Multi-Head Neural Operator for Modelling Interfacial Dynamics | Paper Citation Record

Observation 075da416-a5cb-4a27-8b35-a09ed4a838e2 · outbound

This paper cites Pore-scale modelling and sensitivity analyses of hydrogen- brine multiphase flow in geological porous media.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Pore-scale modelling and sensitivity analyses of hydrogen- brine multiphase flow in geological porous media

Reference 1

Resolution: verified exact; doi, observed 2026-08-06T19:04:49.083864Z

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 8e6d6ab2-d384-4f13-949e-4962ba281f63 · outbound

This paper cites An introduction to phase-field modeling of microstructure evolution.

Multi-Head Neural Operator for Modelling Interfacial Dynamics An introduction to phase-field modeling of microstructure evolution

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.112279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ff11205-926a-4bdd-82b3-09815b2d794f · outbound

This paper cites Phase-field models in materials science.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Phase-field models in materials science

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.116767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55e01121-7270-49e2-9925-e2fb02d2aaa7 · outbound

This paper cites Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities

Reference 4

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.120694Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88bd7ddf-25e0-4c17-ab93-2203cc10dd21 · outbound

This paper cites Quantitative phase-field modeling of solute trapping in rapid solidifi- cation.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Quantitative phase-field modeling of solute trapping in rapid solidifi- cation

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.124453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e711b094-5398-4153-8c68-1fd8c1d55f55 · outbound

This paper cites Phase field modeling and computer implementation: A review.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Phase field modeling and computer implementation: A review

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.128423Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e9affbf-1e82-47c0-8f44-320dc60d4cbf · outbound

This paper cites Phase field simulation of liquid phase separation with fluid flow.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Phase field simulation of liquid phase separation with fluid flow

Reference 7

Resolution: verified exact; doi, observed 2026-08-06T19:04:48.909083Z

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 df814f4e-590c-47f3-ac09-e80750f608cd · outbound

This paper cites Isogeometric analysis of hydrodynamics of vesicles using a mono- lithic phase-field approach.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Isogeometric analysis of hydrodynamics of vesicles using a mono- lithic phase-field approach

Reference 8

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:52.611865Z

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 9beafa6e-d493-4edd-b3bf-4d819a940755 · outbound

This paper cites Phase-field Navier–Stokes model for vesicle doublets hydro- dynamics in incompressible fluid flow.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Phase-field Navier–Stokes model for vesicle doublets hydro- dynamics in incompressible fluid flow

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.139799Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2ab4d81-cb6a-4162-8892-2e8de762abbd · outbound

This paper cites Hydrodynamics of multicomponent vesicles: A phase-field approach.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Hydrodynamics of multicomponent vesicles: A phase-field approach

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.143054Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80eefbc6-53ae-477d-8aa3-c7b7689db48c · outbound

This paper cites A monolithic finite element method for phase-field mod- eling of fully Eulerian fluid–structure interaction.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A monolithic finite element method for phase-field mod- eling of fully Eulerian fluid–structure interaction

Reference 11

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:52.353156Z

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 546a851e-53fc-4190-82a1-d1c04c9b6835 · outbound

This paper cites Phase-field models for microstructure evolution.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Phase-field models for microstructure evolution

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.150211Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39d43fb0-5a5c-4380-958b-1c2efe81fb7f · outbound

This paper cites Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces

Reference 13

Resolution: verified exact; doi, observed 2026-08-06T19:04:48.696565Z

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 1f935ac1-e445-40c9-b1f9-b8fa1f9d7ea2 · outbound

This paper cites Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces

Reference 14

Resolution: verified exact; doi, observed 2026-08-06T19:04:48.531697Z

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 776b5c88-1c71-40d6-ae69-e51db99c4f45 · outbound

This paper cites Accelerating phase-field-based mi- crostructure evolution predictions via surrogate models trained by machine learning methods.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Accelerating phase-field-based mi- crostructure evolution predictions via surrogate models trained by machine learning methods

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.159934Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b818b6c-0ed4-4ce3-8d91-bb9c94f737d2 · outbound

This paper cites A spectral element-based phase field method for incompressible two-phase flows.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A spectral element-based phase field method for incompressible two-phase flows

Reference 16

Resolution: verified exact; doi, observed 2026-08-06T19:04:48.323463Z

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 40140658-4340-4854-a10e-2c54bda25b17 · outbound

This paper cites A comparative review of XFEM, mixed FEM and phase-field models for quasi- brittle cracking.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A comparative review of XFEM, mixed FEM and phase-field models for quasi- brittle cracking

