Cross-geometry pretraining for equivariant neural networks: Improving molecular property prediction under computational constraints

Abstract

Neural operators have revolutionized parametric partial differential equation solving by learning mappings between infinite-dimensional function spaces with unprecedented parameter space generalization. Despite recent advances in physics-informed neural networks and operator learning methods, the challenge of geometry transfer between molecular systems remains a critical bottleneck in computational physics. We present a computationally efficient approach to cross-domain foundation models for electrostatics that demonstrates that biological and electronic structure problems share learnable physics representations. Using two equivariant graph neural network architectures, the E(n)-equivariant graph neural network (EGNN) and the polarizable atom interaction neural network (PaiNN), we implement cross-geometry and cross-physics pretraining strategies within severe computational constraints of a single graphics processing unit (GPU) and less than 100 GPU-hours. Our methodology achieves strong transfer learning performance across diverse molecular geometries while maintaining compatibility with existing datasets, including QM9 and MD17. The results suggest that shared electrostatic representations can be learned across domains even under resource limitations, advancing the development of foundation models for computational physics applications. We provide complete code for dataset downloading and model training to facilitate reproducibility.