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The reconstruction of spectral functions from Euclidean correlation functionsis a well-known, yet ill-posed inverse problem in the fields of many-body andhigh-energy physics. In this paper, we present a comprehensive investigation oftwo recently developed analytic continuation methods, namely stochastic poleexpansion and Nevanlinna analytic continuation, for extracting spectralfunctions from mock lattice QCD data. We examine a range of Euclideancorrelation functions generated by representative models, including theBreit-Wigner model, the Gaussian mixture model, the resonance-continuum model,and the bottomonium model. Our findings demonstrate that the stochastic poleexpansion method, when combined with the constrained sampling algorithm and theself-adaptive sampling algorithm, successfully recovers the essential featuresof the spectral functions and exhibits excellent resilience to noise of inputdata. In contrast, the Nevanlinna analytic continuation method suffers fromnumerical instability, often resulting in the emergence of spurious peaks andsignificant oscillations in the high-energy regions of the spectral functions,even with the application of the Hardy basis function optimization algorithm.

Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation