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Found 13 papers, 2 papers with code
Tree-based Learning for High-Fidelity Prediction of Chaos
Model-free forecasting of the temporal evolution of chaotic systems is crucial but challenging.
Analysis of tidal flows through the Strait of Gibraltar using Dynamic Mode Decomposition
The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features, influenced by topography, tidal forces, instabilities, and nonlinear hydraulic processes, all governed by the nonlinear equations of fluid motion.
Autoencoding for the 'Good Dictionary' of eigen pairs of the Koopman Operator
The encoded data produced by the deep autoencoder is diffeomorphic to a manifold of the dynamical system, and has a significantly lower dimension than the raw data.
Learning Transfer Operators by Kernel Density Estimation
These findings provide valuable insights for researchers and practitioners working on estimating the Frobenius-Perron operator and highlight the potential of density estimation techniques in this area of study.
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.
