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Found 10 papers, 2 papers with code
Learning Transfer Operators by Kernel Density Estimation
Inference of transfer operators from data is often formulated as a classical problem that hinges on the Ulam method.
Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling
Specifically, we analyze the performance of RNNs applied to three tasks: reconstruction of correct Lorenz solutions for a system with a formulation error, reconstruction of corrupted collective motion trajectories, and forecasting of streamflow time series possessing spikes, representing three fields, namely, ordinary differential equations, collective motion, and hydrological modeling, respectively.
Randomized Projection Learning Method forDynamic Mode Decomposition
In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in reduced dimensional space.
On Geometry of Information Flow for Causal Inference
Our main contribution will be to develop analysis tools that will allow a geometric interpretation of information flow as a causal inference indicated by positive transfer entropy.
An information-theoretic, all-scales approach to comparing networks
The Portrait Divergence reveals important characteristics of multilayer and temporal networks extracted from data.
Social and Information Networks Information Theory Information Theory Data Analysis, Statistics and Probability Physics and Society
A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics
Herein, we propose a framework for nonlinear dimensionality reduction that generates a manifold in terms of smooth geodesics that is designed to treat problems in which manifold measurements are either sparse or corrupted by noise.
Go With the Flow, on Jupiter and Snow. Coherence From Model-Free Video Data without Trajectories
We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking.
Detecting phase transitions in collective behavior using manifold's curvature
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure.
Dimensionality Reduction of Collective Motion by Principal Manifolds
Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates.
Identifying manifolds underlying group motion in Vicsek agents
In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents.
