We present SymLearn, a method to automatically infer fault tree (FT) models from data. SymLearn takes as input failure data of the system components and exploits evolutionary algorithms to learn a compact FT matching the input data. SymLearn achieves scalability by leveraging two common phenomena in FTs: (i) We automatically identify symmetries in the failure data set, learning symmetric FT parts only once. (ii) We partition the input data into independent modules, subdividing the inference problem into smaller parts.We validate our approach via case studies, including several truss systems, which are symmetric structures commonly found in infrastructures, such as bridges. Our experiments show that, in most cases, the exploitation of modules and symmetries accelerates the FT inference from hours to under three minutes. This research has been partially funded by NWO under the grant PrimaVera number NWA.1160.18.238 and by the ERC Consolidator grant CAESAR number 864075.