Machine Learning Guided Reduced Order Modeling for PDEs

We developed a hybrid method that combines machine learning and numerical techniques to solve PDEs. The pipeline consists of an operator-learning model followed by a reduced-order model. In the first stage, a Fourier Neural Operator predicts the dominant space-time Proper Orthogonal Decomposition (POD) modes from the initial condition(s). In the second stage, we solve the system in the predicted low-dimensional subspace.