Analytic Continuation by Feature Learning
This work addresses a challenging problem in computational physics for researchers dealing with quantum many-body systems, offering incremental improvements in accuracy and robustness analysis.
The paper tackles the ill-posed problem of analytic continuation for reconstructing real-time spectral functions from imaginary-time Green's functions, proposing a Feature Learning Network (FL-net) that improves prediction accuracy by at least 20% over traditional and previous neural network methods.
Analytic continuation aims to reconstruct real-time spectral functions from imaginary-time Green's functions; however, this process is notoriously ill-posed and challenging to solve. We propose a novel neural network architecture, named the Feature Learning Network (FL-net), to enhance the prediction accuracy of spectral functions, achieving an improvement of at least $20\%$ over traditional methods, such as the Maximum Entropy Method (MEM), and previous neural network approaches. Furthermore, we develop an analytical method to evaluate the robustness of the proposed network. Using this method, we demonstrate that increasing the hidden dimensionality of FL-net, while leading to lower loss, results in decreased robustness. Overall, our model provides valuable insights into effectively addressing the complex challenges associated with analytic continuation.