Improving the deconvolution of spectra at finite temperatures by replacing spectrum with a neural network

In condensed matter physics studies, spectral information plays an important role in understanding the composition of materials. However, it is difficult to obtain a material's spectrum information directly through experiments or simulations. For example, the spectral information deconvoluted by scanning tunneling spectroscopy suffers from the temperature broadening effect, which is a known ill-posed problem and makes the deconvolution results unstable. Existing methods, such as the maximum entropy method, tend to select an appropriate regularization to suppress unstable oscillations. However, the choice of regularization is difficult, and oscillations are not completely eliminated. We believe that the possible improvement direction is to pay different attention to different intervals. Combining stochastic optimization and deep learning, in this paper, we introduce a neural network-based strategy to solve the deconvolution problem. Because the neural network can represent any nonuniform piecewise linear function, our method replaces the target spectrum with a neural network and can find a better approximation solution through an accurate and efficient optimization. Experiments on theoretical datasets using superconductors demonstrate that the superconducting gap is more accurately estimated and oscillates less. Plug in real experimental data, our approach obtains clearer results for material analysis.