Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamics
This work addresses the challenge of enhancing predictive capability in chaotic systems modeling for researchers in computational physics and applied mathematics, representing an incremental advancement over data-only methods.
The paper tackled the problem of improving reduced-order modeling for systems with spatiotemporal chaotic dynamics by developing a hybrid model that blends data and known physics, resulting in substantially improved time-series predictions across scenarios including abundant data, scarce data, and incorrect full-order models.
While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a hybrid reduced order model (ROM), informed by both data and FOM, for evolving spatiotemporal chaotic dynamics on an invariant manifold whose coordinates are found using an autoencoder. This approach projects the vector field of the FOM onto the invariant manifold; then, this physics-derived vector field is either corrected using dynamic data, or used as a Bayesian prior that is updated with data. In both cases, the neural ordinary differential equation approach is used. We consider simulated data from the Kuramoto-Sivashinsky and complex Ginzburg-Landau equations. Relative to the data-only approach, for scenarios of abundant data, scarce data, and even an incorrect FOM (i.e. erroneous parameter values), the hybrid approach yields substantially improved time-series predictions.