Perpustakaan Digital ITB

Understanding and predicting the behavior of complex dynamical systems is a fundamental challenge across many scientific disciplines. This thesis explores the potential of Fourier Neural Operators (FNOs) which leverage spectral domain transformations to capture intricate patterns and dependencies as a surrogate of conventional numerical solvers. This research focuses on four distinct dynamical systems: the Kraichnan- Orszag three-mode problem, the Lorenz system, the Kuramoto-Sivashinsky (KS) equations, and the diffusion-advection problem. By systematically varying the FNO model architecture—particularly the number of Fourier modes and hidden layers—the study demonstrates that increasing model complexity generally enhances predictive accuracy. This enhancement allows the FNO to more effectively capture the nonlinear interactions and chaotic dynamics inherent in these systems. For instance, the model successfully predicts trajectories in the Kraichnan-Orszag problem, the Lorenz system, and the KS equations, while it performs well in forecasting predictions for the Lorenz system, its efficacy diminishes over longer time horizons. The thesis also underscores the critical role of training data size. Larger datasets significantly bolster the model’s performance, underscoring the importance of robust data collection in developing effective predictive models. Despite some challenges, such as error accumulation in recursive predictions for the advection-diffusion problem, the findings establish FNOs as a formidable tool for tackling complex dynamical systems.