Speaker
Description
In this work, we explore a numerical approach to performing the inverse Laplace transformation, with an emphasis on stability and robustness under noisy conditions. Our quadrature-based method integrates reparameterization, data smoothing, optimization techniques, and various approaches to regularizing ill-conditioned systems. Together, these elements enable consistency checks that enhance the reliability of the inversion process. Through a series of controlled tests on toy models, we demonstrate the stability and effectiveness of the method in the presence of noise. Using mock data, we approximate spectral densities from Euclidean correlators, generating smoothed and stable results that accurately reproduce correlator behavior; particularly at large Euclidean times. We also briefly explore the application of this framework to actual lattice simulations. Finally, we discuss possible directions for extending this approach to a broader class of problems in Lattice QCD and theoretical physics, where the inverse Laplace transformation is typically ill-posed.
| Parallel Session (for talks only) | Theoretical developments and applications beyond Standard Model |
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