3D objects (artefacts) are made to fulfill functions. Designing an object often starts with defining a list of functionalities that it should provide, also known as functional requirements. Today, the design of 3D object models is still a slow and largely artisanal activity, with few Computer-Aided Design (CAD) tools existing to aid the exploration of the design solution space. The purpose of the study is to explore the possibility of shape generation conditioned on desired functionalities. To accelerate the design process, we introduce an algorithm for generating object shapes with desired functionalities. We follow the principle form follows function, and assume that the form of a structure is correlated to its function. First, we use an artificial neural network to learn a function-to-form mapping by analysing a dataset of objects labeled with their functionalities. Then, we combine forms providing one or more desired functions, generating an object shape that is expected to provide all of them. Finally, we verify in simulation whether the generated object possesses the desired functionalities, by defining and executing functionality tests on it.
This paper is addressing several research challenges as a method to generate objects with desired functionalities, a method to extract form-to-function mapping, a method to operationally support a functionality arithmetic. The work illustrated in this paper is really interesting and is addressing relevant and open problems in the domain of product design.
Nevertheless the manuscript has a couple of weaknesses, one concerned with the presentation and another related to the design of the study. 
The lack of a consistent choice for the lexicon is sometimes misleading. It is not always clear whether the use of different terms is addressing synonyms or to discriminate between two distinct concepts. For example let consider the following pairs: functionality versus affordance, function versus functional, class versus category, feature versus shape. 
The study addresses several questions. Not always is clear what is the purpose or better the research questions that are driving the design of the experiments. While in the manuscript the are many repetition of the objectives of the study, less attention is devoted to explain what are the working hypothesis underlying the proposed methods. For example, one of the objective is a method to generate objects with desired functionalities. Only in the final Section there is a brief mention of the dichotomy between meash-based versus voxel-based. As reported in Section 2 there are in literature other works but there is not a claim on what is the specific purpose of the present study. The contrast of voxel versus mesh looks like a motivation but it only a speculation. A similar comment might address the dichotomy deterministic (ontology) versus probabilistic (autoencoder). In this case the experiment design should provide some empirical evidence about this contrast.
A minor comment. Figure 7a is illustrating the functional essence of table. According to the caption Figure 5a is illustrating the same functional essence for the same category/class table. Should the pictures look the same?