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.165924Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9805e8da-27af-4bf6-a1e0-e8e434eaa72a · outbound

This paper cites Learning two-phase microstructure evolution using neural operators and autoen- coder architectures.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Learning two-phase microstructure evolution using neural operators and autoen- coder architectures

Reference 18

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.169709Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3bac1611-36bc-4776-8998-495a4e95e5d8 · outbound

This paper cites an unresolved cited work.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.172596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5d6ef03-0680-437f-a207-f91d92fca1ae · outbound

This paper cites Non-linear model reduction for uncertainty quantification in large-scale inverse problems.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Non-linear model reduction for uncertainty quantification in large-scale inverse problems

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.175701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf8adbd3-8929-4c35-b263-f47b5a465b07 · outbound

This paper cites A dual mesh method with adaptivity for stress-constrained topology optimization.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A dual mesh method with adaptivity for stress-constrained topology optimization

Reference 21

Resolution: verified exact; doi, observed 2026-08-06T19:04:48.122198Z

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 517a0a05-ffcb-4e13-bd88-df632959ef9f · outbound

This paper cites Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.181799Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1a8985c-bcfb-4e24-9f23-1700e906a135 · outbound

This paper cites An efficient algorithm for 3D adaptive meshing.

Multi-Head Neural Operator for Modelling Interfacial Dynamics An efficient algorithm for 3D adaptive meshing

Reference 23

Resolution: verified exact; doi, observed 2026-08-06T19:04:47.925036Z

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 35154470-661a-453d-b7b4-91fb4f774166 · outbound

This paper cites Machine-learning-based data-driven discovery of nonlinear phase-field dynamics.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Machine-learning-based data-driven discovery of nonlinear phase-field dynamics

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.188239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2194883-c4f0-47d1-88e0-12f95951bc22 · outbound

This paper cites Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.191270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7157c72b-8506-4822-a9be-579fb1cf5d0a · outbound

This paper cites Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.194859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0a4ce27-a197-41a5-838a-94061f2f2bc8 · outbound

This paper cites Predicting CO2 plume migration in heterogeneous formations using conditional deep convolutional generative adversarial network.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Predicting CO2 plume migration in heterogeneous formations using conditional deep convolutional generative adversarial network

Reference 27

Resolution: verified exact; doi, observed 2026-08-06T19:04:47.732306Z

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 1009c44c-1b28-4c97-9074-76204b896f98 · outbound

This paper cites A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.200969Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cf036af-308a-41f5-a4ec-1fc6f9fd1d67 · outbound

This paper cites Multiphase flow prediction with deep neural networks.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Multiphase flow prediction with deep neural networks

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.203830Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b7bb951-0353-4ce9-9f42-7221be999afc · outbound

This paper cites CCSNet: a deep learning modeling suite for CO2 storage.

Multi-Head Neural Operator for Modelling Interfacial Dynamics CCSNet: a deep learning modeling suite for CO2 storage

Reference 30

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:52.002228Z

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 b0dba6c4-74f4-45c7-aba4-3e41c94d0ddd · outbound

This paper cites Accelerating phase-field predictions via recurrent neural net- works learning the microstructure evolution in latent space.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Accelerating phase-field predictions via recurrent neural net- works learning the microstructure evolution in latent space

Reference 31

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:51.820574Z

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 194f9c99-b734-421f-90f7-0afb1b969285 · outbound

This paper cites Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.213254Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 016e163e-f92f-4329-a730-32aea709028f · outbound

This paper cites Gplasdi: Gaussian process-based interpretable latent space dynamics identification through deep autoencoder.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Gplasdi: Gaussian process-based interpretable latent space dynamics identification through deep autoencoder

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.216921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb6fa3e0-3e0e-4e11-843a-d0341964b662 · outbound

This paper cites A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.220242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71f6cbdf-35e8-4523-8982-44f5fad06a7c · outbound

This paper cites Domain adaptation based transfer learning approach for solving PDEs on complex geometries.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Domain adaptation based transfer learning approach for solving PDEs on complex geometries

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.224451Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4ab7f81-59c3-46e4-bc77-70b276316460 · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.227501Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98824cf3-5167-46af-be24-01c678f77f4b · outbound

This paper cites Physics-constrained deep learning for high-dimensional surrogate modeling and uncer- tainty quantification without labeled data.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Physics-constrained deep learning for high-dimensional surrogate modeling and uncer- tainty quantification without labeled data

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.230601Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 379ba67c-5bfd-442c-be5c-47fa56d4955c · outbound

This paper cites SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks.

