[理论室学术报告] An Artificial Neural Network Approach to the Analytic Continuation Problem
Inverse problems are encountered in many domains of both mathematics and physics, with analytic continuation of the imaginary Green’s function into the real frequency domain being a particularly important example. However, the analytic continuation problem is ill-defined and currently no analytic transformation for solving it is known. We present a general framework for building an artificial neural network that efficiently solves this task with a supervised learning approach, provided that the forward problem is sufficiently stable for creating a large training dataset of physically relevant examples. By comparing with the commonly used maximum entropy approach, we show that our method can reach the same level of accuracy for low-noise input data while performing significantly better when the noise strength increases. We also demonstrate that adding an unsupervised denoising step significantly improves the accuracy of the maximum entropy predictions for noisy inputs. The computational cost of the proposed neural network approach is reduced by almost three orders of magnitude compared to the maximum entropy method. Although the inverse problem we studied is a typical one, our neural network solution is not only limited to the analytic continuation problem, but also can be extended to many other inverse problems.
Dr. QuanSheng Wu obtained his Bachelor (2013) from Beijing normal university and PhD degree (2018) from Institute of Physics, CAS . After that, he worked one year in the Institute of Applied Physics and Computational Mathematics as a research assistant. Then he worked as a postdoc in ETHZ during 2015-2017 and in EPFL from 2018 till now. As a computational physicist, he has been working on the topological materials since his PhD. The open-source software WannierTools that he developed is worldwide used and cited over 100 times since 2018.
Contract: Lei Wang, 9853