Paper Citation Record · LEDGER

Variational volume reconstruction with the Deep Ritz Method

As of 21 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 1 inbound Pith citation observation for arXiv:2508.08309.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.08309 v1

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T22:40:13.115598Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T23:34:48.867421Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

48 of 48 outbound references displayed

verified exact6
verified fuzzy32
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f85a2de9-37ff-4cfa-bd55-3ac407a33d2c · outbound

This paper cites A deep learning energy method for hyperelasticity and viscoelasticity.

Variational volume reconstruction with the Deep Ritz Method A deep learning energy method for hyperelasticity and viscoelasticity

Reference 1

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T22:40:13.457129Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e00f914c-0110-40fb-9ed4-64ec2644f225 · outbound

This paper cites Arigovindan, M.

Variational volume reconstruction with the Deep Ritz Method Arigovindan, M

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.893349Z

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Observation efe5aba9-3283-4d1c-910f-f6768c2c3691 · outbound

This paper cites Three-dimensional reconstruction of complex shapes based on the Delaunay triangulation.

Variational volume reconstruction with the Deep Ritz Method Three-dimensional reconstruction of complex shapes based on the Delaunay triangulation

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.881820Z

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Observation 81c5001d-1737-4c4a-b2d8-02c876315832 · outbound

This paper cites Volume Reconstruction from Slices.

Variational volume reconstruction with the Deep Ritz Method Volume Reconstruction from Slices

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.870170Z

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Observation 82371950-8284-461e-b292-f9206c3ba5e2 · outbound

This paper cites Learning phase field mean curvature flows with neural networks.

Variational volume reconstruction with the Deep Ritz Method Learning phase field mean curvature flows with neural networks

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:40:13.435799Z

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Observation 3968f739-e61f-4365-9101-aed980d98861 · outbound

This paper cites A penalized Allen-Cahn equation for the mean curvature flow of thin structures.

Variational volume reconstruction with the Deep Ritz Method A penalized Allen-Cahn equation for the mean curvature flow of thin structures

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T22:40:09.421273Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d3cfe85-b63e-4d44-bda9-f4271005502a · outbound

This paper cites Variational image segmentation model coupled with image restoration achievements.

Variational volume reconstruction with the Deep Ritz Method Variational image segmentation model coupled with image restoration achievements

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.858603Z

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Observation 6783c5f7-ba40-46ba-84d1-40cf1a596d89 · outbound

This paper cites an unresolved cited work.

Variational volume reconstruction with the Deep Ritz Method Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:13.847599Z

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Observation efb4c909-7206-491a-9ae6-a7f8ebde6ca8 · outbound

This paper cites Introduction to variational image-processing models and applications.

Variational volume reconstruction with the Deep Ritz Method Introduction to variational image-processing models and applications

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-05T22:40:09.667055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a9ed17e-3848-49ee-bfa8-4803b2b7ea1f · outbound

This paper cites Existence of equilibria for the cahn-hilliard equation via local minimizers of the perimeter.

Variational volume reconstruction with the Deep Ritz Method Existence of equilibria for the cahn-hilliard equation via local minimizers of the perimeter

Reference 10

Resolution: verified exact; doi, observed 2026-08-05T22:40:13.154566Z

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Observation df10f5b1-65f3-4e52-a32a-a767a29f4e95 · outbound

This paper cites Surface Reconstruction from Scattered Point via RBF Interpolation on GPU.

Variational volume reconstruction with the Deep Ritz Method Surface Reconstruction from Scattered Point via RBF Interpolation on GPU

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:40:13.313081Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b3fb651f-2b33-4768-bc7c-711d9cb5f7a1 · outbound

This paper cites Surface Reconstruction from Sparse and Mutually Intersected Contours for Freehand 3D Ultrasound Using Variational Method.

Variational volume reconstruction with the Deep Ritz Method Surface Reconstruction from Sparse and Mutually Intersected Contours for Freehand 3D Ultrasound Using Variational Method

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.835473Z

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Observation 0df2f3f3-1461-49cb-88f9-c59f00397b21 · outbound

This paper cites Image Super-Resolution Using Deep Convolutional Networks.

Variational volume reconstruction with the Deep Ritz Method Image Super-Resolution Using Deep Convolutional Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-05T22:40:10.006495Z

Source-reported events for the cited work

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Observation c27d3611-e021-44d7-9985-41930c1338d3 · outbound

This paper cites A level set formulation for Willmore flow.

Variational volume reconstruction with the Deep Ritz Method A level set formulation for Willmore flow

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.823528Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 70c6d535-50bf-4fa8-b1a1-3f1a3868fa91 · outbound

This paper cites Super-resolution reconstruction of single anisotropic 3D MR images using residual convolutional neural network.