Multi-Head Neural Operator for Modelling Interfacial Dynamics SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.234231Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d03c9612-69ff-4074-88f1-f4c188730199 · outbound

This paper cites Variational energy based XPINNs for phase field analysis in brittle fracture.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Variational energy based XPINNs for phase field analysis in brittle fracture

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:04:47.536120Z

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 cca16063-1fd1-472d-bb3d-0ea2db27f838 · outbound

This paper cites Adaptive fourth-order phase field analysis using deep energy minimization.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Adaptive fourth-order phase field analysis using deep energy minimization

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.241857Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d87e4aa8-cab1-4a32-b184-6c6254319b47 · outbound

This paper cites Transfer learning enhanced physics informed neural network for phase-field modeling of fracture.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

Reference 41

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.244861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fbab0844-e043-45a2-af67-b838ebdfcda6 · outbound

This paper cites Deepnetbeam: A Framework for the Analysis of Functionally Graded Porous Beams.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Deepnetbeam: A Framework for the Analysis of Functionally Graded Porous Beams

Reference 42

Resolution: verified exact; doi, observed 2026-08-06T19:04:47.354588Z

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 39fc98af-5292-496e-8e58-9876826fa821 · outbound

This paper cites Deep residual U-net convolution neural networks with autore- gressive strategy for fluid flow predictions in large-scale geosystems.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Deep residual U-net convolution neural networks with autore- gressive strategy for fluid flow predictions in large-scale geosystems

Reference 43

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:51.270625Z

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 25e81a0d-ca88-491a-a4b9-c8bd37a00ab3 · outbound

This paper cites Deep-learning-based surrogate flow modeling and geologi- cal parameterization for data assimilation in 3D subsurface flow.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Deep-learning-based surrogate flow modeling and geologi- cal parameterization for data assimilation in 3D subsurface flow

Reference 44

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:51.036961Z

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 48e510a6-e340-4b86-b29c-3e3feb0db9e5 · outbound

This paper cites Physics-constrained deep learning for data assimilation of subsurface transport.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Physics-constrained deep learning for data assimilation of subsurface transport

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.257193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ab9d00d-7067-4dd5-a1e2-b0c23de4462f · outbound

This paper cites A deep learning method for the dynamics of classic and conservative Allen-Cahn equa- tions based on fully-discrete operators.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A deep learning method for the dynamics of classic and conservative Allen-Cahn equa- tions based on fully-discrete operators

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.260121Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de835123-a5dc-4e58-918e-8e188eab4967 · outbound

This paper cites Rethinking materials simulations: Blending direct numerical simulations with neural operators.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Rethinking materials simulations: Blending direct numerical simulations with neural operators

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.262953Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e45adbb-27ba-4a04-8341-53b37b25e16e · outbound

This paper cites U-FNO—An enhanced Fourier neural operator-based deep-learning model for multi- phase flow.

Multi-Head Neural Operator for Modelling Interfacial Dynamics U-FNO—An enhanced Fourier neural operator-based deep-learning model for multi- phase flow

Reference 48

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.265797Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 332d171c-1243-487f-9066-417bf4ded59d · outbound

This paper cites Simulating fluid flow in complex porous materials by integrating the governing equations with deep-layered machines.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Simulating fluid flow in complex porous materials by integrating the governing equations with deep-layered machines

Reference 49

Resolution: verified exact; doi, observed 2026-08-06T19:04:47.217997Z

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 fc4cf147-e32a-45e4-9d9c-212cf73014cb · outbound

This paper cites A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.271617Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6362a269-0732-4eac-9d9b-223e548da17e · outbound

This paper cites Physics-Informed Neural Networks for 2nd order ODEs with sharp gradients.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Physics-Informed Neural Networks for 2nd order ODEs with sharp gradients

Reference 51

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.274697Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 894fb16a-17cf-4e8f-8e7c-c4c5e872355d · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Characterizing possible failure modes in physics-informed neural networks

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.277430Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab36d346-d128-4605-b790-214d89bede79 · outbound

This paper cites Physics-informed neural networks with residual/gradient-based adaptive sam- pling methods for solving partial differential equations with sharp solutions.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Physics-informed neural networks with residual/gradient-based adaptive sam- pling methods for solving partial differential equations with sharp solutions

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.281187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acf1ff39-018e-4626-b49c-a462a1c61794 · outbound

