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

arXiv: https://arxiv.org/abs/2402.08367 · HTML: https://mlsanity.com/paper/2402.08367/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems](https://mlsanity.com/paper/2211.05520/) (2022)
- [PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery](https://mlsanity.com/paper/2109.04352/) (2021)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [Spline Positional Encoding for Learning 3D Implicit Signed Distance Fields](https://mlsanity.com/paper/2106.01553/) (2021)
- [Trading Positional Complexity vs. Deepness in Coordinate Networks](https://mlsanity.com/paper/2205.08987/) (2022)
- [State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning](https://mlsanity.com/paper/2202.06416/) (2022)
- [Learning Positional Embeddings for Coordinate-MLPs](https://mlsanity.com/paper/2112.11577/) (2021)
- [Physics-Aware Downsampling with Deep Learning for Scalable Flood Modeling](https://mlsanity.com/paper/2106.07218/) (2021)

## Built on by (most cited first, 5 of 5)

- [Enhancing Physics-Informed Neural Networks Through Feature Engineering](https://mlsanity.com/paper/2502.07209/) (2025)
- [Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning](https://mlsanity.com/paper/2601.07760/) (2026)
- [Enforcing hidden physics in physics-informed neural networks](https://mlsanity.com/paper/2511.14348/) (2025)
- [ASPINN: An asymptotic strategy for solving singularly perturbed differential equations](https://mlsanity.com/paper/2409.13185/) (2024)
- [Gaussian Variational Schemes on Bounded and Unbounded Domains](https://mlsanity.com/paper/2410.06219/) (2024)

## 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.