Search Results for author:
Found 13 papers, 3 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.
Autoencoders for discovering manifold dimension and coordinates in data from complex dynamical systems
Analysis of gradient descent dynamics for this architecture in the linear case reveals the role of the internal linear layers in leading to faster decay of a "collective weight variable" incorporating all layers, and the role of weight decay in breaking degeneracies and thus driving convergence along directions in which no decay would occur in its absence.
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.
Deep learning delay coordinate dynamics for chaotic attractors from partial observable data
A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system.
Data-driven low-dimensional dynamic model of Kolmogorov flow
At a model dimension of five for the pattern dynamics, as opposed to the full state dimension of 1024 (i. e. a 32x32 grid), accurate predictions are found for individual trajectories out to about two Lyapunov times, as well as for long-time statistics.
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.
Data-driven discovery of intrinsic dynamics
We demonstrate this approach on several high-dimensional systems with low-dimensional behavior.
Symmetry reduction for deep reinforcement learning active control of chaotic spatiotemporal dynamics
Many systems of flow control interest possess symmetries that, when neglected, can significantly inhibit the learning and performance of a naive deep RL approach.
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.
