用新神经网络提升谱函数重建精度，比传统方法至少高20%
Analytic Continuation by Feature Learning
- 设计特征学习网络FL-net，提升谱函数预测能力
- 相比传统方法，预测精度提升至少20%
- 揭示隐藏层维度越大越不稳健的规律，适合量子模拟研究者
解析延拓旨在从虚时间格林函数重构实时间谱函数；然而这一过程长期面临病态难题。本文提出一种新型神经网络架构——特征学习网络（FL-net），显著提升谱函数预测精度，相较最大熵法（MEM）及以往神经网络方法，精度提升至少20%。此外，我们发展了一种解析方法评估模型鲁棒性：结果表明，增加FL-net的隐藏层维度虽能降低损失，却导致鲁棒性下降。整体上，该模型为应对解析延拓的复杂挑战提供了重要洞见。
原文摘要 · Abstract (English)
Analytic continuation aims to reconstruct real-time spectral functions from imaginary-time Green's functions; however, this process is notoriously ill-posed and challenging to solve. We propose a novel neural network architecture, named the Feature Learning Network (FL-net), to enhance the prediction accuracy of spectral functions, achieving an improvement of at least $20\%$ over traditional methods, such as the Maximum Entropy Method (MEM), and previous neural network approaches. Furthermore, we develop an analytical method to evaluate the robustness of the proposed network. Using this method, we demonstrate that increasing the hidden dimensionality of FL-net, while leading to lower loss, results in decreased robustness. Overall, our model provides valuable insights into effectively addressing the complex challenges associated with analytic continuation.
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