Low-dimensional Model Research Articles

Efficient reduced-order aerodynamic modeling in low-Reynolds-number incompressible flows

This study aims to develop a non-intrusive reduced-order aerodynamic modeling framework for agile motion across a broad operating range in low-Reynolds-number incompressible flows. Since most previous reduced-order models are only valid in the neighborhood of the operating point, large amounts of high-fidelity input-output data have to be generated to cover the interested operating range, which requires expensive computational resources. To tackle such an issue, a signal interpolation approach by combining the discrete empirical interpolation method (DEIM) with Kriging technique is proposed to approximate the aerodynamic responses to a prescribed linear ramp-step maneuver with remarkable accuracy, instead of performing computational fluid dynamics (CFD) simulation at each operating point. The interpolated input-output data can be used to establish low-dimensional state-space aerodynamic models, by identifying the stability derivatives first and subsequently capturing the remaining transient dynamics via the eigensystem realization algorithm (ERA). To demonstrate the proposed framework, unsteady lift coefficients of a two-dimensional flat plate pitching about the leading edge are investigated over the range with Reynolds numbers 100∼500 and base angles of attack 0∼10 deg. Numerical results show good agreement between the reduced-order models and high-fidelity CFD simulations.

Conformal growth rates and spectral geometry on distributional limits of graphs

For a unimodular random graph (G,ρ), we consider deformations of its intrinsic path metric by a (random) weighting of its vertices. This leads to the notion of the conformal growth exponent of (G,ρ), which is the best asymptotic degree of volume growth of balls that can be achieved by such a reweighting. Under moment conditions on the degree of the root, we show that the conformal growth exponent of a unimodular random graph bounds its almost sure spectral dimension. This has interesting consequences for many low-dimensional models. The consequences in dimension two are particularly strong. It establishes that models like the uniform infinite planar triangulation (UIPT) and quadrangulation (UIPQ) almost surely have spectral dimension at most two. It also establishes a conjecture of Benjamini and Schramm (Electron. J. Probab. 6 (2001) no. 23) by extending their recurrence theorem from planar graphs to arbitrary families of H-minor-free graphs. More generally, it strengthens the work of Gurel-Gurevich and Nachmias (Ann. of Math. (2) 177 (2013) 761–781) who established recurrence for distributional limits of planar graphs when the degree of the root has exponential tails. We further present a general method for proving subdiffusivity of the random walk on a large class of models, including UIPT and UIPQ, using only the volume growth profile of balls in the intrinsic metric.

An Autonomous Cyber-Physical Anomaly Detection System Based on Unsupervised Disentangled Representation Learning

Cyber-Physical Systems (CPS) in heavy industry are a combination of closely integrated physical processes, networking, and scientific computing. The physical production process is monitored and controlled by the CPS in question, through advanced real-time networking systems, where high-precision feedback loops can be changed when the overgrid of cooperative computing and communication components that make up the industrial process is required. These CPS operate independently but integrate interaction capabilities as well as with the external environment, creating the connection of the physical with the digital world. The outline is that the most effective modeling and development of high-reliability CPS are directly related to the maximization of the production process, extroversion, and industrial competition. In this paper, considering the high importance of the operational status of CPS for heavy industry, an innovative autonomous anomaly detection system based on unsupervised disentangled representation learning is presented. It is a temporal disentangled variational autoencoder (TDVA) which, mimicking the process of rapid human intuition, using high- or low-dimensional reasoning, finds and models the useful information independently, regardless of the given problem. Specifically, taking samples from the real data distribution representation space, separating them appropriately, and encoding them as separate disentangling dimensions create new examples that the system has not yet dealt with. In this way, first, it utilizes information from potentially inconsistent sources to learn the right representations that can then be broken down into subspace subcategories for easier and simpler categorization, and second, utilizing the latent representation of the model, it performs high-precision estimates of how similar or dissimilar the inputs are to each other, thus recognizing, with great precision and in a fully automated way, the system anomalies.

