Characterization of subgrid-scale dynamics for a nonlinear beam

• We investigate the utility an optimal spatiotemporal reduced order modeling framework.
• A nonlinear beam under the influence of external forcing serves as a testbed.
• Models are developed to account for the effects of unresolved spatiotemporal scales.
• Model construction is simplified through a number of observed statistical properties.
• Results indicate an ability improve the reliability of under-resolved simulations.

Numerical solutions for the response of a geometrically nonlinear beam are investigated within the context of a new data-driven reduced order modeling (ROM) framework called optimal spatiotemporal reduced order modeling (OPSTROM). This modeling framework, which can potentially improve the accuracy of under-resolved simulations, accounts for the interactions between resolved scales and unresolved scales through the construction of subgrid-scale models which are consistent with the underlying spatiotemporal statistical structure of the dynamical system. Through numerical simulation, certain correlations amongst subgrid-scale dynamical quantities are investigated in order to simplify model construction.