Understanding the complexities of galaxy evolution and the role of mergers therein remains a fundamental challenge in astrophysics. Since galaxies can only be observed at a single point in cosmic time, tracing their merging history and its impact on a galaxy's mass assembly is heavily dependent on models or cosmological simulations. However, while simulations provide a powerful tool for tracing galaxy evolution, they carry distinct biases and lack the realism required to match real observational data. Simulation-based inference (SBI), when approached with care, offers a promising avenue for bridging this gap by leveraging simulations to predict unobservable quantities of observational data.

In this work, we take advantage of the power of SBI to acquire, for the first time, predictions for the fraction of stellar mass originating from mergers in a statistically significant sample of nearby galaxies, using data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA). Employing a robust machine learning model trained on mock MaNGA analogs, we manage to set the first observational constrains on the balance of in-situ vs. ex-situ stellar mass in the nearby universe. However, caution must be exercised when interpreting SBI results on real data, as biases can arise from the cosmological simulations one trains on as well as from the limitations of mock datasets. To address these challenges, we employ a systematic approach. First, we calibrate our model across several cosmological simulations to mitigate biases induced by training data. Second, we leverage self-supervised learning techniques to extract meaningful representations even from limited or unbalanced mock datasets, thereby enhancing the robustness of our predictions. Finally, we take special care of providing meaningful measures of uncertainty for the ML model predictions, since no ground truth is available for the observational data.

Our findings reveal valuable insights into the integrated impact of mergers on galaxy evolution. We demonstrate that in-situ stellar mass dominates across the stellar mass spectrum, with accreted mass becoming increasingly significant in more massive galaxies. Notably, the ex-situ stellar mass exhibits significant dependence on galaxy characteristics and environment. Our work provides insights into the broader framework of galaxy evolution while demonstrating how SBI can be systematically employed to extract new non-trivial hidden information from data.