# GaborPINN: Efficient physics informed neural networks using multiplicative filtered networks

arXiv: https://arxiv.org/abs/2308.05843 · HTML: https://mlsanity.com/paper/2308.05843/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 10 Aug 2023.

## Builds on (most cited first, 6 of 6)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting](https://mlsanity.com/paper/2109.14536/) (2021)
- [Solving Seismic Wave Equations on Variable Velocity Models with Fourier Neural Operator](https://mlsanity.com/paper/2209.12340/) (2022)

## Built on by (most cited first, 7 of 7)

- [Physics-informed neural wavefields with Gabor basis functions](https://mlsanity.com/paper/2310.10602/) (2023)
- [Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields](https://mlsanity.com/paper/2502.17134/) (2025)
- [Least-Squares-Embedded Optimization for Accelerated Convergence of PINNs in Acoustic Wavefield Simulations](https://mlsanity.com/paper/2504.16553/) (2025)
- [WellPINN: Accurate Well Representation for Transient Fluid Pressure Diffusion in Subsurface Reservoirs with Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.09330/) (2025)
- [A Family of Adaptive Activation Functions for Mitigating Failure Modes in Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.18328/) (2026)
- [Coordinate Encoding on Linear Grids for Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.22700/) (2026)
- [A Green-Integral-Constrained Neural Solver with Stochastic Physics-Informed Regularization](https://mlsanity.com/paper/2604.21411/) (2026)

## Abstract (arXiv)

The computation of the seismic wavefield by solving the Helmholtz equation is crucial to many practical applications, e.g., full waveform inversion. Physics-informed neural networks (PINNs) provide functional wavefield solutions represented by neural networks (NNs), but their convergence is slow. To address this problem, we propose a modified PINN using multiplicative filtered networks, which embeds some of the known characteristics of the wavefield in training, e.g., frequency, to achieve much faster convergence. Specifically, we use the Gabor basis function due to its proven ability to represent wavefields accurately and refer to the implementation as GaborPINN. Meanwhile, we incorporate prior information on the frequency of the wavefield into the design of the method to mitigate the influence of the discontinuity of the represented wavefield by GaborPINN. The proposed method achieves up to a two-magnitude increase in the speed of convergence as compared with conventional PINNs.