Paper Citation Record · LEDGER

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features

As of 21 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2412.00636.

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pith.paper-citation-record.v1
2412.00636 v1

Coverage vector

measured 32 of 32 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

32 of 32 outbound references displayed

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External citation measurements

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Outbound references

Observation 84c6ad7f-d668-4c0d-8732-536f38535e98 · outbound

This paper cites The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems

Reference 1

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Observation 33505817-c324-4afc-b516-3c2fcb721d95 · outbound

This paper cites Karniadakis.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Karniadakis

Reference 2

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Observation 8af38cf2-1e3b-4cd4-b9e1-92e48a08b1fc · outbound

This paper cites DGM: A deep learning algorithm for solving partial differential equations.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features DGM: A deep learning algorithm for solving partial differential equations

Reference 3

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Observation 17afc991-bbc1-4587-9a64-a37427fecdd6 · outbound

This paper cites Physics- informed neural networks (PINNs) for fluid mechanics: A review.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Physics- informed neural networks (PINNs) for fluid mechanics: A review

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.423840Z

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Observation 0310b854-7273-4b09-bca4-5abe35e2a48d · outbound

This paper cites Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence

Reference 5

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Observation afb8c50d-9706-44c7-8e53-6effddd3a5f6 · outbound

This paper cites Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.407762Z

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Observation e33c79c3-4813-47b2-8ded-2763611433e9 · outbound

This paper cites A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Reference 7

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Observation 84d2b865-5676-496b-928d-decb4dd37c9e · outbound

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

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features fPINNs: Fractional physics-informed neural networks

Reference 8

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Observation bca8fd9b-b613-4b40-8a95-1e970fa8396c · outbound

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

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features A comprehensive study of non- adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 9

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Observation cec19f1c-3085-4d9c-a637-b94085f7e841 · outbound

This paper cites Failure-informed adaptive sampling for PINNs.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Failure-informed adaptive sampling for PINNs

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.379810Z

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Observation 399fb36a-3279-428e-8ce9-bef82e70aa86 · outbound

This paper cites Failure-informed adaptive sampling for PINNs, part II: combining with re-sampling and subset simulation.Communications on Applied Mathematics and Computation, 6(3):1720–1741, 2024.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Failure-informed adaptive sampling for PINNs, part II: combining with re-sampling and subset simulation.Communications on Applied Mathematics and Computation, 6(3):1720–1741, 2024

Reference 11

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Observation fd61def2-18b9-4ead-a708-010cbe0616ca · outbound

This paper cites Jagtap, Kenji Kawaguchi, and George Em Karniadakis.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Jagtap, Kenji Kawaguchi, and George Em Karniadakis

Reference 12

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Observation 97e35151-6ac9-48e6-b8e1-f53b4effc863 · outbound

This paper cites Jagtap, Kenji Kawaguchi, and George Em Karniadakis.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Jagtap, Kenji Kawaguchi, and George Em Karniadakis

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.355700Z

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Observation 4e0d48e5-5e35-47fc-b9c7-a338435b032a · outbound

This paper cites Self-adaptive physics-informed neural networks using a soft attention mechanism.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Self-adaptive physics-informed neural networks using a soft attention mechanism

Reference 14

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Observation ad0f3431-3e72-4915-ad5c-003c9eeb976e · outbound

This paper cites Self-adaptive loss balanced physics-informed neural networks.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Self-adaptive loss balanced physics-informed neural networks

Reference 15

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Observation 524c74bd-463f-421d-bc82-747131a7308a · outbound

This paper cites Taylor, Manuela Bastidas, Victor M.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Taylor, Manuela Bastidas, Victor M

Reference 16

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Observation 83032b9e-20a8-4878-b7bf-1737cb8bd18f · outbound

This paper cites Self-adaptive deep neural network: Numerical approx- imation to functions and PDEs.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Self-adaptive deep neural network: Numerical approx- imation to functions and PDEs

Reference 17

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Observation 606d2370-7409-4221-8df2-10e151323a66 · outbound

This paper cites Adaptive two-layer ReLU neural network: II.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Adaptive two-layer ReLU neural network: II

Reference 18

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Observation b3fe7065-cac8-464a-a0c4-7ff92940a404 · outbound

This paper cites Adaptive two-layer relu neural network: I.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Adaptive two-layer relu neural network: I

Reference 19

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Observation 884abd94-ca2f-43e9-85fb-56b2d5f326ed · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Adam: A Method for Stochastic Optimization

Reference 20

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Observation 51b9d628-9167-4517-b6a7-dcc20e86de05 · outbound

This paper cites Influence of activation functions on the convergence of physics-informed neural networks for 1d wave equation.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Influence of activation functions on the convergence of physics-informed neural networks for 1d wave equation

Reference 21

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Observation 085af41e-cc76-41db-a89c-b3fc57d6678a · outbound

This paper cites On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition

Reference 22

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Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Unresolved cited work

Reference 23

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Observation 65379fba-a866-48c5-8ffc-877e2c9bb17f · outbound

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Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Unresolved cited work

Reference 24

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Observation cbd8336e-f2ac-4d2e-97ff-35a80a56e2f1 · outbound

This paper cites Sprecher and Sorin Draghici.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Sprecher and Sorin Draghici

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.267771Z

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Observation 23d80adc-b749-4f49-8411-86d6935dd7de · outbound

This paper cites The kolmogorov superposition theorem can break the curse of dimensionality when approximating high dimensional functions.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features The kolmogorov superposition theorem can break the curse of dimensionality when approximating high dimensional functions

Reference 26

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Observation d9416839-e69f-4b41-b561-6ebae82c2552 · outbound

This paper cites Kolmogorov’s theorem and multilayer neural networks.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Kolmogorov’s theorem and multilayer neural networks

Reference 27

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Observation a923ab15-9879-4276-9157-849d4ce0e274 · outbound

This paper cites The kolmogorov-arnold representation theorem revisited.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features The kolmogorov-arnold representation theorem revisited

Reference 28

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Observation c14512f0-edc8-4a94-9236-7d5277ffd3f1 · outbound

This paper cites A kol- mogorov high order deep neural network for high frequency partial differential equations in high dimensions.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features A kol- mogorov high order deep neural network for high frequency partial differential equations in high dimensions

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.233437Z

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Observation 91d4b469-5d3b-4566-9ef1-5e7f267f200a · outbound

This paper cites Selected topics in finite element methods.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Selected topics in finite element methods

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.224542Z

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Observation 48c37e45-78e9-4f77-8977-1f09ee1d2f79 · outbound

This paper cites DBSCAN: Density-based spatial clustering of appli- cations with noise.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features DBSCAN: Density-based spatial clustering of appli- cations with noise

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.215146Z

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Observation 1ab55524-5d5a-47b7-9a29-9a91a76cfa3c · outbound

This paper cites Moving sampling physics-informed neural networks induced by moving mesh PDE.

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features Moving sampling physics-informed neural networks induced by moving mesh PDE

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:14:00.206433Z

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