Long-Time Predictive Modeling of Nonlinear Dynamical Systems Using Neural Networks
Abstract
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and the observation of strong correlation between the local error and the maximal singular value of the Jacobian of the ANN, we introduce Jacobian regularization in the loss function. This regularization suppresses the sensitivity of the prediction to the local error and is shown to improve accuracy and robustness. Comparison between the proposed approach and sparse polynomial regression is presented in numerical examples ranging from simple ODE systems to nonlinear PDE systems including vortex shedding behind a cylinder and instability-driven buoyant mixing flow. Furthermore, limitations of feedforward neural networks are highlighted, especially when the training data does not include a low dimensional attractor. Strategies of data augmentation are presented as remedies to address these issues to a certain extent.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 02, 2018
- Source ID
- 10.1155/2018/4801012
Entities
People
- Karthik Duraisamy
- Shaowu Pan
Organizations
- Air Force Office of Scientific Research
- University of Michigan