# PINNslope: seismic data interpolation and local slope estimation with physics informed neural networks

arXiv: https://arxiv.org/abs/2305.15990 · HTML: https://mlsanity.com/paper/2305.15990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting](https://mlsanity.com/paper/2109.14536/) (2021)
- [SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain](https://mlsanity.com/paper/2210.14044/) (2022)
- [Interpolation and Denoising of Seismic Data using Convolutional Neural Networks](https://mlsanity.com/paper/1901.07927/) (2019)
- [Deep-seismic-prior-based reconstruction of seismic data using convolutional neural networks](https://mlsanity.com/paper/1911.08784/) (2019)
- [Coordinate-Based Seismic Interpolation in Irregular Land Survey: A Deep Internal Learning Approach](https://mlsanity.com/paper/2211.11889/) (2022)

## Built on by (most cited first, 1 of 1)

- [Joint Velocity Slope Diffusion Prior for Structurally Constrained Velocity Model Building](https://mlsanity.com/paper/2607.04982/) (2026)

## Abstract (arXiv)

Interpolation of aliased seismic data constitutes a key step in a seismic processing workflow to obtain high quality velocity models and seismic images. Building on the idea of describing seismic wavefields as a superposition of local plane waves, we propose to interpolate seismic data by utilizing a physics informed neural network (PINN). In the proposed framework, two feed-forward neural networks are jointly trained using the local plane wave differential equation as well as the available data as two terms in the objective function: a primary network assisted by positional encoding is tasked with reconstructing the seismic data, whilst an auxiliary, smaller network estimates the associated local slopes. Results on synthetic and field data validate the effectiveness of the proposed method in handling aliased (coarsely sampled) data and data with large gaps. Our method compares favorably against a classic least-squares inversion approach regularized by the local plane-wave equation as well as a PINN-based approach with a single network and pre-computed local slopes. We find that introducing a second network to estimate the local slopes whilst at the same time interpolating the aliased data enhances the overall reconstruction capabilities and convergence behavior of the primary network. Moreover, an additional positional encoding layer embedded as the first layer of the wavefield network confers to the network the ability to converge faster improving the accuracy of the data term.