2024/10/17 by Shuwen Sun, Lihong Feng, Sun, Shuwen +3 · 2 citations
Computer Science · #Generative Adversarial Networks and Image Synthesis #Explainable Artificial Intelligence (XAI) #Adversarial Robustness in Machine Learning
paper · pdf · doi:10.1016/j.cma.2025.118604
Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many methods fail in accurately generalizing in the entire time interval [0, T], when the training data is available only in a training time interval [0, T0], with T0<T. To improve the extrapolation capabilities of the surrogate models in the entire time domain, we propose a new deep learning framework, where kernel dynamic mode decomposition (KDMD) is employed to evolve the dynamics of the latent space generated by the encoder part of a convolutional autoencoder (CAE). After adding the KDMD-decoder-extrapolated data into the original data set, we train the CAE along with a feed-forward deep neural network using the augmented data. The trained network can predict future states outside the training time interval at any out-of-training parameter samples. The proposed method is tested on two numerical examples: a FitzHugh-Nagumo model and a model of incompressible flow past a cylinder. Numerical results show accurate and fast prediction performance in both the time and the parameter domain.