[论文解读] V2Rho-FNO: Fourier Neural Operator for Electronic Density Prediction

Yingdi Jin, Xinming Qin+4 more|arXiv (Cornell University)|Mar 13, 2026

Machine Learning in Materials Science被引用 0

一句话总结

V2Rho-FNO 使用三维傅里叶神经算子学习外部势到密度的映射，实现对未见系统的零-shot泛化和网格尺寸转移，无需重新训练。

ABSTRACT

Density functional theory (DFT) is a cornerstone of computational chemistry and materials science, but its computational cost limits its use in large-scale and high-throughput applications. While machine learning has accelerated energy prediction for specific molecular classes, transferable prediction of electron density across diverse chemical spaces remains challenging. Here, we present a universal framework based on Fourier Neural Operators (FNOs) that directly learns the mapping from external potentials to electron density distributions. Unlike conventional approaches that rely on explicit atomic orbitals, basis sets, or handcrafted descriptors, the proposed method captures global electronic interactions and long-range correlations through operator learning in the spatial-frequency domain. Trained on datasets spanning multiple elements and molecular geometries, the model achieves zero-shot generalization to entirely unseen molecular systems and accurately predicts their electron densities without retraining. This transferability arises from the intrinsic ability of FNOs to represent global structure in continuous fields. Our work establishes neural operator learning as a promising route for fast, accurate, and transferable electronic structure prediction, with potential applications in high-throughput screening and chemical space exploration.

研究动机与目标

• 在DFT/类似DFT框架内推动快速、可转移的电子密度预测。
• 将密度–势的映射框定为与洪恩堡–科恩定理相一致的场到场算子学习问题。
• 开发一个三维傅里叶神经算子，在均匀网格上从外部势预测基态电子密度。
• 证明对未见分子系统在多样化化学空间中的零-shot转移性。

提出的方法

• 将HK映射表述为场到场的算子G: V_ext(r) → ρ(r)。
• 使用三维傅里叶神经算子(FNO)来近似算子，实现离散化不变性。
• 输入V_ext为屏蔽的实空间离子势场；输出是在网格上的ρ。
• 采用三阶段FNO：输入提升、带低频谱混合的堆叠傅里叶层、以及输出投影到密度。
• 保留残差结构并通过最终激活实现密度的非负性约束。
• 在多样化数据集上训练，并在零-shot泛化和分辨率转移上进行测试。

Figure 1: H2O correlation analysis.

实验结果

研究问题

• RQ1 V2Rho-FNO能否在完全未见的分子系统上实现零-shot泛化并预测出准确的电子密度？
• RQ2 算子学习框架是否能够实现对不同分子构型和化学元素的转移？
• RQ3 学习的算子是否能够在不重新训练的情况下跨不同空间分辨率进行预测转移？
• RQ4 外部势场输入在实现物理保真度和可转移性方面的作用是什么？

主要发现

• 该模型对未知分子系统实现零-shot泛化并准确预测密度。
• 从轨迹内插的泛化提升到对随机分子的一般化再到元素级外推，反映出难度的增加。
• 通过光谱零填充实现的分辨率转移，在在中等分辨率训练时仍能得到物理上一致的高分辨率密度。
• 离散化不变的算子学习使得在不同分辨率的网格上进行评估而不需重新训练成为可能。

Figure 2: Bonding environments extrapolation: training on the first 5,000 molecules from QM9, and evaluation on molecules whose local bonding environments are not present in the training set, followed by correlation and error analysis between predicted densities and DFT-calculated densities.