Department of Mechanical and Aerospace Engineering

Daniel Tartakovsky › Publications › lu-2023-drips

H. Lu and D. M. Tartakovsky, "DRIPS: A framework for dimension reduction and
interpolation in parameter space", *J. Comput. Phys.*, vol. 493, doi:10.1016/j.jcp.2023.112455, pp. 112455, 2023

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Moreover, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

@article{lu-2023-drips,

author = {H. Lu and D. M. Tartakovsky},

title = {DRIPS: A framework for dimension reduction and
interpolation in parameter space},

year = {2023},

urlpdf = {http://maeresearch.ucsd.edu/Tartakovsky/Papers/lu-2023-drips.pdf},

journal = {J. Comput. Phys.},

volume = {493},

doi = {10.1016/j.jcp.2023.112455},

pages = {112455}

}