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Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…

This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

Apart from discriminative models for classification and object detection tasks, the application of deep convolutional neural networks to basic research utilizing natural imaging data has been somewhat limited; particularly in cases where a…

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear…

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…

Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…

Parametric analysis is a powerful tool for designing modern embedded systems, because it permits to explore the space of design parameters, and to check the robustness of the system with respect to variations of some uncontrollable…

Lane change decision-making for autonomous vehicles is a complex but high-reward behavior. In this paper, we propose a hybrid input based deep reinforcement learning (DRL) algorithm, which realizes abstract lane change decisions and lane…

This paper presents a distributed simulation based method for harmonic resonance assessment (HRA) in multi-area large-scale power systems. Further consideration is devoted to the early harmonic frequency-scan formulation to shape them into…

This paper proposes an algorithm (RMDA) for training neural networks (NNs) with a regularization term for promoting desired structures. RMDA does not incur computation additional to proximal SGD with momentum, and achieves variance…

Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric…

Robotic manipulation of deformable 1D objects such as ropes, cables, and hoses is challenging due to the lack of high-fidelity analytic models and large configuration spaces. Furthermore, learning end-to-end manipulation policies directly…

This paper presents the syntax and semantics of a novel type of hybrid automaton (HA) with partial differential equation (PDE) dynamic, partial differential hybrid automata (PDHA). In PDHA, we add a spatial domain $X$ and harness a…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

This paper presents a control synthesis algorithm for dynamical systems to satisfy specifications given in a fragment of linear temporal logic. It is based on an abstraction-refinement scheme with nonuniform partitions of the state space. A…