Göttingen 2025 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Theory of Machine Learning (joint session MP/AKPIK)

MP 5.3: Vortrag

Mittwoch, 2. April 2025, 14:25–14:45, ZHG001

Analytic continuation of Greens functions with a neural network — •Martin Rackl, Yanick Thurn, Fakher Assaad, Anika Götz, René Meyer, and Johanna Erdmenger — Julius-Maximilians University Würzburg, Am Hubland, 97074 Würzburg, Germany

An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Greens function. Typically, this Greens function is generated by Monte Carlo methods. As the one-point fermionic kernel diverges for large frequencies, the numerical noise present generically causes instabilities. A standard method to tackle the reconstruction of the spectral density is the maximum entropy method (MaxEnt). In this paper, we follow a different approach and use a convolutional neural network for obtaining the spectral density for a given imaginary time Greens function. The network is very sensitive to the nature of the training data that we create using random Gaussians. Here we improve the training data set available by considering collision centres for Gaussians rather than uniformly distributed Gaussians. Our network is constructed in such a way that its output fulfils the positive semidefiniteness of the spectral density and is ppropriately normalized. We compare the results of this network with results of MaxEnt for the same problem. This com- parison is performed for different cases: artificial test data, spin-charge separation in the 1d Hubbard model. Using the Wasserstein distance as metric, we find that the network performs in the same order of magnitude of accuracy as MaxEnt.

Keywords: Neural Network; Analytic Continuation; AI