This paper cites Nonlocal kernel network (NKN): A stable and resolution-independent deep neural network.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Nonlocal kernel network (NKN): A stable and resolution-independent deep neural network

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.283984Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2050993d-51a0-48e0-87ec-4306f93818a8 · outbound

This paper cites Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.286942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c06298f4-2b10-48e4-860f-1ac0a22cde46 · outbound

This paper cites Physics based deep learning for nonlinear two-phase flow in porous media.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Physics based deep learning for nonlinear two-phase flow in porous media

Reference 56

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:50.456999Z

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 9c943f43-42c0-4bec-8f52-6c9ddcad0369 · outbound

This paper cites Prediction of porous media fluid flow using physics informed neural networks.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Prediction of porous media fluid flow using physics informed neural networks

Reference 57

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:50.258418Z

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 124f5b20-8cbe-48dd-9c60-c03c57b1857f · outbound

This paper cites Physics informed deep learning for flow and transport in porous media.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Physics informed deep learning for flow and transport in porous media

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.296343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de2a2399-79c7-47a0-8886-0086828af2ed · outbound

This paper cites Model reduction and neural networks for parametric PDEs.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Model reduction and neural networks for parametric PDEs

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.299312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd1d135d-bed9-49e0-bbc1-9318e5412055 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.302335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae87dd75-116e-44ae-ab81-5ce0179733e9 · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.305291Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1141179-b165-45e1-8ac1-76149ed0a620 · outbound

This paper cites Variational Physics-informed Neural Operator (VINO) for Solving Partial Differential Equations.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Variational Physics-informed Neural Operator (VINO) for Solving Partial Differential Equations

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.307934Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9478410-f396-4080-9a60-74b7beab8eae · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Fourier Neural Operator for Parametric Partial Differential Equations

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.310738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b32697c-27ce-4638-b5b4-1950aa8fed03 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 64

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.313338Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b27f88b-2963-468d-911d-cec88c14388f · outbound

This paper cites LNO: Laplace Neural Operator for Solving Differential Equations.

Multi-Head Neural Operator for Modelling Interfacial Dynamics LNO: Laplace Neural Operator for Solving Differential Equations

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.316086Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2078436-39db-4acf-bf07-18288abd29a3 · outbound

This paper cites Convolutional Neural Operators for robust and accurate learning of PDEs.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Convolutional Neural Operators for robust and accurate learning of PDEs

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.319041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fa0b11b-18af-4796-b5bf-02ef5030de07 · outbound

This paper cites Solving parametric PDE problems with artificial neural networks.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Solving parametric PDE problems with artificial neural networks

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.321972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ba2c892-03c7-468f-8b81-4a242c4df0b2 · outbound

This paper cites POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition.

Multi-Head Neural Operator for Modelling Interfacial Dynamics POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition

Reference 68

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:50.005394Z

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 d13ec757-7630-4b17-8e0b-9d9555ee9490 · outbound

This paper cites Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals

Reference 69

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.327277Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 831cabce-71a8-49f2-9619-79bb56b8a407 · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to pdes.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Neural operator: Learning maps between function spaces with applications to pdes

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.329866Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49b19886-2606-4c90-adab-17c964cd9050 · outbound

This paper cites Fourier-spectral method for the phase-field equations.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Fourier-spectral method for the phase-field equations

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.332523Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de821b67-d64e-4cdb-8858-7d918c8f935c · outbound

This paper cites Energy-dissipative evolutionary deep operator neural networks.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Energy-dissipative evolutionary deep operator neural networks

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.335263Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4db5849-ad2f-4860-bba8-f658d4cbaf17 · outbound

This paper cites Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.337852Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06c335b5-17d9-4743-95ca-48e49fd1559a · outbound

This paper cites A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systems.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systems

Reference 74

Resolution: verified exact; doi, observed 2026-08-06T19:04:47.021591Z

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 a6dc3dcd-017b-40b1-b09e-355f0665455f · outbound

This paper cites A wavelet-Laplace variational technique for image decon- volution and inpainting.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A wavelet-Laplace variational technique for image decon- volution and inpainting

Reference 75

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:49.648760Z

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 8cac5a75-9c0d-4248-81fd-ca5d7cf483d3 · outbound

This paper cites A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening

Reference 76

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.346381Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7df47823-c18f-4535-b8dd-fd78f7541e6b · outbound

This paper cites Free energy of a nonuniform system. I. Interfacial free energy.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Free energy of a nonuniform system. I. Interfacial free energy

