Fig. 5: Architecture of the Fourier Neural Operator.
From: A Fourier neural operator approach for modelling exciton-polariton condensate systems
The process begins with the input a(x) which undergoes a lifting operation, denoted as \({{\mathcal{P}}}\). This is followed by 4 consecutive Fourier layers. Subsequently, a projector \({{\mathcal{Q}}}\) transforms the data to the desired target dimension, resulting in the output u(x). The inset provides a detailed view of the structure of a Fourier layer. Data initially flow to the layer as ν(x) and are bifurcated into two branches: one undergoes a linear transformation W, and the other first experiences a Fourier transformation, from which the 128 lowest Fourier modes are kept, and the other higher modes are filtered out by undergoing a transformation R, and ends with an inverse Fourier transformation with these left modes. The two data streams then converge, followed by the application of an activation function σ.
