Graphs and Gradients: Machine Learning for Structural Design
How the "Graphs and Gradients" studio at Tongji University's DigitalFUTURES 2026 workshop paired machine-learning structural design with INTER\STITIAL, giving CAUP's Bell Hall a new, AI-optimised roof imagined in photorealistic detail.
8
AI-designed roof structures
500
Force-density optimisation iterations
DF '26
16th DigitalFUTURES workshop
“Watching students pick up computational tools built on the methods from my PhD is one of the most fulfilling experiences of my work so far, and I'm walking away with new ideas on where to take it next.”
“Graphs and Gradients: Machine Learning for Structural Design” was a one-week studio at DigitalFUTURES 2026, hosted at Tongji University’s College of Architecture and Urban Planning (CAUP) in Shanghai. Over the week, participants worked through three methods in sequence: structural form-finding, differentiable optimisation and generative graph-based machine learning. They then put those methods to the test on a real brief, designing a new roof for Bell Hall, CAUP’s own building on the Tongji campus. Rather than draw a shape and check the statics afterwards, teams let force, load and geometry find the form together, then carried each structure from an equilibrium diagram to a finished architectural image.
The image above shows one of those roofs, a tensioned membrane lifted over Bell Hall’s central atrium on slender masts with daylight pouring through its oculi. The render below sets the same kind of intervention back into its context on the Tongji campus.
A new lightweight roof set into the existing building at dusk, the kind of “rebirth” the brief asked for. Click to enlarge.
The method: let the structure find its own form
The studio worked through the same three methods, in sequence, that make up Lazlo Bleker’s PhD research on graph machine learning for structural design. First, a graph-based generative model proposed a whole population of starting topologies: the field of red-and-blue equilibrium diagrams below, tension in red and compression in blue. Next, teams edited each topology by hand, cutting openings, steering rain and sunlight, and recalculating force densities so loads flowed where they were wanted. Finally, differentiable, Force-Density-based optimisation resolved each configuration over hundreds of iterations until the mesh settled into equilibrium. You can read that convergence top-to-bottom in the second board, from tangled linework into clean, buildable shells.
The search space: hundreds of candidate roof structures generated from a pre-trained model, with a handful zoomed in for study. Click to enlarge.
Force-density optimisation in action: each column converges from a chaotic start to a doubly-curved shell in equilibrium. Click to enlarge.
From optimisation to detail
Every team documented its roof the whole way down, from the tension-compression optimisation process to materialisation, plans, sections and joint details. Their boards are collected below; click any to read it full-size.
About the workshop
DigitalFUTURES was launched in 2011, when Neil Leach brought a group of students from USC to Shanghai to work with Philip F. Yuan at Tongji University’s College of Architecture and Urban Planning (CAUP). It has since grown into an annual summer programme of workshops, lectures, conferences and exhibitions, drawing instructors from leading schools of architecture worldwide and spawning a peer-reviewed journal, a series of book publications and an international PhD programme. “Graphs and Gradients” was led by a team spanning structural design and machine learning: Lazlo Bleker, Anass Kariouh, Junwang Yu, Pierluigi D’Acunto, Kam-Ming Mark Tam and Philip F. Yuan. INTER\STITIAL joined as the visualisation partner for the studio’s final images.
What if you could design a structure just by describing it? Our paper, “Text2Structure3D: Graph-based generative modeling of equilibrium structures with diffusion transformers,” is aimed at exactly this goal, and has just been published in Results in Engineering (open access).
Working with INTER\STITIAL
A force-density model carries everything true about a roof: its geometry, its supports, where it pulls and where it pushes. It carries almost nothing about how it would feel to stand beneath it. In a one-week studio there is no time to hand each scheme to a visualiser. INTER\STITIAL co-founder Linus Leander Grimminger opened the AI-rendering side of the studio with a guest tutorial, after which teams brought their optimised models straight into INTER\STITIAL themselves, which returned photographic images that kept the structure exactly as solved while adding daylight, material and the life of the space below. A roof could be re-optimised and re-rendered inside a single afternoon, so the review panel saw not just a diagram of forces but the room those forces would build.
A faceted perforated-metal canopy on a cable net: the same equilibrium model, now a place with light, shadow and people in it. Click to enlarge.
Inside the images
Eight teams, eight ways to re-roof the same building. Each equilibrium diagram became a different kind of space once INTER\STITIAL gave it light and material, from warm timber grid-shells to translucent membranes and crystalline glass.
A timber grid-shell barrel vault, its diagonal lattice filtering daylight over the stepped atrium. Click to enlarge.
A tensioned fabric shell pierced by octagonal skylights, hung from a single spine of masts. Click to enlarge.
Looking straight up into a glass grid-shell on radiating timber beams: the force diagram made transparent. Click to enlarge.
Seen from the roof terrace: a scalloped membrane rising in soft arches over a timber-clad upper floor. Click to enlarge.
The same faceted pod at dusk, lit from the atrium below. Click to enlarge.
The result
By the final review, eight AI-designed roofs had each travelled from a force diagram to a finished image, produced by the students themselves, inside the week. The images gave complex, unfamiliar structures a form the panel could read at a glance, and let the studio spend its time on the question that mattered: not how to draw the roof, but what kind of space it should make.