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Neural P$^3$M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs
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Proposes Neural P^3M, a mesh-based enhancer that adds trainable mesh points and FFT-based Fourier neural operator long-range blocks to geometric GNNs, exchanging information with atoms via atom-mesh assignment.
Problem
Geometric GNNs have localized receptive fields and struggle to capture long-range interactions in large molecules and periodic systems.
Approach
Reimagines the particle-particle particle-mesh (P^3M) Ewald-style decomposition in a trainable way: short-range atom blocks from any geometric GNN are paired with a Fourier neural operator on a mesh, and CFConv-style atom-mesh assignment exchanges information between the two scales.
Key results
- On MD22, ViSNet-NP3M improves over vanilla ViSNet by an average of 34.6% in energy and 21.2% in force MAE, reaching state-of-the-art on the four largest molecules.
- On OE62, Neural P3M gives an average 22% energy MAE improvement across SchNet, PaiNN, DimeNet++, and GemNet-T, outperforming Ewald MP.
- On the Ag toy dataset, single-layer ViSNet with Neural P3M significantly improves energy and force accuracy over vanilla ViSNet and Allegro.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add Neural P³M to ViSNet | ViSNet · MD22 | energy MAE: average improvement of 34.6% | Helped |
| add Neural P³M to ViSNet | ViSNet · MD22 | forces MAE: average improvement of 21.2% | Mixed |
| add Neural P³M to geometric GNNs | SchNet, PaiNN, DimeNet++, GemNet-T · OE62 | energy MAE: average improvement of 22% | Helped |
| increase the number of mesh points (ablation) | Neural P³M with SchNet · OE62 | energy MAE | Hurt |
Surprising findings
- Increasing the number of mesh points degrades energy MAE while increasing forward time, which the authors attribute to atoms being assigned to multiple mesh points.
- Neural P3M is slower than Ewald MP for DimeNet++ in forward and backward passes, despite theoretical FFT efficiency.
Limitations
- Does not thoroughly investigate the number of mesh points.
- Does not explore alternatives to FFT for modeling long-range interactions.
- Computational overhead relative to baseline geometric GNNs (e.g., Neural P3M forward time up to ~185% higher on OE62 SchNet).
Experimental setup
Datasets: Ag MD22 OE62
Benchmarks: Ag MD22 OE62
Metrics: MAE energy MAE forces relative improvement runtime ms/struct
Baselines: ViSNet LSRM Allegro Ewald MP sGDML SO3KRATES Equiformer MACE SchNet-LR PaiNN DimeNet++ GemNet-T
Builds on: Ewald summation P3M Fourier neural operator SchNet ViSNet
Closest papers by meaning
- Neural Atoms: Propagating Long-range Interaction in Molecular Graphs through Efficient Communication Channel (ICLR 2024 · similarity 0.90)
- Pushing the Limits of All-Atom Geometric Graph Neural Networks: Pre-Training, Scaling, and Zero-Shot Transfer (ICLR 2025 · similarity 0.89)
- RISE: Radius of Influence based Subgraph Extraction for 3D Molecular Graph Explanation (ICML 2025 · similarity 0.89)
- Long-Short-Range Message-Passing: A Physics-Informed Framework to Capture Non-Local Interaction for Scalable Molecular Dynamics Simulation (ICLR 2024 · similarity 0.86)
- Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning (ICML 2024 · similarity 0.86)
- Empowering Active Learning for 3D Molecular Graphs with Geometric Graph Isomorphism (NeurIPS 2024 · similarity 0.86)
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