# Physics-informed neural wavefields with Gabor basis functions

arXiv: https://arxiv.org/abs/2310.10602 · HTML: https://mlsanity.com/paper/2310.10602/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 50 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks](https://mlsanity.com/paper/2104.08426/) (2021)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)
- [A Modern Take on the Bias-Variance Tradeoff in Neural Networks](https://mlsanity.com/paper/1810.08591/) (2018)
- [Efficient physics-informed neural networks using hash encoding](https://mlsanity.com/paper/2302.13397/) (2023)
- [PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting](https://mlsanity.com/paper/2109.14536/) (2021)
- [Approximating the solution to wave propagation using deep neural networks](https://mlsanity.com/paper/1812.01609/) (2018)
- [GaborPINN: Efficient physics informed neural networks using multiplicative filtered networks](https://mlsanity.com/paper/2308.05843/) (2023)

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

- [FViT: A Focal Vision Transformer with Gabor Filter](https://mlsanity.com/paper/2402.11303/) (2024)
- [Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields](https://mlsanity.com/paper/2502.17134/) (2025)
- [Separated-Variable Spectral Neural Networks: A Physics-Informed Learning Approach for High-Frequency PDEs](https://mlsanity.com/paper/2508.00628/) (2025)
- [An efficient wavelet-based physics-informed neural network for multiscale problems](https://mlsanity.com/paper/2409.11847/) (2024)
- [DiffPINN: Generative diffusion-initialized physics-informed neural networks for accelerating seismic wavefield representation](https://mlsanity.com/paper/2506.00471/) (2025)

## Abstract (arXiv)

Recently, Physics-Informed Neural Networks (PINNs) have gained significant attention for their versatile interpolation capabilities in solving partial differential equations (PDEs). Despite their potential, the training can be computationally demanding, especially for intricate functions like wavefields. This is primarily due to the neural-based (learned) basis functions, biased toward low frequencies, as they are dominated by polynomial calculations, which are not inherently wavefield-friendly. In response, we propose an approach to enhance the efficiency and accuracy of neural network wavefield solutions by modeling them as linear combinations of Gabor basis functions that satisfy the wave equation. Specifically, for the Helmholtz equation, we augment the fully connected neural network model with an adaptable Gabor layer constituting the final hidden layer, employing a weighted summation of these Gabor neurons to compute the predictions (output). These weights/coefficients of the Gabor functions are learned from the previous hidden layers that include nonlinear activation functions. To ensure the Gabor layer's utilization across the model space, we incorporate a smaller auxiliary network to forecast the center of each Gabor function based on input coordinates. Realistic assessments showcase the efficacy of this novel implementation compared to the vanilla PINN, particularly in scenarios involving high-frequencies and realistic models that are often challenging for PINNs.