Fourier Continuation

Fourier continuation (FC) is a technique extending the representation of a function beyond its initially defined domain, particularly useful for handling non-periodic data in Fourier-based methods. Current research focuses on improving FC's application in diverse areas, including anomaly detection using algorithms like Braced Fourier Continuation and Regression (BFCR), and enhancing the accuracy of physics-informed neural operators (PINOs) for solving partial differential equations by enabling exact derivative computations. These advancements are significant because they improve the efficiency and accuracy of numerical methods across various scientific disciplines, from signal processing to quantum field theory, where accurate handling of non-periodic functions is crucial.