FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation

Understand

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs).

• It leverages the Fourier Neural Operator to learn solution operators in function spaces and leverages physics losses during training to penalize deviations from known physics laws.
• Spectral differentiation provides an efficient way to compute derivatives for the physics losses, but it inherently assumes periodicity.
• When applied to non-periodic functions, this assumption can lead to significant errors, including Gibbs phenomena near domain boundaries which degrade the accuracy of both function representations and derivative computations.