Prediction of physical space parameters for dynamical systems: A POD-ANN approach

Full-Order Models (FOM) parameters provide detailed representations of dynamic systems. However, they often come with high computational costs. This is especially true for large-scale or real-time applications such as structural health monitoring and digital twinning. Reduced-Order Modeling (ROM) techniques, like Proper Orthogonal Decomposition (POD), address this by reducing system dimensionality. This enables more efficient simulations while preserving essential dynamics. However, ROM approaches cannot be used directly to predict parameters (e.g., stiffness) in the physical space. These parameters are crucial for comprehensive system evaluation. This study introduces a novel framework combining POD and Artificial Neural Networks (ANN) to map reduced-order parameters to physical parameters for the case of gradual, global parameter variations. POD extracts significant modes that capture essential dynamics, projecting full-order dynamics onto the reduced space. Subsequently, ANN is trained to map reduced space to physical space parameters, addressing ROM’s limitations. The POD-ANN model is applied to linear and nonlinear dynamic problems, and $50\%$ reduction in modes compared to the full-order dimension is observed in both cases. Furthermore, the achieved relative error is quite low while predicting the full-order stiffness matrix for linear and nonlinear dynamical systems. Once the model is trained, it can be used to predict parameters efficiently.