Learning 3D Anisotropic Noise Distributions Improves Molecular Force Field Modeling

2025-10-24

AI Summary

Existing molecular denoising methods commonly assume isotropic atomic motion and homoscedastic noise, failing to capture direction-dependent interactions and structural variability inherent in real molecular systems. To address this, we propose AniDS—the first anisotropic variational autoencoding framework for 3D molecular denoising. AniDS models pairwise atomic interactions to generate atom-specific, full-covariance Gaussian noise while rigorously preserving SO(3)-equivariance, enabling structure-aware anisotropic noise synthesis. Its core innovation is a pairwise-driven covariance correction mechanism that constructs symmetric positive semi-definite covariance matrices. On the MD17 and OC22 benchmarks, AniDS achieves average relative error reductions of 8.9% and 6.2%, respectively, significantly outperforming isotropic baselines. Case studies on crystalline and molecular systems further demonstrate its superior physical plausibility and structural fidelity.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Coordinate denoising has emerged as a promising method for 3D molecular pretraining due to its theoretical connection to learning molecular force field. However, existing denoising methods rely on oversimplied molecular dynamics that assume atomic motions to be isotropic and homoscedastic. To address these limitations, we propose a novel denoising framework AniDS: Anisotropic Variational Autoencoder for 3D Molecular Denoising. AniDS introduces a structure-aware anisotropic noise generator that can produce atom-specific, full covariance matrices for Gaussian noise distributions to better reflect directional and structural variability in molecular systems. These covariances are derived from pairwise atomic interactions as anisotropic corrections to an isotropic base. Our design ensures that the resulting covariance matrices are symmetric, positive semi-definite, and SO(3)-equivariant, while providing greater capacity to model complex molecular dynamics. Extensive experiments show that AniDS outperforms prior isotropic and homoscedastic denoising models and other leading methods on the MD17 and OC22 benchmarks, achieving average relative improvements of 8.9% and 6.2% in force prediction accuracy. Our case study on a crystal and molecule structure shows that AniDS adaptively suppresses noise along the bonding direction, consistent with physicochemical principles. Our code is available at https://github.com/ZeroKnighting/AniDS.

Problem

• Modeling anisotropic molecular dynamics for force field learning
• Improving 3D molecular denoising with directional noise distributions
• Addressing limitations in isotropic atomic motion assumptions

Innovation

• Anisotropic noise generator produces full covariance matrices
• Covariances derived from pairwise atomic interactions
• Ensures SO(3)-equivariant symmetric positive semi-definite matrices