Related papers: Modeling Soils' Failure Envelope with Virtual Disp…
This work presents an extended formulation of the Least Squares with Virtual Displacements (LSVD) method for estimating shear strength parameters from multiple soil samples under varying resistance conditions including cohesionless,…
Wave equation techniques have been an integral part of geophysical imaging workflows to investigate the Earth's subsurface. Least-squares reverse time migration (LSRTM) is a linearized inversion problem that iteratively minimizes a misfit…
Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…
To push the radial velocity (RV) exoplanet detection threshold, it is crucial to find more reliable radial velocity extraction methods. The Least-Squares Deconvolution (LSD) technique has been used to infer the stellar magnetic flux from…
Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer…
We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can…
A novel approach to shock capturing for high-order flux reconstruction schemes is derived based on the mathematical formalism of the filtered governing equations. While the latter perspective is only typically used for turbulence modeling…
Convergence of a matrix decomposition technique, the multi-field singular value decomposition (MFSVD) which efficiently analyzes nonlinear correlations by simultaneously decomposing multiple fields, is investigated. Toward applications in…
We study $k$-SVD that is to obtain the first $k$ singular vectors of a matrix $A$. Recently, a few breakthroughs have been discovered on $k$-SVD: Musco and Musco [1] proved the first gap-free convergence result using the block Krylov…
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…
We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this…
Nonlinear least squares data-fitting driven by physical process simulation is a classic and widely successful technique for the solution of inverse problems in science and engineering. Known as "Full Waveform Inversion" in application to…
This study presents an experimental investigation of the recently established generalized linear sampling method (GLSM) for non-destructive evaluation of damage in elastic materials. To this end, ultrasonic shear waves are generated in a…
In this paper we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
Least-squares reverse time migration (LSRTM) is one of the classic seismic imaging methods to reconstruct model perturbations within a known reference medium. It can be computed in either data or image domain using different methods by…
For their ability to capture non-linearities in the data and to scale to large training sets, local Support Vector Machines (SVMs) have received a special attention during the past decade. In this paper, we introduce a new local SVM method,…
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…
This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…
Bootstrap methods have long been the cornerstone of ensemble learning in machine learning. This paper presents a theoretical analysis of bootstrap techniques applied to the Least Square Support Vector Machine (LSSVM) ensemble in the context…