Research

A study extending the approximation theorem of the conventional Fourier Neural Operator to non-Markovian processes and proposing an improved architecture for this purpose has been published in the Journal of Scientific Computing. In this study, the research team demonstrated, based on the Wong–Zakai theorem and various approximation methodologies, that path-dependent stochastic processes and fractional Brownian motion can be approximated to arbitrary accuracy using the mirror-padded Fourier Neural Operator (MFNO). The team also designed experiments to support the theory, showing that MFNO is robust to changes in resolution and more efficient than classical methods. This research is expected to serve as foundational work in the field of scientific machine learning for approximating stochastic processes.