Solving the inverse problem is a major challenge in contemporary nano-optics. However, frequently not just a possible solution needs to be found but rather the solution that accommodates constraints imposed by the problem at hand. To select the most plausible solution for a nano-optical inverse problem additional information can be used in general, but how to specifically formulate it frequently remains unclear. Here, while studying the reconstruction of the shape of an object using the electromagnetic field in its proximity, we show how to take advantage of artificial neural networks (ANNs) to produce solutions consistent with prior assumptions concerning the structures. By preparing suitable datasets where the specific shapes of possible scatterers are defined, the ANNs learn the underlying scatterer present in the datasets. This helps to find a plausible solution to the otherwise non-unique inverse problem. We show that topology optimization, in contrast, can fail to recover the scatterer geometry meaningfully but a hybrid approach that is based on both, ANNs and a topology optimization, eventually leads to the most promising performance. Our work has direct implications in fields such as optical metrology.