Zobrazeno 1 - 10
of 84
pro vyhledávání: '"John Harlim"'
Autor:
Shixiao W. Jiang, John Harlim
Publikováno v:
Entropy, Vol 21, Iss 6, p 559 (2019)
In this paper, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie (or to which they are close). The proposed method represents the likelihood function using
Externí odkaz:
https://doaj.org/article/8d3d65531ed24d149a9c0eedf855892b
Publikováno v:
Journal of Computational Physics. 486:112132
In this paper, we propose a mesh-free numerical method for solving elliptic PDEs on unknown manifolds, identified with randomly sampled point cloud data. The PDE solver is formulated as a spectral method where the test function space is the span of t
Publikováno v:
Applied and Computational Harmonic Analysis. 54:145-175
In this paper, we extend the diffusion maps algorithm on a family of heat kernels that are either local (having exponential decay) or nonlocal (having polynomial decay), arising in various applications. For example, these kernels have been used as a
Autor:
Di Qi, John Harlim
Publikováno v:
SSRN Electronic Journal.
Publikováno v:
Geophysical Research Letters. 48
A simple and efficient Bayesian machine learning (BML) training and forecasting algorithm, which exploits only a 20-year short observational time series and an approximate prior model, is developed to predict the Ni\~no 3 sea surface temperature (SST
In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE on unknown smooth manifolds without and with boundaries. The core idea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eb2aa0241daed4ae5a74d3f9b1c69ca5
http://arxiv.org/abs/2105.13835
http://arxiv.org/abs/2105.13835
A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider is a supervised learning task of finding a regression function that takes a delay embedded observable to the o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95007e0d413bb4dcab83b18869060fb6
http://arxiv.org/abs/2007.04286
http://arxiv.org/abs/2007.04286
This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning problem of forecasting the time evolution of an observable under potentia
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b743d3f5d07eb2f37efc556398a52491
http://arxiv.org/abs/2002.07928
http://arxiv.org/abs/2002.07928
Publikováno v:
Inverse Problems. 38:035006
This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matérn-type Gaussian field priors that enable flexible modeling near the bo