2021/12/12 by Lingxiao Wang, Shuzhe Shi, Wang, Lingxiao +3
Computer Science · Decision Sciences · Mathematics · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #High Energy Physics - Lattice (hep-lat) #Machine Learning (cs.LG) #Scientific Measurement and Uncertainty Evaluation #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2112.06206
openalex publication_date 2021/12/12 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in physics. The prior knowledge for specific physical systems routinely offers essential regularization schemes for solving the ill-posed problem approximately. Aiming at this point, we propose an automatic differentiation framework as a generic tool for the reconstruction from observable data. We represent the spectra by neural networks and set chi-square as loss function to optimize the parameters with backward automatic differentiation unsupervisedly. In the training process, there is no explicit physical prior embedding into neural networks except the positive-definite form. The reconstruction accuracy is assessed through Kullback-Leibler(KL) divergence and mean square error(MSE) at multiple noise levels. It should be noted that the automatic differential framework and the freedom of introducing regularization are inherent advantages of the present approach and may lead to improvements of solving inverse problem in the future.