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We are concerned with high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters…
High spatial frequency information, including fine details like textures, significantly contributes to the accuracy of semantic segmentation. However, according to the Nyquist-Shannon Sampling Theorem, high-frequency components are…
This paper proposes an algorithm based on a staged sliding window Transformer architecture to detect abnormal behaviors in the microstructure of the foreign exchange market, focusing on high-frequency EUR/USD trading data. The method…
We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in [Li and Hu, {\it J. Comput. Phys.}, 2021], for efficiently solving subdiffusion equations with heterogeneous coefficients in long time. This…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…
Diffusion models have become the dominant tool for high-fidelity image and video generation, yet are critically bottlenecked by their inference speed due to the numerous iterative passes of Diffusion Transformers. To reduce the exhaustive…
Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…
We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…
Partial differential equations (PDEs) with multiple scales or those defined over sufficiently large domains arise in various areas of science and engineering and often present problems when approximating the solutions numerically. Machine…
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near…
We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain…
We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The…
We address the problem of simultaneously recovering a sequence of point source signals from observations limited to the low-frequency end of the spectrum of their summed convolution, where the point spread functions (PSFs) are unknown. By…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
Any frequency selective device with an ongoing drift will cause observed spectra to be variously and simultaneously scaled in proportion to their source distances. The reason is that detectors after the drifting selection will integrate…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…