RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations | Paper Citation Record

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Highly accurate protein structure prediction with alphafold

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Prob- abilistic weather forecasting with machine learning

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Denoising diffusion probabilistic models

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This paper cites Operator learning for predicting multiscale bubble growth dynamics.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Operator learning for predicting multiscale bubble growth dynamics

Reference 4

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This paper cites Systems biology informed deep learning for inferring parameters and hidden dynamics.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Systems biology informed deep learning for inferring parameters and hidden dynamics

Reference 5

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This paper cites Promising directions of machine learning for partial differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Promising directions of machine learning for partial differential equations

Reference 6

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This paper cites Artifi- cial intelligence for partial differential equations in computational mechanics: A review.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Artifi- cial intelligence for partial differential equations in computational mechanics: A review

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This paper cites Neural operator prediction of linear instability waves in high-speed boundary layers.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Neural operator prediction of linear instability waves in high-speed boundary layers

Reference 8

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This paper cites Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks

Reference 9

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This paper cites A noninvasive method for determining elastic parameters of valve tissue using physics-informed neural networks.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations A noninvasive method for determining elastic parameters of valve tissue using physics-informed neural networks

Reference 10

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This paper cites Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators

Reference 11

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This paper cites Data-driven iden- tification of parametric partial differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Data-driven iden- tification of parametric partial differential equations

Reference 12

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Data-driven deep learning of partial differential equations in modal space

Reference 13

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This paper cites Data driven approximation of parametrized PDEs by reduced basis and neural networks.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Data driven approximation of parametrized PDEs by reduced basis and neural networks

Reference 14

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Observation 652bbe71-1b0a-47bb-b91b-9da1f6aea301 · outbound

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

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 15

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This paper cites DeepXDE: A deep learning library for solving differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations DeepXDE: A deep learning library for solving differential equations

Reference 16

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This paper cites Physics-informed machine learning.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Physics-informed machine learning

Reference 17

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This paper cites Scientific machine learning through physics–informed neural networks: Where we are and what’s next.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Scientific machine learning through physics–informed neural networks: Where we are and what’s next

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This paper cites Physics-informed neural networks for inverse problems in nano-optics and metamaterials.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Physics-informed neural networks for inverse problems in nano-optics and metamaterials

Reference 19

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This paper cites PINNacle: A comprehensive benchmark of physics- informed neural networks for solving PDEs.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations PINNacle: A comprehensive benchmark of physics- informed neural networks for solving PDEs

Reference 20

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Automatic differentiation in PyTorch

Reference 21

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This paper cites fPINNs: Fractional physics-informed neural networks.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations fPINNs: Fractional physics-informed neural networks

Reference 22

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This paper cites Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

Reference 23

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Physics-informed neural networks with hard constraints for inverse design

Reference 24

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Dive into Deep Learning

Reference 25

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Physics-informed multi-LSTM networks for meta- modeling of nonlinear structures

Reference 26

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Approximation theory of the MLP model in neural networks

Reference 27

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 28

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Koop- man neural operator as a mesh-free solver of non-linear partial differential equations

Reference 29

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Approximations of continuous functionals by neural networks with application to dynamic systems

Reference 30

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This paper cites A comprehensive and fair comparison of two neural operators (with practical extensions) based on F AIR data.Computer Methods in Applied Mechanics and Engineering, 393:114778, 2022.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations A comprehensive and fair comparison of two neural operators (with practical extensions) based on F AIR data.Computer Methods in Applied Mechanics and Engineering, 393:114778, 2022

Reference 31

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This paper cites Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport

Reference 32

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This paper cites Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness

Reference 33

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This paper cites A scalable framework for learning the geometry-dependent solution operators of partial differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations A scalable framework for learning the geometry-dependent solution operators of partial differential equations

Reference 34

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This paper cites DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approxi- mation by neural networks.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approxi- mation by neural networks

Reference 35

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This paper cites DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

Reference 36

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This paper cites Stochastic operator network: A stochastic maximum principle based approach to operator learning.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Stochastic operator network: A stochastic maximum principle based approach to operator learning

Reference 37

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Observation 73444aa6-3ea8-41cf-aeb5-bd8d599f40d7 · outbound

This paper cites Fundiff: Diffusion models over function spaces for physics-informed generative modeling.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Fundiff: Diffusion models over function spaces for physics-informed generative modeling

Reference 38

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This paper cites Quantum DeepONet: Neural operators accelerated by quantum computing.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Quantum DeepONet: Neural operators accelerated by quantum computing

Reference 39

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Observation f159f134-6a07-41b9-b451-2d4402a39cfa · outbound

This paper cites MIONet: Learning multiple-input operators via tensor product.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations MIONet: Learning multiple-input operators via tensor product

