Information Theoretic Multi-Target Feature Selection via Output Space Quantization

A key challenge in information theoretic feature selection is to estimate mutual information expressions that capture three desirable terms—the relevancy of a feature with the output, the redundancy and the complementarity between groups of features. The challenge becomes more pronounced in multi-target problems, where the output space is multi-dimensional. Our work presents an algorithm that captures these three desirable terms and is suitable for the well-known multi-target prediction settings of multi-label/dimensional classification and multivariate regression. We achieve this by combining two ideas—deriving low-order information theoretic approximations for the input space and using quantization algorithms for deriving low-dimensional approximations of the output space. Under the above framework we derive a novel criterion, Group-JMI-Rand, which captures various high-order target interactions. In an extensive experimental study we showed that our suggested criterion achieves competing performance against various other information theoretic feature selection criteria suggested in the literature.

A Hybrid Data-Driven Deep Learning Technique for Fluid-Structure Interaction

This paper is concerned with the development of a hybrid data-driven technique for unsteady fluid-structure interaction systems. The proposed data-driven technique combines the deep learning framework with a projection-based low-order modeling. While the deep learning provides low-dimensional approximations from datasets arising from black-box solvers, the projection-based model constructs the low-dimensional approximations by projecting the original high-dimensional model onto a low-dimensional subspace. Of particular interest of this paper is to predict the long time series of unsteady flow fields of a freely vibrating bluff-body subjected to wake-body synchronization. We consider convolutional neural networks (CNN) for the learning dynamics of wake-body interaction, which assemble layers of linear convolutions with nonlinear activations to automatically extract the low-dimensional flow features. Using the high-fidelity time series data from the stabilized finite element Navier-Stokes solver, we first project the dataset to a low-dimensional subspace by proper orthogonal decomposition (POD) technique. The time-dependent coefficients of the POD subspace are mapped to the flow field via a CNN with nonlinear rectification, and the CNN is iteratively trained using the stochastic gradient descent method to predict the POD time coefficient when a new flow field is fed to it. The time-averaged flow field, the POD basis vectors, and the trained CNN are used to predict the long time series of the flow fields and the flow predictions are quantitatively assessed with the full-order (high-dimensional) simulation data. The proposed POD-CNN model based on the data-driven approximation has a remarkable accuracy in the entire fluid domain including the highly nonlinear near wake region behind a freely vibrating bluff body.

Low-Dimensional Approximation for Control of Spatio-Temporal Processes Using Principal Interaction Patterns

Although the first-principal models of the spatio-temporal processes can accurately predict nonlinear and distributed dynamical behaviors, their infinite-dimensional nature does not allow their directly use. In this note, low-dimensional approximations for control of spatio-temporal processes using principal interaction patterns are constructed. Advanced model reduction approach based on spatial basis function expansion together with Galerkin method is used to obtain the low-dimensional approximation. Spatial structure called principal interaction patterns are extracted from the system according to a variational principle and used as basis functions in a Galerkin approximation. The simulations of the burgers equations has illustrated that low-dimensional approximation based on principal interaction patterns for spatio-temporal processes has smaller errors than more conventional approaches using Fourier modes or Empirical Eigenfunctions as basis functions.

Low Dimensional Approximations to Ferroelastic Dynamics and Hysteretic Behavior Due to Phase Transformations

In this paper, a low dimensional model is constructed to approximate the nonlinear ferroelastic dynamics involving mechanically and thermally-induced martensite transformations. The dynamics of the first order martensite transformation is first modeled by a set of nonlinear coupled partial differential equations (PDEs), which is obtained by using the modified Ginzburg–Landau theory. The Chebyshev collocation method is employed for the numerical analysis of the PDE model. An extended proper orthogonal decomposition is then carried out to construct a set of empirical orthogonal eigenmodes of the dynamics, with which system characteristics can be optimally approximated (in a specified sense) within a range of different temperatures and under various mechanical and thermal loadings. The performance of the low dimensional model is analyzed numerically. Results on the dynamics involving mechanically and thermally-induced phase transformations and the hysteresis effects induced by such transformations are presented.

Model Reduction by Proper Orthogonal Decomposition Coupled With Centroidal Voronoi Tessellations (Keynote)

Proper orthogonal decompositions (POD) have been used to define reduced bases for low-dimensional approximations of complex systems, including turbulent flows. Centroidal Voronoi tessellations (CVT) have been used in a variety of data compression and clustering settings. We review both strategies in the context of model reduction for complex systems and propose combining the ideas of CVT and POD into a hybrid method that inherets favorable characteristics from both its parents. The usefulness of such an approach and various practical implementation strategies are discussed.