Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems
For researchers in reduced-order modeling of parametric nonlinear systems, piDMD offers a more robust and data-efficient alternative to interpolation-based parametric DMD methods.
The paper introduces parametric interpolation of dynamic mode decomposition (piDMD), which embeds parameter-affine structure into DMD regression to learn a single surrogate model across multiple parameter samples. piDMD achieves accurate long-horizon predictions and improved robustness over existing methods on fluid flow and plasma simulations, requiring fewer training samples and handling multi-dimensional parameter spaces.
We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods which interpolate modes, eigenvalues, or reduced operators and can be fragile with sparse training data or multi-dimensional parameter spaces, piDMD learns a single parameter-affine Koopman surrogate reduced order model (ROM) across multiple training parameter samples and predicts at unseen parameter values without retraining. We validate piDMD on fluid flow past a cylinder, electron beam oscillations in transverse magnetic fields, and virtual cathode oscillations -- the latter two being simulated using an electromagnetic particle-in-cell (EMPIC) method. Across all benchmarks, piDMD achieves accurate long-horizon predictions and improved robustness over state-of-the-art interpolation-based parametric DMD baselines, with less training samples and with multi-dimensional parameter spaces.