Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems | Paper Citation Record

Observation be1bdf78-76af-44fb-bbc4-1f8343866699 · outbound

This paper cites Learn Singularly Perturbed Solutions via Homotopy Dynamics.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Learn Singularly Perturbed Solutions via Homotopy Dynamics

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:55:57.881339Z

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Observation e7524a8c-5951-4692-9744-d8e4c4df3c8f · outbound

This paper cites Univ., Fachbereich Mathematik und Informatik, 2004.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Univ., Fachbereich Mathematik und Informatik, 2004

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.515715Z

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Observation 12dfd1ac-89ef-4aa2-a49e-1b06f36243c1 · outbound

This paper cites Chunyan.Deep Learning for Studying Materials Stability and Solving Thermodynamically Consistent PDEs with Dynamic Boundary Conditions in Arbitrary Domains.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Chunyan.Deep Learning for Studying Materials Stability and Solving Thermodynamically Consistent PDEs with Dynamic Boundary Conditions in Arbitrary Domains

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.499972Z

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Observation ed520412-c971-4b05-bc06-717a332cc48e · outbound

This paper cites Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling

Reference 4

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Observation 392fa1d8-d61a-4d05-8adc-f2fb5568a420 · outbound

This paper cites A continuum framework for phase field with bulk-surface dynamics.Partial Differential Equations and Applications, 4(1):1, 2023.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems A continuum framework for phase field with bulk-surface dynamics.Partial Differential Equations and Applications, 4(1):1, 2023

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.484856Z

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Observation 8941efb4-925b-4d49-8e79-25c9b69c497d · outbound

This paper cites Generalized halton sequences in 2008: A comparative study.ACM Transactions on Modeling and Computer Simulation (TOMACS),19(4):1–31, 2009.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Generalized halton sequences in 2008: A comparative study.ACM Transactions on Modeling and Computer Simulation (TOMACS),19(4):1–31, 2009

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.468536Z

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Observation 63fd35c0-dbfa-4df1-8535-545df3b69cbf · outbound

This paper cites A cahn–hilliard model in bounded domains with permeable walls.Mathematical methods in the applied sciences, 29(17):2009–2036, 2006.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems A cahn–hilliard model in bounded domains with permeable walls.Mathematical methods in the applied sciences, 29(17):2009–2036, 2006

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.453131Z

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Observation 3ab96c1e-5711-4131-a731-d97a32a9a966 · outbound

This paper cites The non-isothermal allen-cahn equation with dynamic boundary conditions.Discrete Contin.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems The non-isothermal allen-cahn equation with dynamic boundary conditions.Discrete Contin

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.437021Z

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Observation 945318de-0b42-4daa-84c7-82aee160344a · outbound

This paper cites On the cahn–hilliard equation with irregular potentials and dynamic boundary conditions.Commun.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems On the cahn–hilliard equation with irregular potentials and dynamic boundary conditions.Commun

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.421020Z

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Observation 33cd0447-9406-49a8-a506-584dba9e763d · outbound

This paper cites Tcas-pinn: Physics-informed neural networks with a novel temporal causality-based adaptive sampling method.Chinese Physics B, 33(5):050701, 2024.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Tcas-pinn: Physics-informed neural networks with a novel temporal causality-based adaptive sampling method.Chinese Physics B, 33(5):050701, 2024

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.403812Z

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Observation 1e25e5e7-2311-4a9d-8309-8cb849382141 · outbound

This paper cites On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals.Numerische Mathematik, 2:84–90, 1960.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals.Numerische Mathematik, 2:84–90, 1960

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.387848Z

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Observation a9b5b6b6-590d-4947-92c6-51482ec0ee0f · outbound

This paper cites Springer Science & Business Media, 2013.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Springer Science & Business Media, 2013

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.371234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f1f5388e-8c51-4f92-90b4-811a623592ab · outbound

This paper cites Monte carlo methods for solving multivariable problems.Annals of the New York Academy of Sciences, 86(3):844–874, 1960.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Monte carlo methods for solving multivariable problems.Annals of the New York Academy of Sciences, 86(3):844–874, 1960

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.353448Z

Source-reported events for the cited work

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Observation ef27ae19-5bee-43a2-9a58-0eefeb3d0f13 · outbound

