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Found 8 papers, 1 papers with code
Building symmetries into data-driven manifold dynamics models for complex flows
In this work we exploit the symmetries of the Navier-Stokes equations (NSE) and use simulation data to find the manifold where the long-time dynamics live, which has many fewer degrees of freedom than the full state representation, and the evolution equation for the dynamics on that manifold.
Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches
Additionally, we explore a modified approach where the system alternates between spaces of states and observables at each time step -- this approach no longer satisfies the linearity of the true Koopman operator representation.
Turbulence control in plane Couette flow using low-dimensional neural ODE-based models and deep reinforcement learning
The high dimensionality and complex dynamics of turbulent flows remain an obstacle to the discovery and implementation of control strategies.
Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow
For comparison, we show that the models outperform POD-Galerkin models with $\sim$2000 degrees of freedom.
Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learning
We show that the ROM-based control strategy translates well to the true KSE and highlight that the RL agent discovers and stabilizes an underlying forced equilibrium solution of the KSE system.
Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems
We present a data-driven modeling method that accurately captures shocks and chaotic dynamics by proposing a novel architecture, stabilized neural ordinary differential equation (ODE).
Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equations
Then the ODE, in these coordinates, is approximated by a NN using the neural ODE framework.
Deep learning to discover and predict dynamics on an inertial manifold
A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation.
