用重整化思想设计神经网络，高效模拟复杂多体系统。
Renormalization-Inspired Effective Field Neural Networks for Scalable Modeling of Classical and Quantum Many-Body Systems
- 基于连续函数构建新架构，直接实现重整化数学工具
- 小规模训练后可精准预测大尺度系统，且精度随尺寸提升
- 适合物理建模、量子计算等需捕捉深层规律的领域
我们提出有效场神经网络（EFNN），一种基于连续函数的新架构，该函数是重整化中处理发散微扰级数的数学工具。核心洞察是神经网络可直接实现这些连续函数，为多体相互作用提供原理性方法。在三个系统上测试：经典3自旋长程模型、连续经典Heisenberg自旋系统和量子双交换模型，结果表明EFNN优于标准深度网络、ResNet和DenseNet。最突出的是其泛化能力：仅在10×10晶格上训练，即可准确预测高达40×40系统的性质，无需额外训练，且精度随系统尺寸增大而提高，相比精确对角化（ED）在40×40系统上提速10³倍。这表明EFNN捕捉的是底层物理而非单纯数据拟合，因此不仅适用于多体问题，也适用于任何可应用重整化思想的领域。
原文摘要 · Abstract (English)
We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can implement these continued functions directly, providing a principled approach to many-body interactions. Testing on three systems (a classical 3-spin infinite- range model, a continuous classical Heisenberg spin system, and a quantum double exchange model), we find that EFNN outperforms standard deep networks, ResNet, and DenseNet. Most striking is EFNN's generalization: trained on $10 \times 10$ lattices, it accurately predicts behavior on systems up to $40\times 40$ with no additional training -- and the accuracy improves with system size, with a computational time speed-up of $10^{3}$ compared to ED for $40\times 40$ lattice. This demonstrates that EFNN captures the underlying physics rather than merely fitting data, making it valuable beyond many-body problems to any field where renormalization ideas apply.
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