Paper Citation Record · LEDGER

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure

As of 13 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2502.06865.

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

pith.paper-citation-record.v1
2502.06865 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T19:29:47.895711Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

38 of 38 outbound references displayed

verified exact0
verified fuzzy20
unresolved18
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4aae807d-5242-4708-8211-99b591a7a8ad · outbound

This paper cites Bhattacharya, Microstructure of martensite: why it forms and how it gives rise to the shape-memory effect, V ol.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Bhattacharya, Microstructure of martensite: why it forms and how it gives rise to the shape-memory effect, V ol

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.295094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f6269a25-098d-4350-8303-e90b314249fb · outbound

This paper cites Dacorogna, Direct methods in the calculus of variations, V ol.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Dacorogna, Direct methods in the calculus of variations, V ol

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.285560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f5edfc11-8711-44c2-b83e-09f265b08d66 · outbound

This paper cites Luskin, On the computation of crystalline microstructure, Acta numerica 5 (1996) 191–257.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Luskin, On the computation of crystalline microstructure, Acta numerica 5 (1996) 191–257

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.276449Z

Source-reported events for the cited work

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Observation 499fbce8-fa55-4bf1-94b6-0c51dace4cdd · outbound

This paper cites Carstensen, Ten remarks on nonconvex minimisation for phase transition simulations, Computer Methods in Applied Mechanics and Engineering 194 (2) (2005) 169–193.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Carstensen, Ten remarks on nonconvex minimisation for phase transition simulations, Computer Methods in Applied Mechanics and Engineering 194 (2) (2005) 169–193

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.266616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cea96b5e-1aaf-4a7a-94f3-8cb6e65f2332 · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:29:48.256556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a5b7452c-492c-4bfb-a9d4-65a9d995e709 · outbound

This paper cites Carstensen, Numerical analysis of microstructure, Theory and Numerics of Differential Equations: Durham 2000 (2001) 59–126.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Carstensen, Numerical analysis of microstructure, Theory and Numerics of Differential Equations: Durham 2000 (2001) 59–126

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.246739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 03c7666e-7a2e-4572-a2df-9230046dd093 · outbound

This paper cites Bartels, C.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Bartels, C

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.235955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d6a2bba4-709b-4279-a84a-a4fdabd1d053 · outbound

This paper cites Carstensen, P.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Carstensen, P

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.225964Z

Source-reported events for the cited work

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Observation 7c4fd29c-7079-41c4-970f-404fb7a835b5 · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:29:48.216421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9eac9fdf-f625-4b07-8576-eca58340595f · outbound

This paper cites Aranda, P.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Aranda, P

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.206996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0eeef94e-fd94-4b52-aef1-e83c177d6f9b · outbound

This paper cites Carstensen, T.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Carstensen, T

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.198029Z

Source-reported events for the cited work

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Observation cd51efdd-a27b-4d3b-b245-40cb60402c33 · outbound

This paper cites Hornik, M.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Hornik, M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.189022Z

Source-reported events for the cited work

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Observation 5a1b424a-c7bc-42c3-843d-dc4d9e06136c · outbound

This paper cites Hornik, Approximation capabilities of multilayer feedforward networks, Neural networks 4 (2) (1991) 251–257.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Hornik, Approximation capabilities of multilayer feedforward networks, Neural networks 4 (2) (1991) 251–257

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.818986Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1b8cb50-400f-4224-b3c9-5417fc63f7d1 · outbound

This paper cites Raissi, P.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Raissi, P

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.172805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 68cd2fb6-28a8-421b-9313-0b83b3a97b73 · outbound

This paper cites Sirignano, K.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Sirignano, K

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.824892Z

Source-reported events for the cited work

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Observation 686c45ab-f5db-41ae-b6ef-8f73563b4c13 · outbound

This paper cites Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.827842Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7551554b-15c1-4d6c-bbc4-70ff7f870925 · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.830561Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 773acfb8-c205-4eb0-85b9-501c54ce97d6 · outbound

This paper cites A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.833466Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 453068f4-5ee2-49d4-b3f8-a2118a5f0bee · outbound

This paper cites Rahaman, A.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Rahaman, A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.141770Z

Source-reported events for the cited work

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Observation fd1f0171-8346-4e28-a97c-c3e4b35be6eb · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.840190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2d81eaf-e4c3-4ee2-824e-03adaf273deb · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:29:48.125639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 792bce73-1579-459b-a7db-8c14fb39043a · outbound

This paper cites Tancik, P.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Tancik, P

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.114174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 338a0a20-d4e6-44d7-8c90-12f02164d6e7 · outbound

This paper cites Geifman, A.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Geifman, A

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.104678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ed07b979-db5d-4582-b33b-c260fffe33ea · outbound

This paper cites Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.852242Z

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Observation 11a773c2-218e-44e5-96dd-529c2adfca5c · outbound

This paper cites Weinan, B.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Weinan, B

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.093676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 65673a9f-2a07-47bb-81b2-991b133d47e8 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Adam: A Method for Stochastic Optimization

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.858382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e54a4fa9-c918-4c4e-b0e0-de87edd44647 · outbound

This paper cites Jacot, F.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Jacot, F

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.861466Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e4b5aa2-0426-41e1-9fa8-7508d601c8bb · outbound

This paper cites Gradient Descent Provably Optimizes Over-parameterized Neural Networks.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Gradient Descent Provably Optimizes Over-parameterized Neural Networks

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.864952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51d1afc3-2511-4b16-82ab-b8ef0c577c4c · outbound

This paper cites Chizat, E.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Chizat, E

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.075483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2150d0bc-ca16-4abd-b1aa-ca34501a6c3d · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:29:48.064278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bf423686-a842-4804-b0a9-381b960eb58e · outbound

This paper cites Arora, S.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Arora, S

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.874173Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66728b02-5b04-402e-ad94-045f768667ee · outbound

This paper cites Rahimi, B.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Rahimi, B

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.044745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 332bb91e-664e-4a84-81f0-d315a7ac5b6b · outbound

This paper cites Muller, Singular perturbations as a selection criterion for periodic minimizing sequences, Calc.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Muller, Singular perturbations as a selection criterion for periodic minimizing sequences, Calc

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.033026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bc4815dc-95cb-46b1-84c7-706406b6b8a4 · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:29:48.021832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a65b9d4f-c4ff-4e3c-8bc8-9792c7b9a316 · outbound

This paper cites Müller, Variational models for microstructure and phase transitions, Lecture Notes in Math.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Müller, Variational models for microstructure and phase transitions, Lecture Notes in Math

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:48.011385Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 890f7d11-42f3-4ca4-a2e9-99c3688f3fe9 · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:29:47.999721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 39e16500-51a2-405b-ab3f-9040d2d025c5 · outbound

This paper cites Dondl, B.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Dondl, B

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:29:47.988570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 23dc9bae-9179-481a-9d5e-7064665e48fd · outbound

This paper cites an unresolved cited work.

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-08T19:29:47.895711Z

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Unavailable: canonical work link unavailable.

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