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The sensitivity of long-time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction, the uniformly-bounded-in-time solution of the sensitivity equations. Although its existence is…

Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…

Data-driven dimensionality reduction methods such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known…

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…

Detecting Earth twins remains challenging because their shallow, long-period transits are difficult to distinguish from background noise. Motivated by the challenge, we developed Segmented-Polynomial-fitting Least Squares (SPLS), a new…

Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical…

Color-guided depth super-resolution (DSR) is an encouraging paradigm that enhances a low-resolution (LR) depth map guided by an extra high-resolution (HR) RGB image from the same scene. Existing methods usually use interpolation to upscale…

This paper presents a novel method for smoothed particle hydrodynamics (SPH) with thin-walled structures. Inspired by the direct forcing immersed boundary method, this method employs a moving least square method to guarantee the smoothness…

Seismic imaging in challenging sedimentary basins and reservoirs requires acquiring, processing, and imaging very large volumes of data (tens of terabytes). To reduce the cost of acquisition and the time from acquiring the data to producing…

Seismic imaging is a computationally demanding and data-intensive activity in the oil and gas industry. Reverse Time Migration (RTM) used in seismic applications needs to store the forward-propagated wavefield (or source wavefield) on disk.…

The Vera C. Rubin Observatory Wide-Fast Deep (WFD) sky survey will reach unprecedented surface brightness depths over tens of thousands of square degrees. Surface brightness photometry has traditionally been a challenge. Current algorithms…

Seismic images obtained by stacking or migration are usually characterized as low signal-to-noise ratio (SNR), low dominant frequency and sparse sampling both in depth (or time) and offset dimensions. For improving the resolution of seismic…

Multi-frequency subspace migration imaging technique are usually adopted for the non-iterative imaging of unknown electromagnetic targets such as cracks in the concrete walls or bridges, anti-personnel mines in the ground, etc. in the…

This paper presents a formulation of Snapshot Positioning as a mixed-integer least-squares problem. In snapshot positioning one estimates a position from code-phase and possibly Doppler observations of a Global Navigation Satellite Systems…

In this paper, we provide a theoretical study of noise geometry for minibatch stochastic gradient descent (SGD), a phenomenon where noise aligns favorably with the geometry of local landscape. We propose two metrics, derived from analyzing…

The interplay between optimization and privacy has become a central theme in privacy-preserving machine learning. Noisy stochastic gradient descent (SGD) has emerged as a cornerstone algorithm, particularly in large-scale settings. These…

In this work, we present a subdomain discontinuous least-squares (SDLS) scheme for neutronics problems. Least-squares (LS) methods are known to be inaccurate for problems with sharp total-cross section interfaces. In addition, the…

This work introduces a novel method to generate snapshot data for operator inference that guarantees the exact reconstruction of intrusive projection-based reduced-order models (ROMs). To ensure exact reconstruction, the operator inference…

Consider the problem of registering multiple point sets in some $d$-dimensional space using rotations and translations. Assume that there are sets with common points, and moreover the pairwise correspondences are known for such sets. We…

Robust regression techniques rely on least-squares optimization, which works well for Gaussian noise but fails in the presence of asymmetric structured noise. We propose a hybrid neural-symbolic architecture where a transformer encoder…