Curvature-based low-dimensional parametric model for the elastostatics analysis of planar compliant mechanisms under large deflection

<p indent=0mm>Based on<bold> </bold>the approximation of the bending curvature by Bernstein polynomials, a novel parametric model suitable for large deflection analysis is proposed for studying planar compliant mechanisms with uniform slender beam members. The numerical formulation is also presented based on Gaussian quadrature and Newton-Raphson iterations. By considering the bending curvature and coefficients of the Bernstein polynomial as the deformation field and unknown parameters, respectively, the equilibrium equations of the compliant mechanisms with geometric nonlinearity were established based on the principle of the minimum total potential energy. Further, the proposed method effectively avoided the numerical error introduced by using the deformation displacement to derive and calculate strain energy and greatly reduced the smoothness requirement of the trial function. Hence, the novel model possesses the benefits of high modeling accuracy, fast convergence speed in the numerical calculation, and versatility for application to straight and initially curved beams. Meanwhile, the parameterized curvature solutions have great geometric and mechanical significance that allows not only to realize the unified kinematic modeling of rigid and flexible bodies but also to efficiently present the complex and rich deformation information of slender beams under large deflections. The improved performance of the developed models was demonstrated through some classic numerical examples.

A high-dimensional test on linear hypothesis of means under a low-dimensional factor model

A high-dimensional test on linear hypothesis of means under a low-dimensional factor model

Multivariate Analysis of Immune Reconstitution and Relapse Risk Scoring in Children Receiving Allogeneic Stem Cell Transplantation for Acute Leukemias.

Background.A timely and effective immune reconstitution after hematopoietic stem cell transplantation (HSCT) is of crucial importance to enhance graft-versus-leukemia reaction in hematological malignancies. Several factors can influence the yield of this process, and new mathematical models are needed to describe this complex phenomenon.Methods.We retrospectively analyzed immune reconstitution in the early post-HSCT period in a multicenter cohort of 206 pediatric patients affected by acute lymphoblastic leukemia, acute myeloblastic leukemia, and myelodysplastic syndrome who received their first allo-HSCT. All patients were in complete morphological remission at transplantation and were followed-up at least 26 mo post-HSCT. Blood samples for analysis of lymphocyte subset numbers were collected at day 100 (±20 d).Results.The 2-y cumulative incidence of relapse was 22.2% (95% confidence interval [CI], 17.3-27). Using principal component analysis, we identified based on 16 input variables a new multivariate model that enables patients’ description in a low-dimensional model, consisting of the first 2 principal components. We found that the numbers of CD3+/CD4+/CD8+ lymphocyte subsets at day 100 post-HSCT and acute graft-versus-host disease had the greatest impact in preventing relapse. We ultimately derived a risk score defining high- or medium-low–risk groups with 2-y cumulative incidence of relapse: 35.3% (95% CI, 25.6-45) and 15.6% (95% CI, 10.1-20.7), respectively (P = 0.001*).Conclusions.Our model describes immune reconstitution and its main influencing factors in the early posttransplantation period, presenting as a reliable model for relapse risk prediction. If validated, this model could definitely serve as a predictive tool and could be used for clinical trials or for individualized patient counseling.

Active intrinsic conductances in recurrent networks allow for long-lasting transients and sustained activity with realistic firing rates as well as robust plasticity.

Recurrent neural networks of spiking neurons can exhibit long lasting and even persistent activity. Such networks are often not robust and exhibit spike and firing rate statistics that are inconsistent with experimental observations. In order to overcome this problem most previous models had to assume that recurrent connections are dominated by slower NMDA type excitatory receptors. Usually, the single neurons within these networks are very simple leaky integrate and fire neurons or other low dimensional model neurons. However real neurons are much more complex, and exhibit a plethora of active conductances which are recruited both at the sub and supra threshold regimes. Here we show that by including a small number of additional active conductances we can produce recurrent networks that are both more robust and exhibit firing-rate statistics that are more consistent with experimental results. We show that this holds both for bi-stable recurrent networks, which are thought to underlie working memory and for slowly decaying networks which might underlie the estimation of interval timing. We also show that by including these conductances, such networks can be trained to using a simple learning rule to predict temporal intervals that are an order of magnitude larger than those that can be trained in networks of leaky integrate and fire neurons.

