Speaker
Description
Spectral reconstruction is one of the most challenging and important problems in lattice QCD, as spectral functions are directly related to a wide range of phenomenologically relevant observables. In this talk, I present a novel strategy based on reformulating the reconstruction problem within the framework of Operator Learning using DeepONet neural networks. The network is trained in a supervised way, and I introduce an effective approach to generating training datasets that incorporates prior knowledge without relying on a predefined family of parametric models. I also show how systematic uncertainties can be reliably quantified within the machine-learning framework and validate the method on previously unseen mock data. As a benchmark on true lattice data, I reconstruct the inclusive decay rate in the 1+1-dimensional $O(3)$ non-linear $\sigma$ model, recovering the analytical result with high precision. This approach has the potential to improve the precision of the calculation of spectral-density-related observables compared with established non-machine-learning reconstruction methods.