arXiv subjects

Chen Lu

Publications and source records attributed to Chen Lu.

58 records · Page 4Linked to original sources

arXiv2018

Interplay of Sensor Quantity, Placement and System Dimensionality on Energy Sparse Reconstruction of Fluid Flows

Reconstruction of fine-scale information from sparse data is relevant to many practical fluid dynamic applications where the sensing is typically sparse. Fluid flows in an ideal sense are manifestations of nonlinear multiscale PDE dynamical systems with inherent scale separation that impact the system dimensionality. There is a common need to analyze the data from flow measurements or high-fidelity computations for stability characteristics, identification of coherent structures and develop evolutionary models for real-time data-driven control. Given that sparse reconstruction is inherently an ill-posed problem, the most successful approaches require the knowledge of the underlying basis space spanning the manifold in which the system resides. In this study, we employ an approach that learns basis from singular value decomposition (SVD) of training data to reconstruct sparsely sensed information at randomly sampled locations. This allows us to leverage energy sparsity with l2 minimization instead of the more expensive, sparsity promoting l1 minimization. Further, for unknown flow systems where only global operating parameters such as Reynolds (Re) number and raw data are available, it is often not clear what the optimal number of sensors and their placement for near-exact reconstruction needs to be. In this effort, we explore the interplay of data sparsity, sparsity of the underlying flow system and sensor placement on energy sparse reconstruction performance enabled by data- driven SVD basis. To this end, we investigate sparse convolution-based reconstruction performance by characterizing operational bounds for canonical laminar cylinder wake flows in both limit-cycle and transient regimes.

physics.comp-ph↗

arXiv2018

Sparse Convolution-based Markov Models for Nonlinear Fluid Flows

Data-driven modeling for nonlinear fluid flows using sparse convolution-based mapping into a feature space where the dynamics are Markov linear is explored in this article. The underlying principle of low-order models for fluid systems is identifying convolutions to a feature space where the system evolution (a) is simpler and efficient to model and (b) the predictions can be reconstructed accurately through deconvolution. Such methods are useful when real-time models from sensor data are needed for online decision making. The Markov linear approximation is popular as it allows us to leverage the vast linear systems machinery. Examples include the Koopman operator approximation techniques and evolutionary kernel methods in machine learning. The success of these models in approximating nonlinear dynamical systems is tied to the effectiveness of the convolution map in accomplishing both (a) and (b) mentioned above. To assess this, we perform in-depth study of two classes of sparse convolution operators: (i) a pure data-driven POD-convolution that uses left singular vectors of the data snapshots - a staple of Koopman approximation methods and (ii) a sparse Gaussian Process (sGP) convolution that combines sparse sampling with a Gaussian kernel embedding an implicit feature map to an inner product reproducing kernel Hilbert space.

physics.flu-dyn↗

arXiv2018

$d+id$ chiral superconductivity in a triangular lattice from trigonal bipyramidal complexes

We model the newly predicted high-$T_c$ superconducting candidates constructed by corner-shared trigonal bipyramidal complexes with an effective three-orbital tight-banding Hamiltonian and investigate the pairing symmetry of their superconducting states driven by electron-electron interactions. Our combined weak and strong coupling based calculations consistently identify the chiral $d+id$ superconductivity as the leading pairing symmetry in a wide doping range with realistic interaction parameters. This pairing state has nontrivial topological Chern-number and can host gapless chiral edge modes, and the vortex cores under magnetic field can carry Majorana zero modes.

cond-mat.str-el↗

arXiv2016

New Approaches to Identify Gene-by-Gene Interactions in Genome Wide Association Studies

Genetic variants identified to date by genome-wide association studies only explain a small fraction of total heritability. Gene-by-gene interaction is one important potential source of unexplained heritability. In the first part of this dissertation, a novel approach to detect such interactions is proposed. This approach utilizes penalized regression and sparse estimation principles, and incorporates outside biological knowledge through a network-based penalty. The method is tested on simulated data under various scenarios. Simulations show that with reasonable outside biological knowledge, the new method performs noticeably better than current stage-wise strategies, especially when the marginal strength of main effects is weak. The proposed method is designed for single-cohort analyses. However, it is generally acknowledged that only multi-cohort analyses have sufficient power to uncover genes and gene-by-gene interactions with moderate effects on traits, such as likely underlie complex diseases. Multi-cohort, meta-analysis approaches for penalized regressions are developed and investigated in the second part of this dissertation. Specifically, I propose two different ways of utilizing data-splitting principles in multi-cohort settings and develop three procedures to conduct meta-analysis. Using the method developed in the first part of this dissertation as an example of penalized regressions, three proposed meta-analysis procedures are compared to mega-analysis using a simulation study. The results suggest that the best approach is to split the participating cohorts into two groups. In the last part of this dissertation, the novel method developed in the first part is applied to the Framingham Heart Study measures on total plasma Immunoglobulin E (IgE) concentrations, C-reactive protein levels, and Fasting Glucose.

stat.ME↗