Rare but extreme events in complex systems can often efficiently be described by samplepath large deviations: In the limit of some smallness-parameter approaching zero (such as temperature for chemical reactions, inverse number of particles for thermodynamic limits, or inverse timescale separation for multiscale systems), probabilities and most likely pathways of occurrence can be readily accessible. For large and strongly coupled stochastic systems, such as climate, atmosphere, or ocean, the corresponding computations pose a huge numerical challenge. These methods borrow heavily from field theory, and represent the rare probability as a path integral, necessitating the computation of instantons and fluctuation determinants. In this project, we address these challenges, including (1) how to compute the large deviation minimizer (instanton) for large systems, (2) how to compute next-order prefactor corrections, and (3) how to deal with heavy-tailed distributions