mlsanityData to 7 Oct 2026

RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks

arXiv 2402.08367 ↗First posted 13 Feb 2024cs.LGcited by 5

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Abstract (arXiv)

While many recent Physics-Informed Neural Networks (PINNs) variants have had considerable success in solving Partial Differential Equations, the empirical benefits of feature mapping drawn from the broader Neural Representations research have been largely overlooked. We highlight the limitations of widely used Fourier-based feature mapping in certain situations and suggest the use of the conditionally positive definite Radial Basis Function. The empirical findings demonstrate the effectiveness of our approach across a variety of forward and inverse problem cases. Our method can be seamlessly integrated into coordinate-based input neural networks and contribute to the wider field of PINNs research.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 21 of its 38 references that are in the map. First posted on arXiv 13 Feb 2024.

Builds on

21 of 38 references.

References · 21

  1. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  2. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  3. 2018On the Spectral Bias of Neural Networkscited by 1,321
  4. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  5. 2021Neural Fields in Visual Computing and Beyondcited by 539
  6. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  7. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
  8. 2023WIRE: Wavelet Implicit Neural Representationscited by 220
  9. 2021Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPscited by 134
  10. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  11. 2021Efficient training of physics-informed neural networks via importance samplingcited by 109
  12. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 71
9 more
  1. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
  2. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
  3. 2021PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgerycited by 22
  4. 2022NTFields: Neural Time Fields for Physics-Informed Robot Motion Planningcited by 22
  5. 2021Spline Positional Encoding for Learning 3D Implicit Signed Distance Fieldscited by 21
  6. 2022Trading Positional Complexity vs. Deepness in Coordinate Networkscited by 16
  7. 2022State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learningcited by 12
  8. 2021Learning Positional Embeddings for Coordinate-MLPscited by 7
  9. 2021Physics-Aware Downsampling with Deep Learning for Scalable Flood Modelingcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 2; 2026: 1.

5 papers.

  1. 2025Enhancing Physics-Informed Neural Networks Through Feature Engineeringcited by 8
  2. 2025Enforcing hidden physics in physics-informed neural networkscited by 3
  3. 2024ASPINN: An asymptotic strategy for solving singularly perturbed differential equationscited by 2
  4. 2026Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learningcited by 2
  5. 2024Gaussian Variational Schemes on Bounded and Unbounded Domainscited by 0