Physics-informed machine learning for reduced-order modeling of nonlinear problems

Reduced Order Modeling of Nonlinear Control Systems

An Approach for Reduced Order Modeling of Nonlinear Power Systems

-In this paper we present an approach for the reduced order modeling of nonlinear power systems. We describe a combined symbolic-numeric methodology for a local model order reduction which is based on the theory of singularly perturbed systems. Since the properties of power systems are taken into account, we were able to define an easy to use formula which eliminates the necessity of engineerin...

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite element method (FEM)) is often computationally prohibitive, there is a need for a novel computational algorithm able to capture the effective behav...

Reduced Order Modeling for Nonlinear Multi-component Models

Reduced order modeling plays an indispensible role in most real-world complex models. A hybrid application of order reduction methods, introduced previously, has been shown to effectively reduce the computational cost required to find a reduced order model with quantifiable bounds on the reduction errors, which is achieved by hybridizing the application of local variational and global sampling ...

Efficient POD reduced-order modeling for parametrized nonlinear PDE systems

In this paper a model order reduction method for a nonlinear elliptic-parabolic system is developed. Systems of this type arise from mathematical models for lithium ion batteries. A non-intrusive reduced order approach based on proper orthogonal decomposition (POD) is presented. In addition to this the interpolation method introduced by Barrault et al. [3] is applied in order to achieve efficie...