Nonlinear dimensionality reduction for parametric problems: A kernel proper orthogonal decomposition

Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

The numerical solution of partial differential equations (PDEs) depending on parametrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this computational burden, and are nowadays exploited to accelerate real-time analysis, as well as the solution of PDE-constrained optimization and inver...

Parametric nonlinear dimensionality reduction using kernel t-SNE

Novel non-parametric dimensionality reduction techniques such as t-distributed stochastic neighbor embedding (t-SNE) lead to a powerful and flexible visualization of high-dimensional data. One drawback of non-parametric techniques is their lack of an explicit out-of-sample extension. In this contribution, we propose an efficient extension of t-SNE to a parametric framework, kernel t-SNE, which ...

Proper Orthogonal Decomposition Model Order Reduction of nonlinear IC models

Future simulation for nanoelectronics requires that circuit equations can be coupled to electromagnetics, to semiconductor equations, and to heat transfer. The consequence is that one has to deal with large systems. Model Order Reduction (MOR) is a means to speed up simulation of large systems. Existing MOR techniques mostly apply to linear problems and even then they have to be generalized to ...

The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems

The onset of multi-pulsing, a ubiquitous phenomenon in laser cavities, imposes a fundamental limit on the maximum energy delivered per pulse. Managing the nonlinear penalties in the cavity becomes crucial for increasing the energy and suppressing the multi-pulsing instability. A Proper Orthogonal Decomposition (POD) allows for the reduction of governing equations of a mode-locked laser onto a l...

Model Reduction via Proper Orthogonal Decomposition