate cDFT solvers, reducing number of solver steps by 2.0$\times$ and recovering $42\%$ failures of standard cDFT. We will release the underlying cDFT benchmark dataset of 280{,}000 calculations, generated with 3,600 H200 GPU hours, to support future work.