This paper cites Residual-quantile adjustment for adaptive training of physics-informed neural network.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Residual-quantile adjustment for adaptive training of physics-informed neural network

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.337933Z

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Observation 14bb1eb7-24fa-4943-b9ab-5140c03b618d · outbound

This paper cites Multiscale neural networks for approximating green’s functions.arXiv preprint arXiv:2410.18439, 2024.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Multiscale neural networks for approximating green’s functions.arXiv preprint arXiv:2410.18439, 2024

Reference 15

Resolution: verified exact; raw_fallback, observed 2026-08-06T17:55:57.614911Z

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Observation b9514814-c00c-4207-82fe-08f04ead4b71 · outbound

This paper cites Thermodynamically consistent models for coupled bulk and surface dynamics.Entropy, 24(11):1683, 2022.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Thermodynamically consistent models for coupled bulk and surface dynamics.Entropy, 24(11):1683, 2022

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.322182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f0b9f02f-e65a-43f8-b422-16f3fbde450b · outbound

This paper cites Thermodynamically consistent dynamic boundary conditions of phase field models.Communications in Mathematical Sciences, 21(3), 2023.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Thermodynamically consistent dynamic boundary conditions of phase field models.Communications in Mathematical Sciences, 21(3), 2023

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.304900Z

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Observation 6a3ede0d-8a25-42dd-9ff9-8927ee4c559d · outbound

This paper cites Constructing sobol sequences with better two-dimensional projections.SIAM Journal on Scientific Computing, 30(5):2635–2654, 2008.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Constructing sobol sequences with better two-dimensional projections.SIAM Journal on Scientific Computing, 30(5):2635–2654, 2008

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.288060Z

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Observation 86647882-f7d2-4bb5-ac9e-4a9be07d4109 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Adam: A Method for Stochastic Optimization

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:55.505147Z

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Observation a3b751b9-16a4-4b82-b776-2c3e338d1735 · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.Advances in neural information processing systems, 34:26548–26560, 2021.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Characterizing possible failure modes in physics-informed neural networks.Advances in neural information processing systems, 34:26548–26560, 2021

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:55.562853Z

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Observation df15c37c-bc8d-43e5-9963-b0ded7d89252 · outbound

This paper cites Wight and Jia Zhao.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Wight and Jia Zhao

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.259987Z

Source-reported events for the cited work

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Observation 7d51b2e5-2f3c-4a46-8bb0-80f5c026a0c8 · outbound

This paper cites Springer, 2021.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Springer, 2021

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.244223Z

Source-reported events for the cited work

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Observation 03e34bde-462b-4e93-8c59-af4cad22396c · outbound

This paper cites Deepxde: A deep learning library for solving differential equations.SIAM review, 63(1):208–228, 2021.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Deepxde: A deep learning library for solving differential equations.SIAM review, 63(1):208–228, 2021

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:55.746035Z

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Observation a0c13a41-c02f-4e11-8d44-313d26c0b843 · outbound

This paper cites An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:55:57.282938Z

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Observation 0d347032-8cc0-44ee-9cf6-ec537defa8f6 · outbound

This paper cites an unresolved cited work.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:58.218118Z

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Observation 122badb2-7bbd-47af-bd59-6f9bffd40908 · outbound

This paper cites Anovelsequentialmethodtotrainphysicsinformedneural networks for allen cahn and cahn hilliard equations.Computer Methods in Applied Mechanics and Engineering, 390:114474, 2022.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Anovelsequentialmethodtotrainphysicsinformedneural networks for allen cahn and cahn hilliard equations.Computer Methods in Applied Mechanics and Engineering, 390:114474, 2022

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.199904Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bfeb313e-9335-492f-8b34-f1992811db39 · outbound

This paper cites Efficient training of physics-informed neural networks via importance sampling.Computer-Aided Civil and Infras- tructure Engineering, 36(8):962–977, 2021.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Efficient training of physics-informed neural networks via importance sampling.Computer-Aided Civil and Infras- tructure Engineering, 36(8):962–977, 2021

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.183417Z

Source-reported events for the cited work

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Observation d4635db5-efb7-40ef-8aef-85259acdb50c · outbound

This paper cites Springer, 1999.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Springer, 1999

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:56.000287Z

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Observation 77ba045a-8c2b-4f17-9750-6d41b3814e25 · outbound