Reference 40

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Observation 579b8d1f-4920-4e90-9f3a-83a2f17c957e · outbound

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

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Fourier Neural Operator for Parametric Partial Differential Equations

Reference 41

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RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration

Reference 42

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Observation 2fd71e35-759d-4543-8ddc-c2a67037beed · outbound

This paper cites Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems

Reference 43

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This paper cites Laplace neural operator for solving differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Laplace neural operator for solving differential equations

Reference 44

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Observation 5e9ec449-d0c7-4f3f-a063-c987daffb5da · outbound

This paper cites Efficient training of physics-informed neural networks via importance sampling.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Efficient training of physics-informed neural networks via importance sampling

Reference 45

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This paper cites Gradient-enhanced physics- informed neural networks for forward and inverse pde problems.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Gradient-enhanced physics- informed neural networks for forward and inverse pde problems

Reference 46

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Observation 76193420-4614-401e-b55d-8394267cbab3 · outbound

This paper cites A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 47

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Observation 1555c74a-fe4e-4914-a321-da5218faa833 · outbound

This paper cites Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks

Reference 48

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Observation d0600118-5bee-4d9c-9b19-5179938cc9a0 · outbound

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

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-05T12:50:03.059365Z

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Observation f9622b03-1486-427d-9ed6-8fc4fd35c006 · outbound

This paper cites Importance sampling: a review.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Importance sampling: a review

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.650040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5bedffef-dd01-4b76-b1ba-7018fe751b95 · outbound

This paper cites DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.627666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 45927681-e8f3-4e04-b294-c2b35a5b4fa8 · outbound

This paper cites Deep adaptive sampling for surrogate modeling without labeled data.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Deep adaptive sampling for surrogate modeling without labeled data

Reference 52

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:50:04.687230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 611d599d-0ce7-4f99-b2dc-49fb33440c63 · outbound

This paper cites Annealed adaptive importance sampling method in PINNs for solving high dimensional partial differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Annealed adaptive importance sampling method in PINNs for solving high dimensional partial differential equations

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.608716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 654addb5-ef1e-4af7-9401-efc888914420 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Adam: A Method for Stochastic Optimization

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-05T12:50:03.410931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d787b267-845c-43fc-9e55-6847e1705a8a · outbound

This paper cites PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular do- main.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular do- main

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.576110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 360b6ecc-cfba-4c55-8897-04bf0831751b · outbound

This paper cites Machine learning-based soil– structure interaction analysis of laterally loaded piles through physics-informed neural net- works.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Machine learning-based soil– structure interaction analysis of laterally loaded piles through physics-informed neural net- works

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.552130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e74d28e3-3d74-44ce-b16b-37791fbc88da · outbound

This paper cites Physics-informed neural net- works for large deflection analysis of slender piles incorporating non-differentiable soil-structure interaction.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Physics-informed neural net- works for large deflection analysis of slender piles incorporating non-differentiable soil-structure interaction

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.529480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 110ff81e-6ebd-41fb-8767-e250c9762437 · outbound

This paper cites Kernel smoothing.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Kernel smoothing

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-05T12:50:03.679198Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01023545-92e8-496d-b9c6-52f624a7d2f2 · outbound

This paper cites Neural topology optimization via active learning for efficient channel design in turbulent mass transfer.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Neural topology optimization via active learning for efficient channel design in turbulent mass transfer

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.492703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 22dedcc1-b717-4179-8f11-6f4384133a30 · outbound

This paper cites Active operator learning with predictive uncertainty quantification for partial differential equations.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Active operator learning with predictive uncertainty quantification for partial differential equations

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-05T12:50:03.831999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6860861f-d7ea-4932-bb9b-25f69ed85cb7 · outbound

This paper cites A collection of 2D elliptic problems for testing adaptive grid refinement algorithms.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations A collection of 2D elliptic problems for testing adaptive grid refinement algorithms

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.469455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 986c7854-b4c3-4898-b64a-634d77b63455 · outbound

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

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Learning the solution operator of para- metric partial differential equations with physics-informed DeepONets

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-05T12:50:04.006350Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 967052f2-5860-445b-8072-cd98825c127f · outbound

This paper cites Global stabilization of two dimensional viscous Burg- ers’ equation by nonlinear Neumann boundary feedback control and its finite element analysis.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations Global stabilization of two dimensional viscous Burg- ers’ equation by nonlinear Neumann boundary feedback control and its finite element analysis

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:06.186343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7e2283fa-3267-4b5c-a5af-08c8ed0eac86 · outbound

This paper cites PROSE: Predicting multiple operators and symbolic expressions using multimodal transformers.

RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations PROSE: Predicting multiple operators and symbolic expressions using multimodal transformers

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:50:05.945445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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