DeepForm: A Graph Neural Network Surrogate for Real-Time Tensile Membrane Form-Finding Across Anticlastic Typologies

Abstract

Form-finding of tensile membrane structures, the iterative process of determining the equilibrium shape under prescribed prestress and boundary conditions, is computationally expensive when performed with the Dynamic Relaxation (DR) method, the current industry standard. We propose DeepForm, a Graph Neural Network (GNN) surrogate trained once on a dataset of 10,987 DR solver outputs spanning six geometrically distinct anticlastic membrane typologies (hypar saddle, Scherk minimal surface, Enneper minimal surface, monkey saddle, sinc-difference saddle, and Kresge triangular shell) that directly predicts equilibrium node positions from boundary configurations in milliseconds. The membrane is represented as a graph in which nodes encode geometric and structural connectivity features and edges encode cable or membrane element properties, allowing the message-passing architecture to mimic force propagation through the structure. Per-type displacement normalisation is introduced to handle the large variation in deformation magnitude across typologies (spanning approximately a factor of 6 in deformation scale) while sharing a single network. Unlike physics-informed neural network (PINN) approaches that require retraining per geometry, DeepForm generalises across new boundary configurations within each typology without retraining, enabling millisecond GNN based form-finding feedback suitable for interactive structural design workflows.