From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models | Paper Citation Record

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

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This paper cites Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440

Reference 2

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This paper cites McGraw-Hill, London; New York, 3rd edi- tion.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models McGraw-Hill, London; New York, 3rd edi- tion

Reference 3

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This paper cites Cambridge Monographs on Applied and Computational Mathematics.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Cambridge Monographs on Applied and Computational Mathematics

Reference 4

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

Reference 5

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Observation 9bd295ec-0445-4a4c-9488-5ad50ab3139d · outbound

This paper cites DGM: A deep learning algorithm for solving partial differ- ential equations.Journal of Computational Physics, 375:1339–1364.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models DGM: A deep learning algorithm for solving partial differ- ential equations.Journal of Computational Physics, 375:1339–1364

Reference 6

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Observation f6d21c6a-e76b-416a-acc4-ec7980a8723e · outbound

This paper cites Artificial neural networks for solving ordinary and partial differential equations.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Artificial neural networks for solving ordinary and partial differential equations

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.180931Z

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

Reference 8

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

Reference 9

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-05-20T07:33:24.165216Z

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Observation e1d57a63-915f-4998-bad9-599181c4e5ec · outbound

This paper cites Hidden fluid mechanics: Learn- ing velocity and pressure fields from flow visualiza- tions.Science, 367(6481):1026–1030.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Hidden fluid mechanics: Learn- ing velocity and pressure fields from flow visualiza- tions.Science, 367(6481):1026–1030

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.166988Z

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Observation 4d07c9a0-270e-4ffb-86ec-37ee0644d353 · outbound

This paper cites Physics-informed neural networks for cardiac activation mapping.Fron- tiers in Physics, 8:42.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Physics-informed neural networks for cardiac activation mapping.Fron- tiers in Physics, 8:42

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.163145Z

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

Reference 13

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Observation 1efd5a38-a868-4c5c-a29f-93cc72e44fec · outbound

This paper cites Physics-informed neural net- works for inverse problems in nano-optics and meta- materials.Optics Express, 28(8):11618.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Physics-informed neural net- works for inverse problems in nano-optics and meta- materials.Optics Express, 28(8):11618

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.155680Z

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Observation 8383882a-f987-4155-99dc-2230df25bc34 · outbound

This paper cites Scientific machine learning through physics-informed neural networks: Where we are and what’s next.Journal of Scientific Computing, 92(3):88.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Scientific machine learning through physics-informed neural networks: Where we are and what’s next.Journal of Scientific Computing, 92(3):88

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.160957Z

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Observation ce33ed93-24fa-4894-9ec3-4b9e76829812 · outbound

This paper cites Under- standing and mitigating gradient flow pathologies in physics-informed neural networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Under- standing and mitigating gradient flow pathologies in physics-informed neural networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.152073Z

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This paper cites When and why PINNs fail to train: A neural tangent ker- nel perspective.Journal of Computational Physics, 449:110768.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models When and why PINNs fail to train: A neural tangent ker- nel perspective.Journal of Computational Physics, 449:110768

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.153865Z

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Observation 272d7694-9646-4719-bb35-8489ec36b547 · outbound

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

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Characterizing possible failure modes in physics- informed neural networks

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.157363Z

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Observation a45f64ea-86cb-4c13-b16b-2530e5c04605 · outbound

This paper cites Limitations of physics informed machine learning for nonlinear two-phase transport in porous media.Journal of Machine Learn- ing for Modeling and Computing, 1(1):19–37.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Limitations of physics informed machine learning for nonlinear two-phase transport in porous media.Journal of Machine Learn- ing for Modeling and Computing, 1(1):19–37

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.171080Z

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Observation 494d4234-c85a-4bd1-b997-a3b06b649a45 · outbound

This paper cites Hamprecht, Yoshua Bengio, and Aaron Courville.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Hamprecht, Yoshua Bengio, and Aaron Courville

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.149432Z

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Observation edfec15f-24a3-465e-89d5-acdce4040d4c · outbound

This paper cites Frequency principle: Fourier analysis sheds light on deep neural networks.Commu- nications in Computational Physics, 28(5):1746–1767.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Frequency principle: Fourier analysis sheds light on deep neural networks.Commu- nications in Computational Physics, 28(5):1746–1767

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.141281Z

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Observation e24efe58-83bd-49ab-8c5f-4724e1435da0 · outbound

This paper cites Mitigating propagation failures in physics-informed neural networks using retain- resample-release (R3) sampling.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Mitigating propagation failures in physics-informed neural networks using retain- resample-release (R3) sampling

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.143085Z

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-05-20T07:33:24.145896Z

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Observation 6427b1e6-28ef-4da1-b40b-6e3ca9fa3c0d · outbound

This paper cites An adaptive weight physics-informed neural network for vortex-induced vibration problems.Buildings, 15(9):1533.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models An adaptive weight physics-informed neural network for vortex-induced vibration problems.Buildings, 15(9):1533

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.149894Z

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Observation 3677b88a-66b6-439f-917b-62b700aa3a6b · outbound

This paper cites Self- adaptive loss balanced physics-informed neural net- works.Neurocomputing, 496:11–34.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Self- adaptive loss balanced physics-informed neural net- works.Neurocomputing, 496:11–34

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.169190Z

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Observation 81c7aba7-caed-4c2b-ad62-1883d10b76d3 · outbound

This paper cites GradNorm: Gradient normal- ization for adaptive loss balancing in deep multitask networks.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models GradNorm: Gradient normal- ization for adaptive loss balancing in deep multitask networks

