Proper generalized decomposition surrogate modeling with application to the identification of Rayleigh damping parameters

This paper extends the Proper Generalized Decomposition framework to develop a reduced-order model parameterized by Rayleigh damping coefficients. The developed method incorporates damping modes to construct a damped surrogate model effectively. A novel method is introduced for treating the problem in space: during the offline phase, the spatial problem is initially projected onto the subspace spanned by the Ritz vectors of the system to provide an efficient prediction of the spatial modes. The prediction is then refined using a MinRes iterative solver. This two-step, prediction–correction process reduces the computational cost of a full-order solution while improving the accuracy of the reduced model. The resulting Proper Generalized Decomposition surrogate is subsequently employed within a Particle Swarm Optimization algorithm to determine optimal damping coefficients based on a given snapshot. Numerical experiments demonstrate the effectiveness of the developed method. • Low-rank representations of the damped parameterized equation for 3D elastodynamics. • Enhanced performance of the spatial solver by a new prediction–correction strategy. • Damping identification using the surrogate model and Particle Swarm Optimization. • Scalable method for accurate simulations of 3D viscoelastic structures.