Search Results for author: Erik M. Bollt

Found 10 papers, 2 papers with code

Learning Transfer Operators by Kernel Density Estimation

1 code implementation1 Aug 2022 Sudam Surasinghe, Jeremie Fish, Erik M. Bollt

Inference of transfer operators from data is often formulated as a classical problem that hinges on the Ulam method.

Density Estimation

Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling

no code implementations14 Feb 2022 Yonggi Park, Kelum Gajamannage, Dilhani I. Jayathilake, Erik M. Bollt

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.

Time Series Analysis

Randomized Projection Learning Method forDynamic Mode Decomposition

no code implementations22 Sep 2021 Sudam Surasinghe, Erik M. Bollt

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

no code implementations6 Feb 2020 Sudam Surasinghe, Erik M. Bollt

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.

Causal Inference

An information-theoretic, all-scales approach to comparing networks

2 code implementations10 Apr 2018 James P. Bagrow, Erik M. Bollt

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

no code implementations21 Jul 2017 Kelum Gajamannage, Randy Paffenroth, Erik M. Bollt

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.

Dimensionality Reduction

Go With the Flow, on Jupiter and Snow. Coherence From Model-Free Video Data without Trajectories

no code implementations25 Aug 2016 Abd AlRahman AlMomani, Erik M. Bollt

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

no code implementations23 Sep 2015 Kelum Gajamannage, Erik M. Bollt

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

no code implementations13 Aug 2015 Kelum Gajamannage, Sachit Butail, Maurizio Porfiri, Erik M. Bollt

Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates.

Dimensionality Reduction

Identifying manifolds underlying group motion in Vicsek agents

no code implementations12 Aug 2015 Kelum Gajamannage, Sachit Butail, Maurizio Porfiri, Erik M. Bollt

In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents.

Dimensionality Reduction

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