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1 code implementation • 1 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.

no code implementations • 14 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.

no code implementations • 22 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.

no code implementations • 6 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.

2 code implementations • 10 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

no code implementations • 21 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.

no code implementations • 25 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.

no code implementations • 23 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.

no code implementations • 13 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.

no code implementations • 12 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.

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