15. A Physics-Based Reduced Order Model with Machine Learning-Boosted Hyper-Reduction

Physics-Based Reduced Order Models (ROMs) tend to rely on projection-based reduction. This family of approaches utilizes a series of responses of the full-order model to assemble a suitable basis, subsequently employed to formulate a set of equivalent, low-order equations through projection. However, in a nonlinear setting, physics-based ROMs require an additional approximation to circumvent the bottleneck of projecting and evaluating the nonlinear contributions on the reduced space. This scheme is termed hyper-reduction and enables substantial computational time reduction. The aforementioned hyper-reduction scheme implies a trade-off, relying on a necessary sacrifice on the accuracy of the nonlinear terms’ mapping to achieve rapid or even real-time evaluations of the ROM framework. Since time is essential, especially for digital twins representations in structural health monitoring applications, the hyper-reduction approximation serves as both a blessing and a curse. Our work scrutinizes the possibility of exploiting machine learning (ML) tools in place of hyper-reduction to derive more accurate surrogates of the nonlinear mapping. By retaining the POD-based reduction and introducing the machine learning-boosted surrogate(s) directly on the reduced coordinates, we aim to substitute the projection and update process of the nonlinear terms when integrating forward in time on the low-order dimension. Our approach explores a proof-of-concept case study based on a Nonlinear Auto-regressive neural network with eXogenous Inputs (NARX-NN), trying to potentially derive a superior physics-based ROM in terms of efficiency, suitable for (near) real-time evaluations. The proposed ML-boosted ROM (N3-pROM) is validated in a multi-degree of freedom shear frame under ground motion excitation featuring hysteretic nonlinearities.