Revisiting a low-dimensional model with short-range interactions and mean-field critical behavior

In all known local low-dimensional models, scaling at critical points deviates from mean-field behavior —with one possible exception. This exceptional model with “ordinary” behavior is an inherently non-equilibrium model studied some time ago by H.-M. Bröker and myself. In simulations, its 2-dimensional version suggested that two critical exponents were mean-field, while a third one showed very small deviations. Moreover, the numerics agreed almost perfectly with an explicit mean-field model. In the present paper we present simulations with much higher statistics, both for 2d and 3d. In both cases we find that the deviations of all critical exponents from their mean-field values are non-leading corrections, and that the scaling is precisely of mean-field type. As in the original paper, we propose that the mechanism for this is “confusion”, a strong randomization of the phases of feedbacks that can occur in non-equilibrium systems.

The Maximum Likelihood Ensemble Filter with State Space Localization

AbstractA new method for ensemble data assimilation that incorporates state space covariance localization, global numerical optimization, and implied Bayesian inference is presented. The method is referred to as the MLEF with state space localization (MLEF-SSL) due to its similarity with the maximum likelihood ensemble filter (MLEF). One of the novelties introduced in MLEF-SSL is the calculation of a reduced-rank localized forecast error covariance using random projection. The Hessian preconditioning is accomplished via Cholesky decomposition of the Hessian matrix, accompanied with solving triangular system of equations instead of directly inverting matrices. For ensemble update, the MLEF-SSL system employs resampling of posterior perturbations. The MLEF-SSL was applied to Lorenz model II and compared to ensemble Kalman filter with state space localization and to MLEF with observation space localization. The observations include linear and nonlinear observation operators, each applied to integrated and point observations. Results indicate improved performance of MLEF-SSL, particularly in assimilation of integrated nonlinear observations. Resampling of posterior perturbations for an ensemble update also indicates a satisfactory performance. Additional experiments were conducted to examine the sensitivity of the method to the rank of random matrix and to compare it to truncated eigenvectors of the localization matrix. The two methods are comparable in application to low-dimensional Lorenz model, except that the new method outperforms the truncated eigenvector method in case of severe rank reduction. The random basis method is simple to implement and may be more promising for realistic high-dimensional applications.

Linear-Threshold Dynamics for the Study of Epileptic Events

In this letter, we provide a detailed characterization of the equilibria and bifurcations of two-dimensional linear-threshold models. Using the input to the system as the bifurcation parameter, we characterize the location of the admissible equilibria, show that bifurcations can arise only when equilibria lie on the boundary of well-defined regions of the state space, and prove that (codimension-one) bifurcations can only be of three different types: persistent, non-smooth fold, and Hopf. We show how these bifurcations change the qualitative properties of the system trajectories, and how these behaviors resemble prototypical patterns of EEG activity observed before, during, and after seizure events in the human brain. Our findings suggest that low-dimensional linear threshold models can effectively be used to model, analyze, predict, and ultimately regulate the interactions of neuronal populations in the human brain.

Low-order modelling of the wake dynamics of an Ahmed body

We investigate the large-scale signature of the random switches between two mirrored turbulent wake states of flat-backed bodies. A direct numerical simulation (DNS) of the flow around an Ahmed body at a Reynolds number ( $Re$ ) of 10 000 is considered. Using proper orthogonal decomposition (POD), we identify the most energetic modes of the velocity field and build a low-dimensional model based on the first six fluctuating velocity modes capturing the characteristics of the flow dynamics during and between switches. In the absence of noise, the model produces random switches with characteristic time scales in agreement with the simulation and experiments. This chaotic model suggests that random switches are triggered by the increase of the vortex shedding activity. However, the addition of noise results in a better agreement in the temporal spectra of the coefficients between the model and the simulation.

Controllability and state feedback control of a cardiac ionic cell model

A phenomenon called alternans, which is a beat-to-beat alternation in action potential (AP) duration, sometimes precedes fatal cardiac arrhythmias. Alternans-suppressing electrical stimulus protocols are often represented as perturbations to the dynamics of membrane potential or AP duration variables in nonlinear models of cardiac tissue. Controllability analysis has occasionally been applied to cardiac AP models to determine whether different control or perturbation strategies are capable of suppressing alternans or other unwanted behavior. Since almost all previous cardiac controllability studies have focused on low-dimensional models, we conducted the present study to assess controllability of a higher-dimensional model, specifically the Luo Rudy dynamic (LRd) model of a cardiac ventricular myocyte. Higher-dimensional models are of interest because they provide information on the influence of a wider range of measurable quantities, including ionic concentrations, on controllability. After computing modal controllability measures, we found that larger eigenvalues of a linearized LRd model were on average more strongly controllable through perturbations to calcium-ion concentrations compared with perturbations to other variables. When only membrane potential was adjusted, the best time to apply perturbations (in the sense of maximizing controllability of the largest alternans eigenvalue) was near the AP peak time for shorter cycle lengths. Controllability results were found to be similar for both the default model parameters and for an alternans-promoting parameter set. Additionally, we developed several alternans-suppressing state feedback controllers that were tested in simulations. For the scenarios examined, our controllability measures correctly predicted which strategies and perturbation timings would lead to better feedback controller performance.

