Dynamic Mode Decomposition: Theory and Data Reconstruction

Bernhard Eberhardt; Daniel Weiskopf; Tim Krake

RECORD

Dynamic Mode Decomposition: Theory and Data Reconstruction

Tim Krake, Daniel Weiskopf, Bernhard Eberhardt

Numerical Analysis · Submitted 23 Sep 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our main result is the exact reconstruction property.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,707 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide a systematic advancement of these and examine the interrelations. In addition, several results of each variant are proven. Our main result is the exact reconstruction property. To this end, a new modification of scaling factors is presented and a new concept of an error scaling is introduced to guarantee an error-free reconstruction of the data.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena.	background 1.00	0.06	0.02	asserted 1.00
s1	In this paper, we perform a comprehensive theoretical analysis of various variants of DMD.	contribution 1.00	0.94	0.02	asserted 0.98
s2	We provide a systematic advancement of these and examine the interrelations.	contribution 0.99	0.91	0.03	asserted 0.97
s3	In addition, several results of each variant are proven.	contribution 0.85	0.91	0.03	asserted 1.00
s4	Our main result is the exact reconstruction property.	result 0.91	0.90	0.97	asserted 1.00
s5	To this end, a new modification of scaling factors is presented and a new concept of an error scaling is introduced to guarantee an error-free reconstruction of the data.	contribution 0.51	0.95	0.22	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide a systematic advancement of these and examine the interrelations. In addition, several results of each variant are proven. Our main result is the exact reconstruction property. To this end, a new modification of scaling factors is presented and a new concept of an error scaling is introduced to guarantee an error-free reconstruction of the data.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Uses its method or tool 1 paper

The new definition of amplitudes, which uses the second snapshot instead of the first one for the reconstruction, was introduced by Krake et al. [ref] .

Visualization and Selection of Dynamic Mode Decomposition Components for Unsteady Flow · DMD Algorithm · 0.95

Cites it as background 1 paper

Before formulating the algorithm of DMD, we summarize the concepts of DMD [ref] and compare them with DFT.

Visualization and Selection of Dynamic Mode Decomposition Components for Unsteady Flow · Mathematical Foundation · 0.98

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.