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The task of reconstructing smooth signals from streamed data in the form of signal samples arises in various applications. This work addresses such a task subject to a zero-delay response; that is, the smooth signal must be reconstructed…
Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…
Regression spline is a useful tool in nonparametric regression. However, finding the optimal knot locations is a known difficult problem. In this article, we introduce the Non-concave Penalized Regression Spline. This proposal method not…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high…
We provide improved parallel approximation algorithms for the important class of packing and covering linear programs. In particular, we present new parallel $\epsilon$-approximate packing and covering solvers which run in…
Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…
We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory and emerging model discovery tools to find low-dimensional subspaces…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique.…
In this paper we introduce a new method for automatically selecting knots in spline regression. The approach consists in setting a large number of initial knots and fitting the spline regression through a penalized likelihood procedure…
Spiking Neural Networks (SNNs) are more biologically plausible and computationally efficient. Therefore, SNNs have the natural advantage of drawing the sparse structural plasticity of brain development to alleviate the energy problems of…
Based on Stochastic Gradient Descent (SGD), the paper introduces two optimizers, named Interpolational Accelerating Gradient Descent (IAGD) as well as Noise-Regularized Stochastic Gradient Descent (NRSGD). IAGD leverages second-order Newton…
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing methods, SDMD explicitly incorporates sampling time into its…
We investigate the stochastic gradient descent (SGD) method where the step size lies within a banded region instead of being given by a fixed formula. The optimal convergence rate under mild conditions and large initial step size is proved.…
The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…
Intracortical brain-machine interfaces demand low-latency, energy-efficient solutions for neural decoding. Spiking Neural Networks (SNNs) deployed on neuromorphic hardware have demonstrated remarkable efficiency in neural decoding by…
In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling…
This paper extends previous identification method to the asynchronous sampling scenario, enabling the simultaneous handling of asynchronous, non-uniform, and slow-rate sampling conditions. Moving beyond lumped systems, the proposed…
Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…