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Data-Driven Design: Exploring new Structural Forms using Machine Learning and Graphic Statics
Lukas Fuhrimann, Vahid Moosavi, Patrick Ole Ohlbrock, Pierluigi Dacunto
TL;DR
Designers can manually explore only a limited subset of the large equilibrium-form spaces generated by structural form-finding. The paper combines CEM with SOM and UMAP to represent and interpret those spaces; its case study identifies nine form clusters and three classes of parameter correlation.
Problem
Designers can manually explore only a small, sequentially navigated subset of the vast equilibrium-form solution space, limiting their individual design horizons.
Source: §1 · p. 1Method
Results
The case study yields nine clusters; one parameter defines cluster amount, four define regions within clusters, and fourteen do not influence solution-space diversity.
Source: §4 · p. 7Takeaways & Limitations
A form-map organizes formal variation for exploration, and understanding the solution-space manifold can support increasing solution diversity.
Source: §4 · pp. 7–8
Abstract
from arXiv · showhide
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.
1. Introduction
Equilibrium-based design can generate a vast solution space, but designers can manually explore only a limited, experience-shaped subset. The paper combines form-finding with machine learning to support broader, diversity-driven exploration.
1. Introduction
- Designers can explore only a small, sequentially navigated subset of the vast equilibrium-form solution space, shaped by their experience and design references.The authors describe this as an individual design horizon limited in both size and quality.Source: §1 · p. 1
- The work aims to extend designers’ approachable design horizons and support diversity-driven exploration in early design, for abstract studies or defined briefs.The approach combines form-finding with machine-learning algorithms.Source: §1 · p. 1
- CEM efficiently generates equilibrium networks, while SOM and UMAP analyze the design space and its relation to input parameters.A large but finite data sample is used to represent the infinite solution space for given inputs.Source: §1 · p. 2
2. Combinatorial Equilibrium Modelling
CEM generates spatial networks in equilibrium by combining graphic-statics diagrams with a topological representation that controls network connectivity and member properties. The case study reduces a complex topology to a manageable parameterization, generates candidate forms, and filters them geometrically.
2. Combinatorial Equilibrium Modelling
- CEM uses form and force diagrams alongside a topological diagram to control network connectivity, tension or compression state, member lengths, and internal forces.Trail members lie on shortest paths to supports; other members are deviation members.Source: §2 · p. 2
2.1. Topological Set-Up
- The case-study topology has 400 trail and 400 deviation members, with 400 deviation-force parameters, 420 constraint-plane parameters, and one radius parameter.Start vertices are fixed and equally distributed on a circle whose radius varies.Source: §2.1 · p. 3
2.2. Parametric Set-Up
- Sinusoidal functions relate parameters within structural layers and correlate amplitudes across layers, reducing 821 inputs to 18 parameters plus one for first-layer external forces.The 19 parameters describe the solution space; each is randomly chosen for automated form generation.Source: §2.2 · pp. 3–4
2.3. Form Generation and Evaluation
- Of 252,000 generated equilibrium networks, 35,800 passed the projected-intersection criterion and were used to train SOM and UMAP.Forms with intersections between elements in any one or more layers were discarded.Source: §2.3 · p. 4
3. Self Organizing Map and Uniform Manifold Approximation and Projection
SOM and UMAP reduce high-dimensional form data for clustering and visualization while retaining different representations of the design space. The study uses normalized nodal coordinates to compare forms by their Euclidean-space similarity.
3. Self Organizing Map and Uniform Manifold Approximation and Projection
- SOM maps high-dimensional data to a low-dimensional space while preserving topology, supporting clustering and visualization of smoothly changing data patterns.Its map is typically a two-dimensional planar grid with a fixed number of nodes.Source: §3 · p. 4
- UMAP represents similar high-dimensional objects as nearby two-dimensional points and dissimilar objects as distant points in an open space.Unlike SOM, UMAP is not restricted to a fixed number of points on a planar grid.Source: §3 · p. 4
- The study trains SOM using normalized nodal coordinates (n=1260), making Euclidean distances between corresponding nodes the measure of form similarity.The designer’s clustering objective determines the input-vector dimension for SOM and UMAP.Source: §3 · p. 4
4. Solution Spaces, Self Organizing Maps and Uniform Manifold Approximation and Projection
The study maps sampled equilibrium forms into a form-map and uses UMAP to examine clusters and their relationships to CEM input parameters. In this case study, parameter correlations distinguish within-cluster variation from cluster membership, and sensitivity tests support the role of GE in setting cluster count.
4. Solution Spaces, Self Organizing Maps and Uniform Manifold Approximation and Projection
- Each accepted CEM equilibrium form is abstracted as a vector of 1,260 nodal coordinates; SOM visualizes and clusters this data, while UMAP examines input-parameter correlations with form clusters.The resulting form-map is an interactive clustered design space.Source: §4 · pp. 4–5
4.1. SOM of Equilibrium Structures
- The SOM form-map groups similar forms at nodes, with gaps delineating clusters; interactive exploration lets designers inspect forms that are difficult to design manually.An 80x80 SOM grid is trained, then inputs are assigned to their best-matching nodes; unassigned inputs produce gaps.Source: §4.1 · p. 5, Figure 3 · p. 5
- Three selected nodes illustrate distinct form families, each assigned to a different node in the form-map.The figure shows examples selected to examine the map at finer resolution.Source: §4.1 · p. 5, Figure 4 · p. 6
3.4. UMAP Representation of Cluster and CEM Parameters
- UMAP represents each input form as a point; point clouds indicate similar forms, distances between clouds indicate cluster resemblance, and nine clusters are distinguishable.Figure 5 presents the clustered UMAP space.Source: §3.4 · p. 6, Figure 5 · p. 6
- Three parameter-correlation classes emerge: parameters steer forms within a cluster, vary arbitrarily within clusters, or identify cluster membership.These classes are shown in the parameter representation accompanying the clustered UMAP space.Source: §3.4 · p. 6, Figure 5 · p. 6
- Fixing A_B=5 leaves the cluster count unchanged, while restricting GE to 8–12 yields three clusters; GE sets cluster count, and values above 20 cannot add clusters for this topology.The authors attribute the limit to GE's sinusoid frequency being discretized by the topology's 20 trails; they conclude the case-study clustered space's diversity is represented.Source: §3.4 · p. 7, Figure 6 · p. 7
4. Conclusion
The paper combines CEM with SOM and UMAP to generate, represent, and interpret large solution spaces of equilibrium networks. In the case study, this approach distinguishes nine clusters and three parameter-correlation classes, while showing how a solution-space manifold can be grasped with minimal data and used to increase solution diversity.
4. Conclusion
- CEM, SOM, and UMAP provide strategies to generate, represent, and evaluate large solution spaces of novel equilibrium networks.The methodology is demonstrated through a case study.Source: §4 · p. 7
- The form-map clusters funicular geometries by Euclidean-space variation, letting designers explore infinite, ordered variations of spatial equilibrium networks.The authors describe the map as a “city of equilibrium forms.”Source: §4 · p. 7, Figure 7 · p. 8
- The case study yields nine clusters: one parameter defines cluster count, four define regions within clusters, and fourteen do not affect solution-space diversity.The authors say this clarifies the entire infinite solution space for the specified topology and parameter setup.Source: §4 · p. 7
- The authors present an approach for grasping a solution-space manifold with minimal data and changing it to increase solution diversity.Further investigation of the concept is planned.Source: §4 · p. 8