  The aim of this research is to introduce a novel structural design process
that allows architects and engineers to extend their typical design space
horizon and thereby promoting the idea of creativity in structural design. The
theoretical base of this work builds on the combination of structural
form-finding and state-of-the-art machine learning algorithms. In the first
step of the process, Combinatorial Equilibrium Modelling (CEM) is used to
generate a large variety of spatial networks in equilibrium for given input
parameters. In the second step, these networks are clustered and represented in
a form-map through the implementation of a Self Organizing Map (SOM) algorithm.
In the third step, the solution space is interpreted with the help of a Uniform
Manifold Approximation and Projection algorithm (UMAP). This allows gaining
important insights in the structure of the solution space. A specific case
study is used to illustrate how the infinite equilibrium states of a given
topology can be defined and represented by clusters. Furthermore, three
classes, related to the non-linear interaction between the input parameters and
the form space, are verified and a statement about the entire manifold of the
solution space of the case study is made. To conclude, this work presents an
innovative approach on how the manifold of a solution space can be grasped with
a minimum amount of data and how to operate within the manifold in order to
increase the diversity of solutions.
