PINNslope: physics informed neural network slope prediction and interpolation with positional encoding

Under the assumption that seismic wavefields can be represented as superposition of local plane waves, we propose to interpolate seismic data utilizing a physics informed neural network (PINN) assisted by the local slope attribute. The implementation comprises two fully-connected neural networks trained using the local plane wave differential equation as well as the available data as two terms in the objective function. The main network assisted by positional encoding reconstructs the seismic data, while the smaller one predicts the local slope field that simultaneously satisfies the differential equation. In the proposed work, four different encoding functions (Linear Fourier Features, modified Linear Fourier Features, Random Fourier Features, Gaussian Encoding) are compared to evaluate which one will benefits our framework the most in terms of reconstruction accuracy and convergence speed. We find that our proposed modified Linear Fourier Feature helps our framework in achieving a faster and less oscillatory convergence while accurately reconstructing the data.