Thermal field reconstruction based on weighted dictionary learning

Dynamic thermal management (DTM) is applied to address the thermal problem of high performance very-large-scale integrated chips. The false alarm rate (FAR) can be used to evaluate the impact of full-chip thermal field reconstruction accuracy on DTM. A low FAR relies on the accurate reconstruction of the full thermal field, especially near the temperature triggering threshold of DTM. However, little attention is currently being paid to such temperature ranges. To reduce FAR, a new full-chip thermal field reconstruction strategy is proposed. A low-dimensional linear model is used to accurately represent the thermal fields. The dictionary learning technology is exploited to train the model and the minimum weighted mean square error evaluation method is incorporated to improve the reconstruction accuracy near the temperature triggering threshold. A temperature sensor placement algorithm using the heuristic algorithm to solve the NP-hard problem is also proposed. The experimental results show that the proposed strategy can reconstruct the full thermal field with a more precise accuracy near the triggering threshold and achieve the lowest FAR compared to the state of the art.

Low-dimensional models for real time simulations of monolith reactors with dual washcoat layers

We present a novel and accurate procedure with local property dependent internal and external mass transfer coefficient matrices for real time simulations of monolith reactors with dual washcoat layers. Our approach extends the prior work based on the Thiele matrix method for accurately describing the washcoat diffusional effects in single layered systems. It combines the vector form of the multi-scale averaged model with calculation of the local property dependent internal, external and cross-Sherwood number matrices for multi-component systems. We illustrate the usefulness of the reduced order model using the example of a dual-layered model system with first washcoat layer of selective catalytic reduction (SCR) catalyst and second washcoat layer of lean NOx trap (LNT) catalyst. We determine the mesh size independent solutions of the full 1+1D detailed model and compare the same with that obtained with the reduced order model. We show that the proposed method has the same accuracy as the mesh size independent detailed solution while speeding up calculations by about three orders of magnitude for the example studied, and possibly by several more orders of magnitude for real systems with complex and detailed micro-kinetic models to describe the storage and reactions in the catalytic layers.

Bifurcation analysis of vortex-induced vibration of low-dimensional models of marine risers

A low-dimensional model of a top-tensioned riser under excitations from vortices and time-varying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding. The governing partial differential equations describing the fluid–structure interactions are formulated and multi-mode approximations are obtained using the Galerkin projection method. The one mode approximation is applied in this study and two different resonances are investigated by employing the method of multiple scales. They are the 1:1 internal resonance between the structure and wake oscillator (also known as ‘lock-in’ phenomenon) and the combined 1:1 internal and 1:2 parametric resonances. Bifurcations under the varying nondimensional shedding frequency for different mass–damping parameters are investigated and the results of multiple-scale analysis are compared with direct numerical simulations. Analytical responses are calculated using the continuation method and their stability is determined by examining the eigenvalues of the corresponding characteristic equations. Effects of the system parameters including the amplitude of the tension variation, vortex shedding frequency and mass–damping parameter on the system bifurcations have been investigated. The analytical approach has allowed to probe bifurcations occurring in the system and to identify stable and unstable responses. It is shown that the combined resonances can induce large-amplitude vibration of the structure. Counter-intuitively, the amplitude of such responses increases rapidly as the amplitude of the tension variation grows. Comparisons between the analytical and numerical results confirm that the span of the system vibration can be accurately predicted analytically with respect to the obtained response amplitudes of responses. The proposed multi-mode approximation and presented findings of this study can be used to enhance design process of top tension risers.

