2020
DOI: 10.3390/a13020030
|View full text |Cite
|
Sign up to set email alerts
|

Learning Manifolds from Dynamic Process Data

Abstract: Scientific data, generated by computational models or from experiments, are typically results of nonlinear interactions among several latent processes. Such datasets are typically high-dimensional and exhibit strong temporal correlations. Better understanding of the underlying processes requires mapping such data to a low-dimensional manifold where the dynamics of the latent processes are evident. While nonlinear spectral dimensionality reduction methods, e.g., Isomap, and their scalable variants, are conceptu… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2020
2020
2023
2023

Publication Types

Select...
2
2

Relationship

0
4

Authors

Journals

citations
Cited by 4 publications
(2 citation statements)
references
References 41 publications
0
2
0
Order By: Relevance
“…ISOMAP calculates residual variance by comparing geodesic distances, computed in G represented by matrix D G ( G is a neighborhood graph), to the pairwise distances of the mapped data Y , represented by matrix D Y [ 68 ], , Here, ρ is standard linear correlation coefficient, taken over all entries of D G and D Y . Fig.…”
Section: Resultsmentioning
confidence: 99%
“…ISOMAP calculates residual variance by comparing geodesic distances, computed in G represented by matrix D G ( G is a neighborhood graph), to the pairwise distances of the mapped data Y , represented by matrix D Y [ 68 ], , Here, ρ is standard linear correlation coefficient, taken over all entries of D G and D Y . Fig.…”
Section: Resultsmentioning
confidence: 99%
“…Feature engineering [21] and dimensionality reduction techniques [22] compress the high-dimensional image data to a small number of parameters. Recently, it was found that the learned low-dimensional manifold for the spinodal decomposition images is well correlated with the free energy barrier and average concentration [23,24]. Here we take the inverse problem approach; rather than creating a forward mapping from physical properties to patterns, we ask what physical properties can be accurately inferred from the patterns.…”
Section: Introductionmentioning
confidence: 99%