# Model Reduction and Operator Splitting

#### Abstract

Modeling and simulation for large scale nonlinear systems can be expensive. Thus, the need for model reduction arises. POD is a commonly used method for approximating large-scale nonlinear systems with a reduced order model. However, POD may not be able to capture what has not been observed i.e. the results of POD might be input-dependent. In order to mitigate this limitation we propose an approach that combines operator splitting and model reduction for solving nonlinear systems. In other words, we consider the linear and nonlinear terms in the dynamical system separately. First, we reduce the linear terms using some optimal model reduction algorithm. Then, we approximate the nonlinear terms using POD. Once we have reduced the model, we apply operator splitting i.e. in each step we numerically integrate the linear and nonlinear parts separately. The implemented operator splitting first evolves the linear terms, and then uses the result to evolve the nonlinear terms.

*This paper has been withdrawn.*

Model Reduction and Operator Splitting

Modeling and simulation for large scale nonlinear systems can be expensive. Thus, the need for model reduction arises. POD is a commonly used method for approximating large-scale nonlinear systems with a reduced order model. However, POD may not be able to capture what has not been observed i.e. the results of POD might be input-dependent. In order to mitigate this limitation we propose an approach that combines operator splitting and model reduction for solving nonlinear systems. In other words, we consider the linear and nonlinear terms in the dynamical system separately. First, we reduce the linear terms using some optimal model reduction algorithm. Then, we approximate the nonlinear terms using POD. Once we have reduced the model, we apply operator splitting i.e. in each step we numerically integrate the linear and nonlinear parts separately. The implemented operator splitting first evolves the linear terms, and then uses the result to evolve the nonlinear terms.