Physics-Guided Spectral Parametric Reduced-Order Modeling for Transient Prediction of Controlled Dynamical Systems

Efficient parametric transient prediction at unseen parameter values and under new operating conditions remains challenging because repeated high-fidelity simulations are computationally prohibitive.

Existing data-driven surrogates and parametric reduced-order models perform well within sampled ranges but often lose reliability beyond them.

This study proposes a physics-guided spectral parametric reduced-order modeling framework for controlled dynamical systems.

Parameter-dependent reduced spectral operators are identified from transient snapshots using Dynamic Mode Decomposition with control, separating intrinsic dynamics from external control effects.

After physics-guided parameter transformation, aligned spectral quantities and reduced operator components are propagated across parameter conditions using Secondary Dynamic Mode Decomposition, with linear and radial basis function regressions as baselines.

Baseline regularization and nondimensional time mapping improve robustness.

Validation uses a mechanical transmission system, a Helium-Xenon closed Brayton cycle, and a Karman vortex street, covering linear transient, nonlinear transient, and nonlinear periodic dynamics.

For the mechanical and Brayton systems, system-level multivariable responses at unseen parameter values and under new operating conditions are predicted with relative norm errors below 1%.

For the vortex-street system, nondimensional time mapping preserves dominant vortex-shedding structures across Reynolds numbers.

Further analyses compare the framework with an LSTM surrogate and assess extrapolation confidence using an auxiliary error-prediction model.

Overall, the framework extends parametric reduced-order modeling from in-domain approximation toward extrapolative transient prediction of controlled dynamical systems under unseen conditions.