Variational volume reconstruction with the Deep Ritz Method Super-resolution reconstruction of single anisotropic 3D MR images using residual convolutional neural network

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.812205Z

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Observation a3fe1c0e-4784-4e5a-af38-736509c57da2 · outbound

This paper cites The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems.

Variational volume reconstruction with the Deep Ritz Method The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-05T22:40:10.237745Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf1bad7e-945c-41d9-9189-3fb3c63eb69d · outbound

This paper cites Miller, Harini Veeraraghavan, Bernd Freisleben, Alexandra J.

Variational volume reconstruction with the Deep Ritz Method Miller, Harini Veeraraghavan, Bernd Freisleben, Alexandra J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.800289Z

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Observation 7b51389c-c899-4597-889f-6ddaf1233a3b · outbound

This paper cites Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow.

Variational volume reconstruction with the Deep Ritz Method Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:40:13.257321Z

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Observation a658eab1-35e4-4b78-a6f4-075d492a2947 · outbound

This paper cites an unresolved cited work.

Variational volume reconstruction with the Deep Ritz Method Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:13.789141Z

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Observation 1823f1bc-5c41-456f-8407-48442f992df5 · outbound

This paper cites Jimack, and René de Borst.

Variational volume reconstruction with the Deep Ritz Method Jimack, and René de Borst

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.777404Z

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Observation ec89911c-57b7-41c8-80db-f020372608f4 · outbound

This paper cites Giannakopoulos, Matthew J.

Variational volume reconstruction with the Deep Ritz Method Giannakopoulos, Matthew J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.765932Z

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Observation 96709d6c-76eb-47e2-8369-d0cd8da6d1db · outbound

This paper cites A simple shape transformation method based on phase-field model.

Variational volume reconstruction with the Deep Ritz Method A simple shape transformation method based on phase-field model

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.753664Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 08768486-0b9c-4e12-a20b-c547a87392b3 · outbound

This paper cites A Variational Approach for Volume -to- Slice Registration.

Variational volume reconstruction with the Deep Ritz Method A Variational Approach for Volume -to- Slice Registration

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.741150Z

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Observation 6ed39cde-938f-4b78-9d54-ff038e696803 · outbound

This paper cites an unresolved cited work.

Variational volume reconstruction with the Deep Ritz Method Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:13.729592Z

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Observation ddc27206-01c6-4291-9836-dd4a319f21e4 · outbound

This paper cites Osher, and R.

Variational volume reconstruction with the Deep Ritz Method Osher, and R

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.717942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1368cb6f-ba83-4c4e-92b3-8a10dc25b3e5 · outbound

This paper cites C1-continuous Terrain Reconstruction from Sparse Contours.

Variational volume reconstruction with the Deep Ritz Method C1-continuous Terrain Reconstruction from Sparse Contours

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.706025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation eaac1a4b-77bf-48d8-86bc-10d9ef15945c · outbound

This paper cites Three-dimensional volume reconstruction from multi-slice data using a shape transformation.

Variational volume reconstruction with the Deep Ritz Method Three-dimensional volume reconstruction from multi-slice data using a shape transformation

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.693926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ba34c7fc-74bc-4fc1-9f48-29d224069373 · outbound

This paper cites Accurate Surface Reconstruction in 3D Using Two -dimensional Parallel Cross Sections.

Variational volume reconstruction with the Deep Ritz Method Accurate Surface Reconstruction in 3D Using Two -dimensional Parallel Cross Sections

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.681263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 07d559a1-3c8c-40bb-bec3-9a3a86bdcc6c · outbound

This paper cites An efficient volume repairing method by using a modified Allen - Cahn equation.

Variational volume reconstruction with the Deep Ritz Method An efficient volume repairing method by using a modified Allen - Cahn equation

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.669082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 12c58a5d-3f1f-4ee4-8fac-54ab1684a687 · outbound

This paper cites Three-dimensional volume reconstruction from slice data using phase-field models.

Variational volume reconstruction with the Deep Ritz Method Three-dimensional volume reconstruction from slice data using phase-field models

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.657025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8a827e8e-1826-430f-9724-b2e5f4f9b91f · outbound

This paper cites Weighted 3D volume reconstruction from series of slice data using a modified Allen – Cahn equation.

Variational volume reconstruction with the Deep Ritz Method Weighted 3D volume reconstruction from series of slice data using a modified Allen – Cahn equation

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.644630Z

Source-reported events for the cited work

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Observation ef9be59a-d8d7-476c-acf8-d60a6c2e6940 · outbound

This paper cites Multicomponent volume reconstruction from slice data using a modified multicomponent Cahn – Hilliard system.

