Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems

• URL: http://arxiv.org/abs/2604.12103v1
• Date: Mon, 13 Apr 2026 22:23:29 GMT
• Title: Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems
• Abstract summary: piDMD embeds known parameter-affine structure directly into the regression step.<n>We validate piDMD on fluid flow past a cylinder, electron beam oscillations in transverse magnetic fields, and virtual oscillations.
• Score: 34.448905454207406
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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