A generalizable neural operator for full-field deformation prediction in robotic design

• Proposed a new neural operator for rapid robot full-field deformation prediction. • Geometric-load graph constructed to unify structure and force representation. • 6000 times faster than finite element analysis while maintaining high accuracy. • Generalizable and applicable to varying geometries, postures, and loading conditions. Robotic design and optimization often require extensive simulation-based iterations, particularly for predicting static deformations under varying postures, external loads, and gravitational conditions. Conventional finite element simulations can achieve high accuracy but are computationally expensive, limiting their use in large-scale design optimization. Data-driven approaches have emerged to accelerate prediction; however, most existing methods are restricted to simplified scenarios, such as fixed geometries with varying poses or fixed poses with varying loads, and typically predict only partial deformation at points rather than the full deformation field. To enable fast and generalizable deformation prediction, a new neural operator architecture named Robot-NO is developed. A geometric–load graph based on the finite element mesh connectivity, where each node encodes spatial coordinates with local load conditions is constructed. A graph neural network is then employed to extract a unified global representation that captures both geometric structure and external force distribution. A query–decoder module combines global features with arbitrary query-coordinates to predict the full deformation field. This query-based formulation enables accurate continuous deformation prediction across varying robot geometries, postures, and load conditions. Experimental results demonstrate that the proposed model achieves a root mean square error of 0.91 μ m in deformation prediction and is 6000 times faster than conventional finite element simulations. This significant improvement enables rapid design, analysis and optimization for robotic mechanisms.