# A characteristic dynamic mode decomposition

@article{Sesterhenn2019ACD, title={A characteristic dynamic mode decomposition}, author={J{\"o}rn Sesterhenn and Amir Shahirpour}, journal={Theoretical and Computational Fluid Dynamics}, year={2019}, pages={1-25} }

Temporal or spatial structures are readily extracted from complex data by modal decompositions like proper orthogonal decomposition (POD) or dynamic mode decomposition (DMD). Subspaces of such decompositions serve as reduced order models and define either spatial structures in time or temporal structures in space. On the contrary, convecting phenomena pose a major problem to those decompositions. A structure traveling with a certain group velocity will be perceived as a plethora of modes in…

## 12 Citations

### Symmetry-reduced Dynamic Mode Decomposition of Near-wall Turbulence

- Engineering
- 2021

Data-driven dimensionality reduction methods such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have proven to be useful for exploring complex phenomena within ﬂuid…

### Data‐driven identification of the spatiotemporal structure of turbulent flows by streaming dynamic mode decomposition

- PhysicsGAMM-Mitteilungen
- 2022

Streaming Dynamic Mode Decomposition (sDMD) is a low‐storage version of dynamic mode decomposition (DMD), a data‐driven method to extract spatiotemporal flow patterns. Streaming DMD avoids storing…

### Projection-based model reduction with dynamically transformed modes

- Computer Science, Mathematics
- 2019

A new model reduction framework for problems that exhibit transport phenomena that employs time-dependent transformation operators and generalizes MFEM to arbitrary basis functions is proposed, suitable to obtain a low-dimensional approximation with small errors even in situations where classical model order reduction techniques require much higher dimensions.

### Nonlinear Galerkin Model Reduction for Systems with Multiple Transport Velocities

- Computer Science, MathematicsArXiv
- 2019

A new model reduction framework for problems that exhibit transport phenomena that employs time-dependent transformation operators and generalizes MFEM to arbitrary basis functions that is suitable to obtain a low-dimensional approximation with small errors even in situations where classical model order reduction techniques require much higher dimensions.

### Manifold Approximations via Transported Subspaces: Model reduction for transport-dominated problems

- Computer Science, MathematicsArXiv
- 2019

Numerical experiments with transport through heterogeneous media and the Burgers' equation show orders of magnitude speedups of the proposed nonlinear reduced models based on transported subspaces compared to traditional linear reduced models and full models.

### Reduced basis methods for time-dependent problems

- Computer ScienceActa Numerica
- 2022

This article surveys the state of the art of reduced basis methods for time-dependent problems and draws together recent advances in three main directions, discussing structure-preserving reduced order models designed to retain key physical properties of the continuous problem.

### Permuted proper orthogonal decomposition for analysis of advecting structures

- Computer ScienceJournal of Fluid Mechanics
- 2021

This example demonstrates how the different inner product spaces, which order the PPOD and space-only POD modes according to different measures of variance, provide unique ‘lenses’ into features of advection-dominated flows, allowing complementary insights.

### Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems

- Computer ScienceArXiv
- 2020

Reduced deep networks are introduced, a generalization of classical reduced models formulated as deep neural networks, and it is proved depth separation results showing that reduced deep networks approximate solutions of parametrized hyperbolic partial differential equations with approximation error $\epsilon$ with $\mathcal{O}(|\log(\EPsilon)|)$ degrees of freedom, even in the nonlinear setting where solutions exhibit shock waves.

### Hybrid Scheme of Kinematic Analysis and Lagrangian Koopman Operator Analysis for Short-term Precipitation Forecasting

- Environmental ScienceArXiv
- 2020

The proposed method decomposes time evolutions of the phenomena between advection currents under a velocity field and changes in physical quantities under Lagrangian coordinates and shows that the development and decay of precipitation are properly captured relative to conventional methods and that stable predictions over long periods are possible.

### Supersonic Underexpanded Jet Features Extracted from Modal Analyses of High-Speed Optical Diagnostics

- Engineering, PhysicsAIAA Journal
- 2021

An experimental study concerning an underexpanded, screeching, Mach 1.5 jet operating at a stagnation-to-ambient pressure ratio of 4.4 is presented. Experimental data were acquired from high-speed ...

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