This paper cites Maximal regularity and asymptotic behav- ior of solutions for the cahn–hilliard equation with dynamic boundary conditions.Annali di Matematica Pura ed Applicata, 185:627–648, 2006.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Maximal regularity and asymptotic behav- ior of solutions for the cahn–hilliard equation with dynamic boundary conditions.Annali di Matematica Pura ed Applicata, 185:627–648, 2006

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.154667Z

Source-reported events for the cited work

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Observation d17bc861-dfa4-4a7d-8178-a368bf317f95 · outbound

This paper cites The Cahn-Hilliard equation with dynamic boundary conditions.Advances in Differential Equations, 8(1):83 – 110, 2003.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems The Cahn-Hilliard equation with dynamic boundary conditions.Advances in Differential Equations, 8(1):83 – 110, 2003

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.138934Z

Source-reported events for the cited work

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Observation f3dd7790-17ba-4139-8d60-2f55c8e5e9aa · outbound

This paper cites an unresolved cited work.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:56.132319Z

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Observation 84a784fb-83f8-42cb-9890-b41d7548b8ae · outbound

This paper cites On the distribution of points in a cube and the approximate evaluation of integrals.Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 7(4):784–802, 1967.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems On the distribution of points in a cube and the approximate evaluation of integrals.Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 7(4):784–802, 1967

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.112831Z

Source-reported events for the cited work

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Observation 59cabd8d-60d5-424c-a242-34a31325e0b1 · outbound

This paper cites Large sample properties of simulations using latin hypercube sampling.Tech- nometrics, 29(2):143–151, 1987.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Large sample properties of simulations using latin hypercube sampling.Tech- nometrics, 29(2):143–151, 1987

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.096012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 922e8b38-b9f3-4f25-8aff-45a852385747 · outbound

This paper cites A posteriori error estimation and adaptive mesh-refinement techniques.Jour- nal of Computational and Applied Mathematics, 50(1-3):67–83, 1994.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems A posteriori error estimation and adaptive mesh-refinement techniques.Jour- nal of Computational and Applied Mathematics, 50(1-3):67–83, 1994

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.078019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f71dac6f-f2f0-4c89-857a-ebfb03cf1e20 · outbound

This paper cites Respecting causality for training physics-informed neural networks.Computer Methods in Applied Mechanics and Engineering, 421:116813, 2024.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Respecting causality for training physics-informed neural networks.Computer Methods in Applied Mechanics and Engineering, 421:116813, 2024

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:56.478791Z

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Unavailable: canonical work link unavailable.

Observation c3f2648e-16a9-4e4f-8399-19095eb6579d · outbound

This paper cites an unresolved cited work.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:58.050764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fb4ea537-f3c3-40ff-9381-040adfb365ac · outbound

This paper cites Convergence to equilibrium for the cahn–hilliard equation with dynamic boundary conditions.Journal of differential equations, 204(2):511–531, 2004.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Convergence to equilibrium for the cahn–hilliard equation with dynamic boundary conditions.Journal of differential equations, 204(2):511–531, 2004

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.033919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d65c8d60-673a-4053-a47b-2da3afccaf02 · outbound

This paper cites Overview frequency principle/spectral bias in deep learning.Communications on Applied Mathematics and Computation, pages 1–38, 2024.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Overview frequency principle/spectral bias in deep learning.Communications on Applied Mathematics and Computation, pages 1–38, 2024

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.017581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8514a007-5697-4c47-aa64-87de03097121 · outbound

This paper cites Variational embedding domain method for thermo- dynamically consistent allen-cahn model in arbitrary domains.submitted.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Variational embedding domain method for thermo- dynamically consistent allen-cahn model in arbitrary domains.submitted

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:58.001228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation daf169a6-17ce-4575-bb55-db53772a3722 · outbound

This paper cites Elsevier, 2005.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Elsevier, 2005

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:57.983656Z

Source-reported events for the cited work

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Observation ad35037c-b3a0-48cc-afe7-6bf14de98b84 · outbound

This paper cites Multi-scale deep neural network (mscalednn) for solving poisson-boltzmann equation in complex domains.Communications in Computational Physics, 28(5):1970–2001, 2020.

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems Multi-scale deep neural network (mscalednn) for solving poisson-boltzmann equation in complex domains.Communications in Computational Physics, 28(5):1970–2001, 2020

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:57.966854Z

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