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.348919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 362a4cda-0e68-4c46-84b5-9f7b48c2fd4b · outbound

This paper cites Numerical simulation of a binary alloy of 2D Cahn–Hilliard model for phase sepa- ration.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Numerical simulation of a binary alloy of 2D Cahn–Hilliard model for phase sepa- ration

Reference 78

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T19:04:46.867551Z

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 808fe889-cb3d-4beb-8e19-b5f99c7c110c · outbound

This paper cites Continuum-scale modelling of polymer blends using the Cahn–Hilliard equa- tion: transport and thermodynamics.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Continuum-scale modelling of polymer blends using the Cahn–Hilliard equa- tion: transport and thermodynamics

Reference 79

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.354819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b51eb1a-61c5-4180-8438-2d334813c1e3 · outbound

This paper cites Two-dimensional Cahn–Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Two-dimensional Cahn–Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures

Reference 80

Resolution: verified exact; doi, observed 2026-08-06T19:04:46.659686Z

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 db42e2a3-90da-4e1c-ba3d-dcd7b6c96431 · outbound

This paper cites Turbulent superstructures in Rayleigh-B´ enard convec- tion.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Turbulent superstructures in Rayleigh-B´ enard convec- tion

Reference 81

Resolution: verified exact; doi, observed 2026-08-06T19:04:46.632452Z

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 ba615d21-2f03-42a8-b504-20e87ab44227 · outbound

This paper cites Hyperbolic chaos of Turing patterns.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Hyperbolic chaos of Turing patterns

Reference 82

Resolution: verified exact; doi, observed 2026-08-06T19:04:46.602234Z

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 80ee3c3b-596b-4737-96b0-1d5c06f9d951 · outbound

This paper cites Hydrodynamic fluctuations at the convective instability.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Hydrodynamic fluctuations at the convective instability

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.368305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0074659d-01c5-423a-8d79-444304416fec · outbound

This paper cites Nucleation and bulk crystallization in binary phase field theory.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Nucleation and bulk crystallization in binary phase field theory

Reference 84

Resolution: verified exact; doi, observed 2026-08-06T19:04:46.557369Z

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 209f181d-9605-4abe-bebf-a4780cafa485 · outbound

This paper cites Phase-field crystal modeling and classical density functional theory of freezing.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Phase-field crystal modeling and classical density functional theory of freezing

Reference 85

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.375022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c86f35d-0882-4bef-bf7e-cc94ce34fb6c · outbound

This paper cites A phase field crystal theory of the kinematics of dislocation lines.

Multi-Head Neural Operator for Modelling Interfacial Dynamics A phase field crystal theory of the kinematics of dislocation lines

Reference 86

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T19:04:49.316374Z

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 e82f1f90-85d2-402e-af9f-41654d115d8d · outbound

This paper cites Modeling elasticity in crystal growth.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Modeling elasticity in crystal growth

Reference 87

Resolution: verified exact; doi, observed 2026-08-06T19:04:46.520797Z

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 7563220a-f7d6-41c1-8b8f-25f6754165cd · outbound

This paper cites Semiconductor molecular-beam epitaxy at low temperatures.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Semiconductor molecular-beam epitaxy at low temperatures

Reference 88

Resolution: verified exact; doi, observed 2026-08-06T19:04:46.471411Z

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 58dd92f5-b1b8-46b6-b180-404e24e617bd · outbound

This paper cites Selective area epitaxy of GaN nanostructures: MBE growth and morphological analysis.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Selective area epitaxy of GaN nanostructures: MBE growth and morphological analysis

Reference 89

Resolution: verified exact; doi, observed 2026-08-06T19:04:46.440954Z

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 e6de23c1-f428-438d-82af-feba215b2ac6 · outbound

This paper cites An adaptive time-stepping strategy for the molecular beam epitaxy models.

Multi-Head Neural Operator for Modelling Interfacial Dynamics An adaptive time-stepping strategy for the molecular beam epitaxy models

Reference 90

Resolution: unresolved; no resolver link, observed 2026-08-06T19:04:46.391242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ffeef85d-f57d-4b20-bbe9-2079e7cf0586 · outbound

This paper cites Regularized linear schemes for the molecular beam epitaxy model with slope selection.

Multi-Head Neural Operator for Modelling Interfacial Dynamics Regularized linear schemes for the molecular beam epitaxy model with slope selection

Reference 91

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:04:46.394899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Coverage vector

Reference resolution

Outbound references

Pith citing papers