Multigrid Training for Molecular Generation using Graph Neural Networks

Deep learning has demonstrated significant success for modeling biochemical molecular systems, where inputs are commonly represented as graphs or 3D grids. A major challenge is that computational cost scales with resolution, making full graph/grid computation of molecular densities expensive and often unstable. We introduce a multigrid training strategy that leverages low-resolution optimization to accelerate learning at higher resolution through parameter transfer across discretizations. For graph molecular representations, we progressively transfer parameters learned from a coarse graph to a sequence of increasingly finer graphs via biased random walk upsampling. For 3D molecular generation, we voxelize the molecular structures at multiple resolutions, pretrain a coarse-resolution conditional Variational Autoencoder (CVAE), and initialize a fine-resolution CVAE by transferring shape compatible convolutional parameters from the coarse model. Numerical experiments on receptor-conditioned 3D Ligand generation show that multigrid training accelerates convergence and improves generalization compared to training from scratch.