Fig. 1
From: U-DeepONet: U-Net enhanced deep operator network for geologic carbon sequestration
Architecture of U-FNO. In (A) the full U-FNO architecture is shown, where \(v(x)\) is the input function, \(P\) is a fully connected neural network that lifts the input to a higher dimensional space, followed by Fourier layers then U-Fourier layers; \(Q\) is a fully connected neural network that maps the output \(\text{z}(\text{x})\) to the original dimensional space. (B) is the Fourier layer, where \(\mathcal{F}\) denotes the Fourier transform, \(\mathcal{R}\) is a weight matrix, \({\mathcal{F}}^{-1}\) is the inverse Fourier transform, \(W\) is another weight matrix, and \(\sigma \) is the activation function. (C) is the U-Fourier layer, U denotes the additional U-Net block in the Fourier layer.
