Related papers: Multiscale solution decomposition of nonlocal-in-t…
We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability…
In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This…
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…
Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…
Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable…
Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed…
Example-based mesh deformation methods are powerful tools for realistic shape editing. However, existing techniques typically combine all the example deformation modes, which can lead to overfitting, i.e. using a overly complicated model to…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
Time-series forecasting often faces challenges due to data volatility, which can lead to inaccurate predictions. Variational Mode Decomposition (VMD) has emerged as a promising technique to mitigate volatility by decomposing data into…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…
This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical,…
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…