Function Of Model Order Research Articles

Parametric Reduced Order Models for wave propagation in 1D media containing defects

This paper presents analyses of reduced order models (ROM) for wave propagation in media containing material defects. Parametric ROMs based on POD (Proper Orthogonal Decomposition) are used here to take into account parameters that characterize local defects such as center position, extension and magnitude (localized loss of stiffness). Local and adaptive (based on the Grassmann interpolation) POD strategies are used. Sequential analyses regarding parametric dependence with one, two and three parameters are performed along with accuracy and speed up as a function of model order. Furthermore, the accuracy of ROMs is also investigated for uncertainty quantification analyses. Our results show that the choice of ROM technique is not straightforward and the best solution, which is case dependent, is not always the most complex one.

Analysis of Interpolating Regression Models and the Double Descent Phenomenon

A regression model with more parameters than data points in the training data is overparametrized and has the capability to interpolate the training data. Based on the classical bias-variance tradeoff expressions, It is commonly assumed that models which interpolate noisy training data are poor to generalize. In some cases, this is not true. The best models obtained are overparametrized and the testing error exhibits the double descent behavior as the model order increases. In this contribution, we provide some analysis to explain the double descent phenomenon, first reported in the machine learning literature. We focus on interpolating models derived from the minimum norm solution to the classical least-squares problem and also briefly discuss model fitting using ridge regression. We derive a result based on the behavior of the smallest singular value of the regression matrix that explains the peak location and the double descent shape of the testing error as a function of model order.

Factors That Influence the Choice of Markov Model Order in Discriminating DNA Sequences from Different Sources.

Markov models have frequently been used in genetic sequence analysis. The number of parameters of a Markov model increases exponentially with model order, so it is often recommended that the order be chosen based on the size of data being modeled, lower orders for small and higher orders for large dataset sizes. Approaches based on model selection criterion have also been proposed. An important problem in microbiology and evolutionary biology is to decipher chimeric genomes of microbes, particularly, identify segments of distinct ancestries in genomes and reconstruct the plausible evolutionary scenarios that might have shaped the chimeric genomes in the microbial world. In this study, we assessed a Markov model-based segmentation method for its ability to detect compositionally disparate segments in chimeric sequence constructs as a function of model order, sequence length, and phylogenetic divergence. Our results show that the choice of Markov model order depends on both sequence size and composition. Higher order Markov models were found to be more effective in delineating sequence segments arising from closely related organisms in longer constructs; on the other hand, lower order Markov models were found to be more appropriate in delineating sequence segments arising from distantly related organisms in shorter constructs. These findings are important and timely, with broad implications in fields such as epidemiology that has to deal with the emergence of novel pathogenic chimeras that arise by foreign DNA acquisition, and ecology where chimeric structures may arise in various ecosystems, necessitating more robust approaches for their deconstruction and interpretation.

The effect of model order selection in group PICA

Independent component analysis (ICA) of functional MRI data is sensitive to model order selection. There is a lack of knowledge about the effect of increasing model order on independent components' (ICs) characteristics of resting state networks (RSNs). Probabilistic group ICA (group PICA) of 55 healthy control subjects resting state data was repeated 100 times using ICASSO repeatability software and after clustering of components, centrotype components were used for further analysis. Visual signal sources (VSS), default mode network (DMN), primary somatosensory (S(1)), secondary somatosensory (S(2)), primary motor cortex (M(1)), striatum, and precuneus (preC) components were chosen as components of interest to be evaluated by varying group probabilistic independent component analysis (PICA) model order between 10 and 200. At model order 10, DMN and VSS components fuse several functionally separate sources that at higher model orders branch into multiple components. Both volume and mean z-score of components of interest showed significant (P < 0.05) changes as a function of model order. In conclusion, model order has a significant effect on ICs characteristics. Our findings suggest that using model orders < or =20 provides a general picture of large scale brain networks. However, detection of some components (i.e., S(1), S(2), and striatum) requires higher model order estimation. Model orders 30-40 showed spatial overlapping of some IC sources. Model orders 70 +/- 10 offer a more detailed evaluation of RSNs in a group PICA setting. Model orders > 100 showed a decrease in ICA repeatability, but added no significance to either volume or mean z-score results.

Experimental Feedback Control of Flow-Induced Cavity Tones

Discrete-time, linear quadratic methods were used to design feedback controllers for reducing tones generated by flow over a cavity. The dynamics of a synthetic jet actuator mounted at the leading edge of the cavity as observed by two microphones in the cavity were modeled over a broad frequency range using state space models computed from experimental data. Variations in closed loop performance as a function of model order, control order, control bandwidth, and state estimator design were studied using a cavity in the Probe Calibration Tunnel at NASA Langley. The controller successfully reduced the levels of multiple cavity tones at the tested flow speeds of Mach 0.275, 0.35, and 0.45. In some cases, the closed loop results were limited by excitation of sidebands of the cavity tones, or the creation of new tones at frequencies away from the cavity tones. Nonetheless, the results validate the combination of optimal control and experimentally-generated state space models, and suggest this approach may be useful for other flow control problems. The models were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

On the family of ML spectral estimates for mixed spectrum identification

A recently developed point spectrum identification procedure based on a family of AR and ML spectral estimates is exploited to arrive at a mixed spectrum identification procedure. To this end, a variety of properties of the AR and ML estimates as a function of model order are described. These properties relate to amplitude convergence, resolution and a characterization of the AR spectral artifact which is used to arrive at improved continuous spectral estimates. A variety of examples are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>