In this section
@article{Tam:2026:10.1016/j.aei.2025.103870,
author = {Tam, KMM and Brown, NC and Bronstein, M and Mele, TV and Block, P},
doi = {10.1016/j.aei.2025.103870},
journal = {Advanced Engineering Informatics},
title = {Learning constrained static equilibrium for thrust network inverse form-finding via physics-informed geometric deep learning on CW complexes},
url = {http://dx.doi.org/10.1016/j.aei.2025.103870},
volume = {70},
year = {2026}
}
TY - JOUR
AB - This work integrates Geometric Deep Learning (GDL) with physics-informed modelling to approximate solutions to a constrained, ill-conditioned, and nonlinear inverse shell form-finding problem across diverse geometries and patterns. Given a target geometry and pattern design as meshes, the proposed neural framework predicts a funicular shell—defined by edge forces and vertex positions—that satisfies static equilibrium and closely matches the target form. Three main contributions are introduced: (1) a relaxed, numerically stable physics objective using efficient differentiable graph operators to mitigate the ill-conditioning of the nonlinear problem; (2) a stochastic augmentation strategy that enriches training with geometries of varying funicular feasibility, enhancing generalisation to infeasible inputs; and (3) a hierarchical GDL architecture that learns directly from irregular n -gon surface meshes, modelled as cell complexes to incorporate vertex, edge, and face features in both inputs and outputs. This approach eliminates the need for simplification of graph datastructures common in existing methods, improving mesh modelling versatility. Extensive studies examine the numerical stability of physics formulations, robustness for out-of-distribution designs, and the expressivity of the GDL architecture. While focused on a specific inverse form-finding task, this work offers general insights into addressing ill-posed inverse problems, showing how physics-based learning can support optimisation of mesh-based architectural structures under variable connectivity and design constraints.
AU - Tam,KMM
AU - Brown,NC
AU - Bronstein,M
AU - Mele,TV
AU - Block,P
DO - 10.1016/j.aei.2025.103870
PY - 2026///
SN - 1474-0346
TI - Learning constrained static equilibrium for thrust network inverse form-finding via physics-informed geometric deep learning on CW complexes
T2 - Advanced Engineering Informatics
UR - http://dx.doi.org/10.1016/j.aei.2025.103870
VL - 70
ER -