相关论文: The Sparse-Grid-Based Adaptive Spectral Koopman Me…

The estimation of equations from data is of interest in physics. One of the famous methods is the sparse identification of nonlinear dynamics (SINDy), which utilizes sparse estimation techniques to estimate equations from data. Recently, a…

In this paper we present an active-set method for the solution of $\ell_1$-regularized convex quadratic optimization problems. It is derived by combining a proximal method of multipliers (PMM) strategy with a standard semismooth Newton…

In this paper, we consider a class of convex programming problems with linear equality constraints, which finds broad applications in machine learning and signal processing. We propose a new adaptive balanced augmented Lagrangian (ABAL)…

In this work we approach the dual optimal reach-safe control problem using sparse approximations of Koopman operator. Matrix approximation of Koopman operator needs to solve a least-squares (LS) problem in the lifted function space, which…

We present a fully parallelized grid-based parameter estimation algorithm for investigating multidimensional likelihoods called Snake, and apply it to cosmological parameter estimation. The basic idea is to map out the likelihood grid-cell…

Proximal methods such as the Alternating Direction Method of Multipliers (ADMM) are effective at solving constrained quadratic programs (QPs). To tackle infeasible QPs, slack variables are often introduced to ensure feasibility, which…

The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…

The alternating direction method of multipliers (ADMM) is a powerful optimization solver in machine learning. Recently, stochastic ADMM has been integrated with variance reduction methods for stochastic gradient, leading to SAG-ADMM and…

We consider convex optimization problems with a possibly nonsmooth objective function in the form of a mathematical expectation. The proposed framework (AN-SPS) employs Sample Average Approximations (SAA) to approximate the objective…

In this paper, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method…

Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models…

This paper proposes a general adaptive procedure for budget-limited predictor design in high dimensions called two-stage Sampling, Prediction and Adaptive Regression via Correlation Screening (SPARCS). SPARCS can be applied to high…

Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with systems having high input dimensionality, reliability estimation becomes a daunting task. A popular approach to overcome…

Nonlinearity presents a significant challenge in problems involving dynamical systems, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. In this paper, we introduce the Koopman…

This paper presents a simple, efficient, and high-order accurate sliding-mesh interface approach to the spectral difference (SD) method. We demonstrate the approach by solving the two-dimensional compressible Navier-Stokes equations on…

PINNs enhance scientific computing by incorporating physical laws into neural network structures, leading to significant advancements in scientific computing. However, PINNs struggle with multi-scale and high-frequency problems due to…

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…

We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…