The fault behavior of Inverter Interfaced Distributed Generators (IIDGs) diverges from that of synchronous generators. When a substantial number of IIDGs are integrated into the distribution network, the conventional short-circuit current calculation technique, grounded in a mechanical framework, struggles to simultaneously satisfy the demands for both rapid computation and precision. This study introduces an alternative approach reliant on data analysis, enabling swift and precise computation of short-circuit currents across the IIDG-infused distribution grid. The investigation delves into the efficacy of multi-output regression techniques and the selection of the foundational learning algorithm. Specifically, two strategies are advanced: Multi-Target Regressor Stacking and Regressor Chains, both utilizing the Light Gradient Boosting Machine as the base learner. The influence of varying sample sizes on the multi-output computational model's performance is assessed. To ascertain the real-world viability of the multi-output regression methodology, two distinct fault characteristics pertaining to data-driven short-circuit current calculation are scrutinized using existing distribution network measurement conditions. The study reveals that, given a known distribution network structure, the proposed method can compute network-wide short-circuit currents across diverse IIDG penetration levels and fault scenarios through a singular model, maintaining a balance between computation precision and speed. If the distribution network's structure undergoes minor modifications, the model demonstrates reasonable adaptability, yet a retraining of the short-circuit current calculation model is recommended to ensure sustained accuracy in the face of significant network changes.