Nonparametric Uncertainty Quantification for Stochastic Gradient Flows

DOI10.1137/14097940XzbMath1339.60067arXiv1407.6972MaRDI QIDQ2945163

John Harlim, Tyrus Berry

Publication date: 9 September 2015

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6972

zbMATH Keywords

nonlinear filteringdiffusion mapsnonlinear responsestatistical predictionstochastic gradient systemsnonparametric uncertainty quantification

Mathematics Subject Classification ID

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Forecasting turbulent modes with nonparametric diffusion models: learning from noisy data ⋮ Data-driven probability density forecast for stochastic dynamical systems ⋮ Reduced-space Gaussian process regression for data-driven probabilistic forecast of chaotic dynamical systems ⋮ On the Koopman Operator of Algorithms ⋮ Semiparametric modeling: correcting low-dimensional model error in parametric models ⋮ Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Local kernels and the geometric structure of data
• Dynamically orthogonal field equations for continuous stochastic dynamical systems
• Reconstruction of diffusion using spectral data from time series
• Variable bandwidth diffusion kernels
• Fundamentals of stochastic filtering
• Variable kernel density estimation
• A powerful numerical technique solving Zakai equation for nonlinear filtering
• Principal component analysis.
• Forecasting turbulent modes with nonparametric diffusion models: learning from noisy data
• Diffusion maps
• Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
• On Galerkin Approximations for the Zakai Equation with Diffusive and Point Process Observations
• Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
• Remarks on Some Nonparametric Estimates of a Density Function
• Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
• Spectral Methods for Uncertainty Quantification
• On Locally Adaptive Density Estimation
• Extracting macroscopic dynamics: model problems and algorithms
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability
• Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems
• Filtering Complex Turbulent Systems
• Information Theory and Stochastics for Multiscale Nonlinear Systems
• On Estimation of a Probability Density Function and Mode

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