The quest for nonlinear system identification models that are both physically interpretable and highly flexible remains a critical challenge. While classical methods offer structure at the cost of rigid parametric forms, and Neural ODEs provide expressiveness at the expense of transparency, a gap persists. Physics-Informed Neural Networks (PINNs) have bridged this divide, but their inverse variants falter when governing equations are unknown or state-dependent. Addressing this, the researchers introduce SOLIS, a framework that advances SOLIS nonlinear system identification by modeling unknown dynamics with a state-conditioned second-order surrogate model.
Unlocking Quasi-LPV Representations from Sparse Data
SOLIS fundamentally reframes system identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation. This approach decouples trajectory reconstruction from parameter estimation, enabling the recovery of interpretable physical quantities such as natural frequency, damping, and gain without presupposing a global governing equation. This is particularly crucial for complex systems where the underlying dynamics are not readily apparent or change with the system's state. The framework has demonstrated accurate parameter-manifold recovery and coherent physical rollouts even from sparse datasets, succeeding in regimes where conventional inverse methods encounter identifiability failures.
Stabilizing Training with Local Physics Hints
A significant innovation in the SOLIS nonlinear system identification approach lies in its robust training methodology. To combat the optimization collapse often seen in complex inverse problems, SOLIS employs a cyclic curriculum and a novel Local Physics Hints mechanism. This windowed ridge-regression anchoring provides stable, localized physical guidance during training, ensuring that the model converges to meaningful and physically consistent parameters. This enhanced stability is key to achieving reliable identification of unknown nonlinear dynamics.
