期刊
PHYSICAL REVIEW D
卷 102, 期 9, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.102.096001
关键词
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资金
- DFG [STA 283/16-2]
- Heidelberg University
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy [EXC 2181/1-390900948]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under the Collaborative Research Centre [SFB 1225]
- ExtreMe Matter Institute
- BMBF [05P18VHFCA]
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 parametrized 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 labeled training data in a supervised setting and the freedom in defining an optimization 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.
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