Spectral Reconstruction with Deep Neural Networks
Spectral Reconstruction with Deep Neural Networks
复制标题
使用深度神经网络进行谱重建
DOI：
10.1103/physrevd.102.096001
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Felix Ziegler
中科院分区：
文献类型：
--
作者：
Lukas Kades;J. Pawlowski;A. Rothkopf;M. Scherzer;Julian M. Urban;S. Wetzel;Nicolas Wink;Felix Ziegler
我们探索了人工神经网络作为从虚时间格林函数重建谱函数的工具，这是一个经典的病态反问题。我们的ANSATZ是基于有监督的学习框架，其中先验知识被编码在训练数据中，并且逆变换流形通过神经网络被显式地参数化。我们系统地研究了这种新的重建方法，详细分析了它在物理激励模拟数据上的性能，并将其与已有的贝叶斯推理方法进行了比较。重建精度被发现至少是可比的，并且潜在地更好，特别是在较大的噪声水平下。我们认为，在有监督的环境中使用标记的训练数据和定义优化目标的自由是本方法的固有优势，并可能在未来导致相对于最先进方法的重大改进。并对进一步研究的方向进行了详细讨论。
We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which prior knowledge is encoded in the training data and the inverse transformation manifold is explicitly parametrised through a neural network. We systematically investigate this novel reconstruction approach, providing a detailed analysis of its performance on physically motivated mock data, and compare it to established methods of Bayesian inference. The reconstruction accuracy is found to be at least comparable, and potentially superior in particular at larger noise levels. We argue that the use of labelled training data in a supervised setting and the freedom in defining an optimisation objective are inherent advantages of the present approach and may lead to significant improvements over state-of-the-art methods in the future. Potential directions for further research are discussed in detail.
影响因子：
5.8
作者：
Carpenter, Bob;Gelman, Andrew;Riddell, Allen
通讯作者：
Riddell, Allen