  Function is defined as the ensemble of tasks that enable the product to
complete the designed purpose. Functional tools, such as functional modeling,
offer decision guidance in the early phase of product design, where explicit
design decisions are yet to be made. Function-based design data is often sparse
and grounded in individual interpretation. As such, function-based design tools
can benefit from automatic function classification to increase data fidelity
and provide function representation models that enable function-based
intelligent design agents. Function-based design data is commonly stored in
manually generated design repositories. These design repositories are a
collection of expert knowledge and interpretations of function in product
design bounded by function-flow and component taxonomies. In this work, we
represent a structured taxonomy-based design repository as assembly-flow
graphs, then leverage a graph neural network (GNN) model to perform automatic
function classification. We support automated function classification by
learning from repository data to establish the ground truth of component
function assignment. Experimental results show that our GNN model achieves a
micro-average F${_1}$-score of 0.832 for tier 1 (broad), 0.756 for tier 2, and
0.783 for tier 3 (specific) functions. Given the imbalance of data features,
the results are encouraging. Our efforts in this paper can be a starting point
for more sophisticated applications in knowledge-based CAD systems and
Design-for-X consideration in function-based design.
