Symmetry-Reduced Physics-Informed Learning of Tensegrity Dynamics
This work addresses computational complexity and unstable optimization in physics-informed learning for tensegrity structures, which is important for engineers and researchers in structural dynamics, though it appears incremental as it builds on existing PINN approaches.
The authors tackled the problem of predicting tensegrity dynamics by proposing a symmetry-reduced physics-informed neural network (SymPINN) that embeds group-theory-based symmetry into the model, resulting in significantly improved prediction accuracy and computational efficiency compared to standard methods.
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.