Variational volume reconstruction with the Deep Ritz Method Multicomponent volume reconstruction from slice data using a modified multicomponent Cahn – Hilliard system

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.632283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 222aa050-2cbc-4d6f-8362-aa3591743cb5 · outbound

This paper cites Measuring three-dimensional tibiofemoral kinematics using dual-slice real-time magnetic resonance imaging.

Variational volume reconstruction with the Deep Ritz Method Measuring three-dimensional tibiofemoral kinematics using dual-slice real-time magnetic resonance imaging

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.620333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c92e896a-f828-4d7e-86bd-bc22df9f42e9 · outbound

This paper cites Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials, August 2023.

Variational volume reconstruction with the Deep Ritz Method Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials, August 2023

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.608330Z

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Observation ea7900fd-264e-410a-af6f-6021ee5fdfc4 · outbound

This paper cites Deep Ritz method with adaptive quadrature for linear elasticity.

Variational volume reconstruction with the Deep Ritz Method Deep Ritz method with adaptive quadrature for linear elasticity

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.595840Z

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Observation 2744dacd-4495-4dd0-9211-2c857cea71fd · outbound

This paper cites Manav, R.

Variational volume reconstruction with the Deep Ritz Method Manav, R

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.582802Z

Source-reported events for the cited work

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Observation 4e061e39-ed36-49f2-b573-fbaac6f84230 · outbound

This paper cites NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis.

Variational volume reconstruction with the Deep Ritz Method NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-05T22:40:12.392720Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95fc97ea-895d-433c-83b0-955a948d504a · outbound

This paper cites Real time 3D reconstruction for enhanced cybersecurity of additive manufacturing processes.

Variational volume reconstruction with the Deep Ritz Method Real time 3D reconstruction for enhanced cybersecurity of additive manufacturing processes

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.570674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 40f67a16-c757-4c5b-8964-e92809a03457 · outbound

This paper cites Interpolating Implicit Surfaces From Scattered Surface Data Using Compactly Supported Radial Basis Functions.

Variational volume reconstruction with the Deep Ritz Method Interpolating Implicit Surfaces From Scattered Surface Data Using Compactly Supported Radial Basis Functions

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.558148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ee9d4c52-8438-4bd5-acf2-4e9d72b96c40 · outbound

This paper cites Brain MRI super-resolution using deep 3D convolutional networks.

Variational volume reconstruction with the Deep Ritz Method Brain MRI super-resolution using deep 3D convolutional networks

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.543998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 330f32ad-01a4-40db-8006-58abad10dc20 · outbound

This paper cites A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction.

Variational volume reconstruction with the Deep Ritz Method A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction

Reference 41

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T22:40:13.217618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 51a62a8a-d5d1-4189-bda2-dcc93835e1aa · outbound

This paper cites Variational methods with application to medical image segmentation: A survey.

Variational volume reconstruction with the Deep Ritz Method Variational methods with application to medical image segmentation: A survey

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.530402Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c59561b8-3f23-4617-b73d-2620dee49d48 · outbound

This paper cites Variational Methods for Image Segmentation.

Variational volume reconstruction with the Deep Ritz Method Variational Methods for Image Segmentation

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.515482Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c41453ce-0b66-48ca-9b35-49b48ea6bd20 · outbound

This paper cites Sukumar and Ankit Srivastava.

Variational volume reconstruction with the Deep Ritz Method Sukumar and Ankit Srivastava

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.501143Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9fd0d268-f888-40d9-9955-0eed4a43f9ec · outbound

This paper cites Deep variational network for rapid 4D flow MRI reconstruction.

Variational volume reconstruction with the Deep Ritz Method Deep variational network for rapid 4D flow MRI reconstruction

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:40:13.197274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c75c1127-00c2-4f6a-a5c9-e6887539673c · outbound

This paper cites Young, Yaël Balbastre, Bruce Fischl, Polina Golland, and Juan Eugenio Iglesias.

Variational volume reconstruction with the Deep Ritz Method Young, Yaël Balbastre, Bruce Fischl, Polina Golland, and Juan Eugenio Iglesias

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.485660Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 79e52bef-9af7-4091-9918-b90fb2a5693c · outbound

This paper cites Super-Resolution Surface Reconstruction from Few Low-Resolution Slices.

Variational volume reconstruction with the Deep Ritz Method Super-Resolution Surface Reconstruction from Few Low-Resolution Slices

Reference 47

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:40:13.175797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 46dc6429-e93e-49cb-9b70-c0f6f758bed8 · outbound

This paper cites Image Segmentation Using Euler ’s Elastica as the Regularization.

Variational volume reconstruction with the Deep Ritz Method Image Segmentation Using Euler ’s Elastica as the Regularization

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:13.470772Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 243a5312-46df-40a5-b905-adaa0ff96276 · inbound

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization cites this paper.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Variational volume reconstruction with the Deep Ritz Method

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:48.867421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.