ACFlowSensitivity

ACFlowSensitivity is a Julia package that reimplements and enhances analytic continuation methods from ACFlow. It provides tools for analyzing the sensitivity of these algorithms using automatic differentiation and other advanced techniques.

For input $\mathcal{G}={G(iw_n)}_{n=1}^N$ and analytic continuation algorithm

Here $\text{reA}$ means the reconstructed spenctral density function and $w_j$ is the integral weight of the output mesh.

As a result we calculate:

Our purpose is to implement following methods (not all) and their sensitivity analysis (RI means reimplement. SA means Sensitivity Analysis for both fermionic and bosonic systems (Only fermionic now). cont,delta,mixed are spectrum types):

Method	RI cont	RI delta	RI mixed	SA cont	SA delta	SA mixed
BarRat	✅	✅		✅	✅
MaxEnt Chi2kink	✅	✅		✅	✅
MaxEnt Bryan	✅	✅		✅	✅
MaxEnt Classic	✅	✅		✅	✅
MaxEnt Historic	✅	✅		✅	✅
SAN	✅	✅			✅
SAC	✅	✅			✅
SPX	✅	✅			✅
SOM	✅	✅			✅
NAC	✅	✅			✅

Example of using ACFlowSensitivity to plot the error bound of a specific method is shown in the file folder plot.

By using ACFlowSensitivity, you can get a error bound like this: