Related papers: Multi-Scale Proper Orthogonal Decomposition of Com…

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode…

Data-driven decompositions of Particle Image Velocimetry (PIV) measurements are widely used for a variety of purposes, including the detection of coherent features (e.g., vortical structures), filtering operations (e.g., outlier removal or…

The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by…

Multiscale Proper Orthogonal Decomposition (mPOD) decomposes fluid flows into energy-optimal modes within prescribed frequency bands by combining Proper Orthogonal Decomposition with a multiresolution analysis (MRA). In its classical…

The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques…

In the era of the Big Data revolution, methods for the automatic discovery of regularities in large datasets are becoming essential tools in applied sciences. This article presents an open software package, named MODULO (MODal mULtiscale…

We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…

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…

We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection.…

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved…

This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique…

We present a formalism for dissipation-optimized decomposition of the strain rate tensor (SRT) of turbulent flow data using Proper Orthogonal Decomposition (POD). The formalism includes a novel inverse spectral SRT operator allowing the…

We consider the frequency domain form of proper orthogonal decomposition (POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space-time POD problem for statistically stationary flows and leads to…

Two data-driven modal analysis approaches, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are applied to analyze the unsteady flow obtained by solving the Reynolds-averaged Navier-Stokes (RANS) equations in a…

The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…