Applications of Dynamic Mode Decomposition and Sparse Reconstruction in the Data-Driven Dynamic Analysis of Physical Systems

Recent advancements in data collection methods and equipment have resulted in a huge increase in the amount of data collected by observing various types of physical phenomena. Regardless of the amount of data collected, it is well known for many physical systems, the so-called information rank of the collected data is much lower than the rank of the data itself. This usually means the data may be represented sparsely in terms of a properly-chosen basis. This realization has led to methods for storing large amounts of data through compression by sacrificing negligible data quality. More importantly, with the advent of compressed sensing techniques, using an appropriate representation basis and sampling technique, it is now possible to sample data far below the Shannon-Nyquist limit thus speeding up data acquisition and also reducing the complexity of data-acquisition hardware. In this research, we explore the application of various modern data analysis techniques such as proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), compressed sensing, and Kalman filter and smoother in the data-driven analysis of dynamic systems with many degrees of freedom. This research has resulted in four novel methods. The first method is developed for denoising and spatial resolution enhancement of 4D-Flow MRI data based on POD and sparse reconstruction. The second method combines DMD and compressed sensing and takes discrete cosine transform (DCT) as the representation basis for dynamic denoising and gappy data reconstruction in 2D. The third method is a fast and parameter-free dynamic denoising method which combines a reduced-order model (ROM), a Kalman filter and smoother, and a DMD-based forward model. The fourth method is developed for reconstructing a 2D incompressible flow field by taking sparse measurements from the Fourier domain. As the reconstruction basis, a custom divergence-free set of basis vectors are derived and implemented

Dynamic Denoising and Gappy Data Reconstruction Based on Dynamic Mode Decomposition and Discrete Cosine Transform

Dynamic Mode Decomposition (DMD) is a data-driven method to analyze the dynamics, first applied to fluid dynamics. It extracts modes and their corresponding eigenvalues, where the modes are spatial fields that identify coherent structures in the flow and the eigenvalues describe the temporal growth/decay rates and oscillation frequencies for each mode. The recently introduced compressed sensing DMD (csDMD) reduces computation times and also has the ability to deal with sub-sampled datasets. In this paper, we present a similar technique based on discrete cosine transform to reconstruct the fully-sampled dataset (as opposed to DMD modes as in csDMD) from sub-sampled noisy and gappy data using l 1 minimization. The proposed method was benchmarked against csDMD in terms of denoising and gap-filling using three datasets. The first was the 2-D time-resolved plot of a double gyre oscillator which has about nine oscillatory modes. The second dataset was derived from a Duffing oscillator. This dataset has several modes associated with complex eigenvalues which makes them oscillatory. The third dataset was taken from the 2-D simulation of a wake behind a cylinder at Re = 100 and was used for investigating the effect of changing various parameters on reconstruction error. The Duffing and 2-D wake datasets were tested in presence of noise and rectangular gaps. While the performance for the double-gyre dataset is comparable to csDMD, the proposed method performs substantially better (lower reconstruction error) for the dataset derived from the Duffing equation and also, the 2-D wake dataset according to the defined reconstruction error metrics

Dynamic Denoising and Gappy Data Reconstruction Based on Dynamic Mode Decomposition and Discrete Cosine Transform

Dynamic Mode Decomposition (DMD) is a data-driven method to analyze the dynamics, first applied to fluid dynamics. It extracts modes and their corresponding eigenvalues, where the modes are spatial fields that identify coherent structures in the flow and the eigenvalues describe the temporal growth/decay rates and oscillation frequencies for each mode. The recently introduced compressed sensing DMD (csDMD) reduces computation times and also has the ability to deal with sub-sampled datasets. In this paper, we present a similar technique based on discrete cosine transform to reconstruct the fully-sampled dataset (as opposed to DMD modes as in csDMD) from sub-sampled noisy and gappy data using l 1 minimization. The proposed method was benchmarked against csDMD in terms of denoising and gap-filling using three datasets. The first was the 2-D time-resolved plot of a double gyre oscillator which has about nine oscillatory modes. The second dataset was derived from a Duffing oscillator. This dataset has several modes associated with complex eigenvalues which makes them oscillatory. The third dataset was taken from the 2-D simulation of a wake behind a cylinder at Re = 100 and was used for investigating the effect of changing various parameters on reconstruction error. The Duffing and 2-D wake datasets were tested in presence of noise and rectangular gaps. While the performance for the double-gyre dataset is comparable to csDMD, the proposed method performs substantially better (lower reconstruction error) for the dataset derived from the Duffing equation and also, the 2-D wake dataset according to the defined reconstruction error metrics

Formation and activation induction of primordial follicles using granulosa and cumulus cells conditioned media : ATRABI et al.

Fertility preservation of prepubertal girls subjected to invasive cancer therapy necessitates defining protocols for activation of isolated primordial follicles. Granulosa (GCs) and cumulus cells (CCs) play pivotal role in oocyte development. Although GCs and CCs share some similarities, they differ in growth factors production. The current study was conducted to evaluate the effects of GCs, CCs and their conditioned media on mice primordial follicles activation. One-day-old mice ovaries were subjected to 6-day culture with base medium (BM), GC conditioned medium (GCCM), GC coculture (GCCC), CC conditioned medium (CCCM) or CC coculture (CCCC). Follicular growth and primordial to primary follicle transition was observed during 6-day culture, and follicular activation rate tended to be greater in GCCM than other groups (0.05 <P < 0.10). On Day 6, the expression of phosphatase and tensin homolog (PTEN) in GCCM group was lower than that in BM group (P = 0.020), the expression of phosphoinositide-3-kinase was higher in CCCC group than BM, GCCM and CCCM groups (P < 0.05), and the expression of connexin 37 was greater in the CCCM group as compared with BM, GCCC, and CCCC groups (P < 0.01). In conclusion, the current study showed that condition medium of GCs could enhance in vitro activation of primordial follicles, probably through downregulation of PTEN