The mining of models from data finds widespread use in industry. There exists a variety of model inference methods for perfectly deterministic behaviour, however, in practice, the provided data often contains noise due to faults such as message loss or environmental factors that many of the inference algorithms have problems dealing with. We present a novel model mining approach using Partial Max-SAT solving to infer the best possible automaton from a set of noisy execution traces. This approach enables us to ignore the minimal number of presumably faulty observations to allow the construction of a deterministic automaton. No pre-processing of the data is required. The method’s performance as well as a number of considerations for practical use are evaluated, including three industrial use cases, for which we inferred the correct models.