p-GIN: a graph isomorphism network based on p-laplacian operator to enhance molecular property prediction

Accurately predicting molecular properties is crucial in chemistry and materials science, as it facilitates faster discovery, minimizes experimental costs, and guides rational molecular design. While traditional quantum chemistry approaches remain widely adopted, they often demand significant computational resources. Recently, Graph Neural Networks (GNNs) have gained attention as effective tools for molecular property prediction. Nevertheless, many GNN methods rely on conventional aggregation mechanisms for node feature updates, which may be too limited to capture the intricate and nonlinear dependencies within molecular graphs. To address this shortcoming, we propose p-GIN, an enhanced variant of the Graph Isomorphism Network that introduces a new update mechanism. Instead of using the standard message-passing framework, p-GIN integrates a trainable multilayer perceptron (MLP) with nonlinear p-Laplacian diffusion. This design enables the model to control feature smoothing adaptively, represent both fine-grained and sharp structural variations, and produce richer molecular embeddings. We assess the effectiveness of p-GIN on the QM9 dataset for four key molecular properties: dipole moment, isotropic polarizability, HOMO-LUMO gap, and zero-point vibrational energy (ZPVE). The results demonstrate that our model consistently surpasses widely used baselines in terms of mean absolute error, mean squared error, and relative error. Additionally, we examine two dropout-based variants, p-GIN(0.25) and p-GIN(0.5), corresponding to dropout probabilities of 25% and 50%, to study the influence of regularization. The main innovation of our work lies in coupling p-Laplacian diffusion with a learnable MLP transformation, providing a more accurate and computationally efficient approach to molecular property prediction.