Symmetry-Reduced Physics-Informed Learning of Tensegrity Dynamics

TL;DR

This paper introduces SymPINN, a symmetry-aware physics-informed neural network that leverages geometric symmetries in tensegrity structures to improve prediction accuracy and computational efficiency in modeling their dynamics.

Contribution

The paper develops a novel symmetry-reduced PINN framework that embeds group-theory-based symmetry into neural network architecture for tensegrity dynamics prediction.

Findings

Significantly improved prediction accuracy over standard PINNs

Enhanced computational efficiency in modeling tensegrity structures

Effective preservation of geometric symmetry in dynamic predictions

Abstract

Tensegrity structures possess intrinsic geometric symmetries that govern their dynamic behavior. However, most existing physics-informed neural network (PINN) approaches for tensegrity dynamics do not explicitly exploit these symmetries, leading to high computational complexity and unstable optimization. In this work, we propose a symmetry-reduced physics-informed neural network (SymPINN) framework that embeds group-theory-based symmetry directly into both the solution expression and the neural network architecture to predict tensegrity dynamics. By decomposing nodes into symmetry orbits and representing free nodal coordinates using a symmetry basis, the proposed method constructs a reduced coordinate representation that preserves geometric symmetry of the structure. The full coordinates are then recovered via symmetry transformations of the reduced solution learned by the network, ensuring that the predicted configurations automatically satisfy the symmetry constraints. In this framework, equivariance is enforced through orbit-based coordinate generation, symmetry-consistent message passing, and physics residual constraints. In addition, SymPINN improves training effectiveness by encoding initial conditions as hard constraints, incorporating Fourier feature encoding to enhance the representation of dynamic motions, and employing a two-stage optimization strategy. Extensive numerical experiments on symmetric T-bars and lander structures demonstrate significantly improved prediction accuracy and computational efficiency compared to standard physics-informed models, indicating the great potential of symmetry-aware learning for structure-preserving modeling of tensegrity dynamics.