Analytical temperature profiles for laser-irradiated gold nanorod immersed in an optically non-absorbing medium

Laser heating of gold nanorods immersed in an optically non-absorbing medium is important in both therapeutic and diagnostic medical procedures. For both continuous wave and pulsed lasers, we derive analytical temperature solutions by modeling a nanorod as a prolate spheroid. For the continuous wave laser irradiation, an exact analytical solution for the steady state heat transfer case using integer-degree Legendre function expansions in prolate spheroidal coordinates is presented. The steady state solution reveals that for the case of gold nanorod immersed in water, there is insignificant temperature variations on any single spheroidal surface that is coincident or confocal to the prolate spheroid surface, and the temperature only changes across spheroidal surfaces within the immediate surrounding water. This is found to be due to the very high thermal conductivity of gold which is more than a hundred-fold higher than that of water. The insight that the temperature rise is nearly invariant on any single spheroidal surface, along with a dimensional analysis, helps reduce the complexity of the heat equation in the unsteady regime of a pulsed laser illumination, and leads to a simple, lower dimensional model of unsteady heat equation, which takes into account the temporal dependency and spatial dependency in the direction across spheroidal surfaces. For the reduced unsteady heat equation, a simple, efficient, and insightful solution algorithm based on the Laplace transform and complex-degree Legendre functions is proposed. The maximum temperature and temperature profiles as functions of laser power, and nanorod geometries are obtained, revealing that for a fixed laser fluence and fixed nanorod mass, the more stretched nanorods yield higher temperatures in the spheroid and its immediate surroundings. In other words, more stretched nanorods are more efficient in converting the laser energy into localized, elevated temperatures. The obtained temperature solutions are useful in designing a parameter space for optimum therapeutic procedures for ablating cancer cells using high temperatures generated in the immediate vicinity of nanoparticles. The unsteady temperature solutions can also be used to obtain solutions to thermo-elastic models which are used to compute the photoacoustic signals that can, in turn, be used for cellular imaging and diagnostics.

Inference for High-Dimensional Censored Quantile Regression

With the availability of high-dimensional genetic biomarkers, it is of interest to identify heterogeneous effects of these predictors on patients’ survival, along with proper statistical inference. Censored quantile regression has emerged as a powerful tool for detecting heterogeneous effects of covariates on survival outcomes. To our knowledge, there is little work available to draw inferences on the effects of high-dimensional predictors for censored quantile regression (CQR). This article proposes a novel procedure to draw inference on all predictors within the framework of global CQR, which investigates covariate-response associations over an interval of quantile levels, instead of a few discrete values. The proposed estimator combines a sequence of low-dimensional model estimates that are based on multi-sample splittings and variable selection. We show that, under some regularity conditions, the estimator is consistent and asymptotically follows a Gaussian process indexed by the quantile level. Simulation studies indicate that our procedure can properly quantify the uncertainty of the estimates in high-dimensional settings. We apply our method to analyze the heterogeneous effects of SNPs residing in lung cancer pathways on patients’ survival, using the Boston Lung Cancer Survival Cohort, a cancer epidemiology study on the molecular mechanism of lung cancer.

Character classification algorithm based on the low-dimensional feature-optimized model

Character classification algorithm based on the low-dimensional feature-optimized model

Lower-dimensional approximation models of tangential strain rate of turbulent flames

Lower-dimensional approximation models of tangential strain rate of turbulent flames

Event-Based Air Transport Network Resiliency Management with Meta-Population Epidemic Model

This paper aims to provide a resiliency management strategy of the air transportation network through network stability theory. To ensure the network to recover quickly from an upset condition, an optimization problem has been introduced through network stability upon the meta-population epidemic process model, which is a low-dimensional approximate model of the air traffic flow network. The delay propagation over air traffic network has been modeled as an epidemic spreading process model, which allows to define the whole network through a few states of the individuals (i.e., flights) and recovery rates of the nodes (i.e., airports). The physical parameters of the network extracted from real flight data set are transformed into a parameter set of the epidemic model enabling to simulate the propagation of delay. Moreover, self-organizing maps are used, generating the discretized representation of the input space through an artificial neural network to analyze the European air traffic network with regard to resiliency metrics. Through examples with historical real flight data, it is shown that the applied methodology to control the infection rates, which has the direct projection to operational applications such as ground holding and flight cancellation, effectively enhances the resiliency of the air traffic network under disruptive events.