Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models

TL;DR

This paper introduces a novel deep learning framework combining kernel dynamic mode decomposition with autoencoders to significantly improve the extrapolation capabilities of surrogate models for complex dynamical systems.

Contribution

The paper proposes a new data-augmented deep neural network approach that enhances extrapolation in time and parameters by integrating KDMD with convolutional autoencoders.

Findings

Accurate predictions for FitzHugh-Nagumo model.

Effective extrapolation in flow past a cylinder.

Fast computation with high accuracy.

Abstract

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 $[0, T_0]$, with $T_0<T$. 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.