[論文レビュー] Directional Message Passing for Molecular Graphs

Johannes Gasteiger, Janek Groß+1 more|arXiv (Cornell University)|Mar 6, 2020

Computational Drug Discovery Methods被引用数 345

ひとこと要約

DimeNetは球対称フーリエ-Bessel基底を用いた方向的メッセージ伝播を導入し、原子間の距離と角度を符号化して、分子特性予測を最先端にし、MDのエネルギー保守的な力予測を滑らかに微分可能にする。

ABSTRACT

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

研究の動機と目的

• Incorporate directional information into GNNs to capture angular and torsional effects in molecules.
• Develop principled, orthogonal basis representations for distances and angles using spherical Bessel functions and spherical harmonics.
• Propose the DimeNet architecture to predict molecular properties and enable energy-conserving molecular dynamics simulations.

提案手法

• Embed messages as directional embeddings associated with atom pairs rather than atom centers.
• Represent distances with radial basis functions and angles with a 2D spherical Fourier-Bessel basis.
• Update and aggregate directional message embeddings in an analogy to belief propagation with angle- and distance-dependent interactions.
• Ensure rotational, translational, permutation, and inversion invariances; enable continuous differentiability for MD.

実験結果

リサーチクエスチョン

• RQ1 How can directional information (angles between neighbor directions) be integrated into GNNs for molecules?
• RQ2 Do spherical Bessel and spherical harmonics bases improve efficiency and accuracy for representing interatomic distances/angles?
• RQ3 Can a GNN with directional message passing set new state-of-the-art on QM9 and MD17 benchmarks?

主な発見

Target	Unit	PPGN	SchNet	PhysNet	MEGNet-s	Cormorant	DimeNet
µ	D	0.047	0.033	0.0529	0.05	0.13	0.0286
α	a03	0.131	0.235	0.0615	0.081	0.092	0.0469
ϵHOMO	meV	40.3	41	32.9	43	36	27.8
ϵLUMO	meV	32.7	34	24.7	44	36	19.7
Δϵ	meV	60.0	63	42.5	66	60	34.8
R2	a02	0.592	0.073	0.765	0.302	0.673	0.331
ZPVE	meV	3.12	1.7	1.39	1.43	1.98	1.29
U0	meV	36.8	14	8.15	12	28	8.02
U	meV	36.8	19	8.34	13	-	7.89
H	meV	36.3	14	8.42	12	-	8.11
G	meV	36.4	14	9.40	12	-	8.98
cv	cal	mol K	0.055	0.033	0.0280	0.029	0.031	0.0249
std. MAE	%	1.84	1.76	1.37	1.80	2.14	1.05
logMAE	-	-	−4.64	−5.17	−5.35	−5.17	−4.75	−5.57

• DimeNet outperforms prior GNNs by 76% on MD17 and 31% on QM9 on average.
• Using spherical Bessel basis representations reduces parameter count while improving performance compared to Gaussian radial bases.
• Ablation shows that directional information and the 2D spherical Fourier-Bessel basis substantially impact performance (e.g., NSHBF=1 degrades MAE; removing directional messages severely harms results).
• DimeNet achieves state-of-the-art performance on 11 of 12 QM9 targets and provides competitive MD results with 1000 training samples.
• The model is twice continuously differentiable and suitable for predicting both energies and atomic forces, enabling energy-conserving MD simulations.