Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T14:12:25.276247Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:1908.03688.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T14:12:25.276247Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
54 of 54 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation bdf891b7-66f2-4da1-9f0a-f03fa7a35359 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena These equations become highly nonlinear when advection velocity and/or diffusion coefficient depend (s) on a system state, e.g., in the case of multiphase flows in porous media [1]
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4932606e-3565-450a-b599-5e6adced06ab · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 13fe0d97-babc-4281-a566-e1486aacac0c · outbound
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9740a433-52b7-4b7f-a20a-f4b7eccd9e3f · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9e4d06b2-70ba-4641-9cf5-774de813fe69 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c28727bc-a9d5-47f8-ac80-5c0e21e77a61 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Each column of Φ is a DMD mode corresponding to a particular eigenvalue in Λ
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation be02631a-8667-49b3-9b59-b3ac6fc4a1be · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena In th e semi-Lagrangian frame, (2.1) is written as dX(t) dt = f (u(X(t), t )), du(x, t ) dt ⏐ ⏐ ⏐ ⏐ x=X(t) = [ ∂ ∂x ( D(x, t, u ) ∂u(x, t ) ∂x )] ⏐ ⏐ ⏐ ⏐ x=X(t)
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2f24a8fe-d0fa-4a75-81db-0ba7ff6b2db5 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7f7bc694-8367-488e-ad82-1a473fa2a9bb · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8bddb73c-d8fd-4b78-9389-d9421133459f · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 07516543-62fc-46aa-a3e4-797c386d5a4a · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 223412f5-c226-4972-a28d-dff344a862db · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Eigenvalues are Λ and eigenvectors are Φ = UW.140 11
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7a6bd407-3281-4a24-9c42-7225065e3824 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8301a2af-5ed6-4aa2-bc18-fb973f6f4437 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena (3.10) In data-driven modeling, judicious selection of the observables is cr ucial to the accuracy and efficiency of a Koopman operator’s approximation
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 764eb6db-c927-4294-aa11-c17020d2c799 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena In all tests, the reference solutions are145 computed in the Eulerian framework using (2.3)
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fd34130e-5871-4e4b-ab4f-e29b06f75aaf · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9600ec9c-8980-4ab9-ad4f-8b6a84fd1e42 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena A new physic-aware DMD, based on the Lagrangian framework, is propos ed to overcome the shortcomings of reduced order models (ROMs) of advection-dominated nonlinear phenomena
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 736dfc09-2a4e-49aa-81d5-f1026f50bc1a · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0c60dcae-36ea-4807-aff1-0c937e94e380 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 20fae539-f26c-4b9c-9fff-f6e3aba0f660 · outbound
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 54d55276-aff3-44f6-9451-0712197c90d1 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Quarteroni, G
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d975f9f1-b0a6-4a00-a331-26f1d4ede109 · outbound
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4a1d9ed1-20dd-418f-af48-6ef1c40dbbe5 · outbound
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b97e63ec-071e-4226-bf52-567addb52a3d · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7df1e549-66c5-4f1c-a12a-d8b8af6c8997 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Volkwein, Model reduction using proper orthogonal decompo sition, Lecture Notes, Insti-250 tute of Mathematics and Scientific Computing, University of Graz
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 74d0f158-29e6-436a-86f9-babf911f75a3 · outbound
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 68b1ee3a-b85f-446f-8401-ce167a2fa1e1 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Chaturantabut, D
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d1d9509a-757c-438f-be5b-360edf5a11af · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e295143e-2cca-44ef-bf1f-49aca85a2e10 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Mezi´ c, Analysis of fluid flows via spectral properties of the Koopman operator, Annu
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4be10377-8d78-499b-964a-3dd1fa3251fe · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 80a16774-1ce3-4933-bad0-e548fdbcf9fe · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Mezi´ c, Spectral properties of dynamical systems, mode l reduction and decompositions, Nonlin
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 86c95bcf-a87b-4928-a1e9-293d57b7feda · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f8440ed6-c3a6-4796-90f6-874136638858 · outbound
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ae16b18d-a4ed-4a81-b740-bb85cb198597 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fc61eb44-f202-468e-86b3-ae0fbf46eccf · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ff3e0969-fec0-4cc3-ba6f-daa2b9019195 · outbound
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 53a8c579-0997-4798-b407-bdaff0969e49 · outbound
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c7e9a19f-43cb-427c-84e9-0ebd5579de39 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 37ba20f3-7448-48ae-bd9a-5d2db2aeb793 · outbound
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bedf80fb-6736-4615-9f14-420273175fd5 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 355c7669-fffa-4854-8317-9cc3ea989f8d · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Carlberg, Adaptive h-refinement for reduced-order mode ls, Int
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 01af5265-1030-43b5-bbf1-517e8ebdf1c6 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 74fdf3a9-6462-4d28-8f0a-71c57124c254 · outbound
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 81e2b480-fcb1-4034-8419-8461340865a2 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 66405d2f-d6dd-4c6a-87ab-241abd9277c4 · outbound
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 67ed291b-7cfa-4527-93b8-c1fab4e67b9a · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6592ab06-f3d8-4b29-8a60-fa06879ad9ef · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fb799556-d80e-4732-a154-982e3f9d66f4 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7cc00eb3-6ca4-4091-b695-2ae4d6089da1 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6fb360a9-ce07-44ab-9a82-4e503a3ce4a2 · outbound
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 94eec8ec-edf5-41cf-bde0-0d456fa5cb28 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Thiffeault, Advection-diffusion in Lagrangian coordinates, Phys
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4f7696f3-6664-41ed-aea5-6f510861c2ad · outbound
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d811bdd1-c483-4135-9e7b-da0d2abb1342 · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a87cf7a2-b3e5-4027-8460-fc77fb3b944d · outbound
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena Unresolved cited work
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
No inbound Pith citation observations are available.