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Traditional ground-penetrating radar (GPR) data inversion leverages iterative algorithms which suffer from high computation costs and low accuracy when applied to complex subsurface scenarios. Existing deep learning-based methods focus on…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
Subsampling is a widely used and effective approach for addressing the computational challenges posed by massive datasets. Substantial progress has been made in developing non-uniform, probability-based subsampling schemes that prioritize…
The global demand for unconventional energy sources such as geothermal energy and white hydrogen requires new exploration techniques for precise subsurface structure characterization and potential reservoir identification. The…
Implicit functions such as Neural Radiance Fields (NeRFs), occupancy networks, and signed distance functions (SDFs) have become pivotal in computer vision for reconstructing detailed object shapes from sparse views. Achieving optimal…
Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…
We present a framework for supervised subspace tracking, when there are two time series $x_t$ and $y_t$, one being the high-dimensional predictors and the other being the response variables and the subspace tracking needs to take into…
Uncertainty estimation is an important research area to make deep neural networks (DNNs) more trustworthy. While extensive research on uncertainty estimation has been conducted with unimodal data, uncertainty estimation for multimodal data…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
Gravity inversion is the problem of estimating subsurface density distributions from observed gravitational field data. We consider the two-dimensional (2D) case, in which recovering density models from one-dimensional (1D) measurements…
Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…
Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important…
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing…
We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…
We address the estimation of seismic wavefields by means of Multidimensional Deconvolution (MDD) for various redatuming applications. While offering more accuracy than conventional correlation-based redatuming methods, MDD faces challenges…
Results of numerical simulations obtained by a staggered finite difference scheme together with an efficient immersed boundary method are presented to understand the effects of the shape of three-dimensional obstacles on the transition of a…
Implicit neural representations (INRs) have been successfully used to compress a variety of 3D surface representations such as Signed Distance Functions (SDFs), voxel grids, and also other forms of structured data such as images, videos,…
How to effectively explore multi-scale representations of rain streaks is important for image deraining. In contrast to existing Transformer-based methods that depend mostly on single-scale rain appearance, we develop an end-to-end…
Dimension reduction (DR) aims to learn low-dimensional representations of high-dimensional data with the preservation of essential information. In the context of manifold learning, we define that the representation after…
Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still in widespread use today. Originally introduced in the 1950's, MDS was not designed with high-dimensional data in mind; while it remains…