Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Neural P$^3$M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs

Yusong Wang, Chaoran Cheng, Shaoning Li, Yuxuan Ren, Bin Shao, Ge Liu, Pheng-Ann Heng, Nanning Zheng

TL;DR

Neural P$^3$M, a versatile enhancer of geometric GNNs to expand the scope of their capabilities by incorporating mesh points alongside atoms and reimaging traditional mathematical operations in a trainable manner, exhibits flexibility across a wide range of molecular systems.

Abstract

Geometric graph neural networks (GNNs) have emerged as powerful tools for modeling molecular geometry. However, they encounter limitations in effectively capturing long-range interactions in large molecular systems. To address this challenge, we introduce Neural P$^3$M, a versatile enhancer of geometric GNNs to expand the scope of their capabilities by incorporating mesh points alongside atoms and reimaging traditional mathematical operations in a trainable manner. Neural P$^3$M exhibits flexibility across a wide range of molecular systems and demonstrates remarkable accuracy in predicting energies and forces, outperforming on benchmarks such as the MD22 dataset. It also achieves an average improvement of 22% on the OE62 dataset while integrating with various architectures.

Neural P$^3$M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs

TL;DR

Neural PM, a versatile enhancer of geometric GNNs to expand the scope of their capabilities by incorporating mesh points alongside atoms and reimaging traditional mathematical operations in a trainable manner, exhibits flexibility across a wide range of molecular systems.

Abstract

Geometric graph neural networks (GNNs) have emerged as powerful tools for modeling molecular geometry. However, they encounter limitations in effectively capturing long-range interactions in large molecular systems. To address this challenge, we introduce Neural PM, a versatile enhancer of geometric GNNs to expand the scope of their capabilities by incorporating mesh points alongside atoms and reimaging traditional mathematical operations in a trainable manner. Neural PM exhibits flexibility across a wide range of molecular systems and demonstrates remarkable accuracy in predicting energies and forces, outperforming on benchmarks such as the MD22 dataset. It also achieves an average improvement of 22% on the OE62 dataset while integrating with various architectures.
Paper Structure (39 sections, 52 equations, 4 figures, 4 tables)

This paper contains 39 sections, 52 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Ewald Summation
  4. Meshing up the Ewald Summation
  5. Method
  6. Mesh Construction
  7. Embedding Block
  8. Neural P$^3$M Block
  9. Short-Range Block
  10. Long-Range Block
  11. Representation Assignment
  12. Decoder Block
  13. Experiment
  14. Experimental Setup
  15. Toy Dataset: Ag
  16. ...and 24 more sections

Figures (4)

  • Figure 1: Illustration of Particle–Particle Particle-Mesh (P$^3$M) and its relationship with our Neural P$^3$M framework. The Atom2Atom block corresponds to the short-range term. The Atom2Mesh and Mesh2Atom block are similar to the charge assignment and back-interpolation. The Mesh2Mesh block corresponds to the long-range term.
  • Figure 2: Overall framework architecture and details of each block. Geometric GNN models short-range interactions, Fourier neural operator (FNO) captures global long-range interactions, and continuous filter convolution (CFConv) exchanges information between two parts.
  • Figure 3: Mean absolute errors (MAEs) for energy and force predictions on Ag dataset are compared among Allegro, ViSNet, and our proposed framework.
  • Figure 4: The relationship between the number of meshes and forward time (a) as well as energy MAE (b).