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08/05/2022
Quantum Mechanics for Closure of Dynamical Systems
We propose a scheme for data-driven parameterization of unresolved dimen...
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06/27/2022
Data Assimilation in Operator Algebras
We develop an algebraic framework for sequential data assimilation of pa...
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04/30/2021
Graph-theoretic algorithms for Kolmogorov operators: Approximating solutions and their gradients in elliptic and parabolic problems on manifolds
We employ kernel-based approaches that use samples from a probability di...
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07/08/2020
Kernel-based Prediction of Non-Markovian Time Series
A nonparametric method to predict non-Markovian time series of partially...
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05/13/2020
Kernel Analog Forecasting: Multiscale Test Problems
Data-driven prediction is becoming increasingly widespread as the volume...
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04/05/2020
An information-geometric approach to feature extraction and moment reconstruction in dynamical systems
We propose a dimension reduction framework for feature extraction and mo...
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02/18/2020
Bridging data science and dynamical systems theory
This short review describes mathematical techniques for statistical anal...
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05/30/2019