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.198948Z

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Observation d99c67f8-a3f4-4ef0-a051-4a8a121fa0eb · outbound

This paper cites Gradient-enhanced physics- informed neural networks for forward and inverse PDE problems.Computer Methods in Applied Mechanics and Engineering, 393:114823.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Gradient-enhanced physics- informed neural networks for forward and inverse PDE problems.Computer Methods in Applied Mechanics and Engineering, 393:114823

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.204457Z

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Observation a2c43e89-68e1-4221-a2b7-9c15b36dfba3 · outbound

This paper cites LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks

Reference 28

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Observation 004f3a83-dd9b-4a7e-94aa-17468358d7f9 · outbound

This paper cites A stacked adaptive residual PINN (STAR- PINN) approach to 2D time-domain magnetic diffu- sion in nonlinear materials.IEEE Access, 13:141380– 141394.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models A stacked adaptive residual PINN (STAR- PINN) approach to 2D time-domain magnetic diffu- sion in nonlinear materials.IEEE Access, 13:141380– 141394

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.190973Z

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Observation 9724c32e-eb1d-4818-afd6-30610eff80f6 · outbound

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

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Efficient training of physics- informed neural networks via importance sampling

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.201031Z

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Observation 43e3a287-4d69-4762-b2e1-56c2d57a5016 · outbound

This paper cites Annealed adap- tive importance sampling method in PINNs for solving high dimensional partial differential equations.Jour- nal of Computational Physics, 521:113561.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Annealed adap- tive importance sampling method in PINNs for solving high dimensional partial differential equations.Jour- nal of Computational Physics, 521:113561

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.185133Z

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Observation 251f200b-c10d-4907-a8a8-561e5b04b1c3 · outbound

This paper cites A Gaussian mixture distribution- based adaptive sampling method for physics-informed neural networks.Engineering Applications of Artificial Intelligence, 135:108770.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models A Gaussian mixture distribution- based adaptive sampling method for physics-informed neural networks.Engineering Applications of Artificial Intelligence, 135:108770

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.194543Z

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Observation a12a9863-0593-4f7d-a369-069dc5cb3eca · outbound

This paper cites Parallel physics-informed neural networks via domain decomposition.Journal of Com- putational Physics, 447:110683.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Parallel physics-informed neural networks via domain decomposition.Journal of Com- putational Physics, 447:110683

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.197147Z

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From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-05-20T07:33:24.202715Z

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Observation f8a5206b-5812-4fe6-83e3-06d9c8a63f26 · outbound

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

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Respecting causality for training physics-informed neural networks.Computer Methods in Applied Me- chanics and Engineering, 421:116813

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.155979Z

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Observation e4f5ffb6-7c43-4ef8-b557-27e612c45df8 · outbound

This paper cites Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems.Journal of Computa- tional Physics, 397:108850.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems.Journal of Computa- tional Physics, 397:108850

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.171423Z

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Observation 7a936670-89f1-439c-bbaa-e38eda6c7ee5 · outbound

This paper cites Adversarial uncer- tainty quantification in physics-informed neural net- works.Journal of Computational Physics, 394:136– 152.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Adversarial uncer- tainty quantification in physics-informed neural net- works.Journal of Computational Physics, 394:136– 152

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Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.173193Z

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Observation 2e923498-f520-4943-8b0b-002a0ff0198a · outbound

This paper cites Curriculum learning.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Curriculum learning

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.169548Z

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Observation 1b338d40-ed13-4220-8f1e-71c20f321f3b · outbound

This paper cites Training physics-informed neural networks: One learning to rule them all?Results in Engineering, 18:101023.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Training physics-informed neural networks: One learning to rule them all?Results in Engineering, 18:101023

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.154158Z

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Observation 367074a2-531d-4e8a-92b0-bff4b0839459 · outbound

This paper cites Dynamic curricu- lum regularization for enhanced training of physics- informed neural networks.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Dynamic curricu- lum regularization for enhanced training of physics- informed neural networks

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.161735Z

Source-reported events for the cited work

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Observation 1c160611-66f1-4a08-951d-9023fe8d58d6 · outbound

This paper cites Curriculum-enhanced adaptive sampling for physics-informed neural net- works: A robust framework for stiff PDEs.Mathemat- ics, 13(24):3996.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Curriculum-enhanced adaptive sampling for physics-informed neural net- works: A robust framework for stiff PDEs.Mathemat- ics, 13(24):3996

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.159704Z

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Observation a2fb4174-a22d-4502-9a92-a815ad785c65 · outbound

This paper cites Adaptive task decomposition physics- informed neural networks.Computer Methods in Ap- plied Mechanics and Engineering, 418:116561.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Adaptive task decomposition physics- informed neural networks.Computer Methods in Ap- plied Mechanics and Engineering, 418:116561

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.163717Z

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Observation 7c51a623-fc16-47d6-a06c-65228da418a3 · outbound

This paper cites Automatic differentiation in machine learning: A survey.Journal of Machine Learning Research, 18(153):1–43.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models Automatic differentiation in machine learning: A survey.Journal of Machine Learning Research, 18(153):1–43

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.157775Z

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Observation 4d829ae9-6227-4a44-9fb2-969f8f374c57 · outbound

This paper cites A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics.Computer Methods in Applied Mechanics and Engineering, 379:113741.

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics.Computer Methods in Applied Mechanics and Engineering, 379:113741

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T07:33:24.173310Z

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