A genetic algorithm is used to learn a non-deterministic Petri netbased model of non-linear gene interactions, or statistical epistasis. Petri nets are computational models of concurrent processes. However, often certain global assumptions (e.g. transition priorities) are required in order to convert a non-deterministic Petri net into a simpler deterministic model for easier analysis and evaluation. We show, by converting a Petri net into a set of state trees, that it is possible to both retain Petri net non-determinism (i.e. allowing local interactions only, thereby making the model more realistic), whilst also learning useful Petri nets with practical applications. Our Petri nets produce predictions of genetic disease risk assessments derived from clinical data that match with over 92% accuracy.