Automatic differentiation approach for reconstructing spectral functions with neural networks
This provides a generic tool for solving ill-posed inverse problems in physics, though it appears incremental as it adapts existing neural network and automatic differentiation techniques to this domain.
The authors tackled the inverse problem of reconstructing spectral functions from Euclidean Green's functions in physics by proposing an automatic differentiation framework using neural networks, achieving reconstruction accuracy assessed through KL divergence and MSE at multiple noise levels without explicit physical priors.
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.