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Path integral Monte Carlo (PIMC) simulations are a cornerstone for studyingquantum many-body systems. The analytic continuation (AC) needed to estimatedynamic quantities from these simulations is an inverse Laplace transform,which is ill-conditioned. If this inversion were surmounted, then dynamicalobservables (e.g. dynamic structure factor (DSF) $S(q,\omega)$) could beextracted from the imaginary-time correlation functions estimates.  Although of important, the AC problem remains challenging due to itsill-posedness. To address this challenge, we express the DSF as a linearcombination of kernel functions with known Laplace transforms that have beentailored to satisfy its physical constraints. We use least-squares optimizationregularized with a Bayesian prior to determine the coefficients of this linearcombination. We explore various regularization term, such as the commonly usedentropic regularizer, as well as the Wasserstein distance and $L^2$-distance aswell as techniques for setting the regularization weight. A key outcome is theopen-source package PyLIT (\textbf{Py}thon \textbf{L}aplace \textbf{I}nverse\textbf{T}ransform), which leverages Numba and unifies the presentedformulations. PyLIT's core functionality is kernel construction andoptimization.  In our applications, we find PyLIT's DSF estimates share qualitative featureswith other more established methods. We identify three key findings. Firstly,independent of the regularization choice, utilizing non-uniform grid pointdistributions reduced the number of unknowns and thus reduced our space ofpossible solutions. Secondly, the Wasserstein distance, a previously unexploredregularizer, performs as good as the entropic regularizer while benefiting fromits linear gradient. Thirdly, future work can meaningfully combine regularizedand stochastic optimization.  (text cut for char. limit)

PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods