Reference health
A Comprehensive and Fair Comparison between Mlp and Kan Representations for Differential Equations and Operator Networks
32/32 checkable references clean · checked 2026-08-03
Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.
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The 32 checked references that resolve
resolves10.1016/S0893-6080(01)00107-1
Space-filling curves and Kolmogorov superposition-based neural networks
resolves10.1016/S0893-6080(96)00127-X
Discovering Neural Nets with Low Kolmogorov Complexity and High Generalization Capability
resolves10.1016/j.jcp.2019.109136
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
resolves10.1016/j.neunet.2022.04.029
ExSpliNet: An interpretable and expressive spline-based neural network
resolves10.1016/j.jcp.2018.10.045
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
resolves10.1038/s42256-021-00302-5
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
resolves10.1109/JSAIT.2020.2991561
The Information Bottleneck Problem and its Applications in Machine Learning
resolves10.1016/j.jcp.2022.111902
Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons
resolves10.1016/j.jcp.2020.109913
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
resolves10.1016/j.cma.2020.113250
PPINN: Parareal physics-informed neural network for time-dependent PDEs
resolves10.1016/j.cma.2023.116647
Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression
resolves10.1137/23M1561397
Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems
resolves10.1007/s10921-020-00705-1
Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks
resolves10.1109/MSP.2021.3118904
A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems
resolves10.1093/acprof:oso/9780198528692.001.0001
Spectral/hp Element Methods for Computational Fluid Dynamics
resolves10.1017/jfm.2018.808
An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe
resolves10.1016/0001-6160(72)90037-5
Ground state structures in ordered binary alloys with second neighbor interactions
resolves10.1016/j.cma.2022.115346
Bayesian Physics Informed Neural Networks for real-world nonlinear dynamical systems
The 48 references without a DOI — listed, not checked
no DOI — not checkedref1
no DOI — not checkedAttention is all you need
no DOI — not checkedDeep residual learning for image recognition
no DOI — not checkedVisualizing the loss landscape of neural nets
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no DOI — not checkedA comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
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no DOI — not checkedPhysics-informed neural networks for highspeed flows
no DOI — not checkedref46
no DOI — not checkedCorrecting model misspecification in physicsinformed neural networks (PINNs)
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no DOI — not checkedA comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
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no DOI — not checkedOn the spectral bias of neural networks
no DOI — not checkedHamiltonian neural networks
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no DOI — not checkedref69
no DOI — not checkedNSFnets (Navier-Stokes flow nets): Physicsinformed neural networks for the incompressible Navier-Stokes equations
no DOI — not checkedA generative modeling framework for inferring families of biomechanical constitutive laws in datasparse regimes
no DOI — not checkedref76
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