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Idealized and comprehensive ocean models at low resolutions cannot reproduce nominally-resolved flow structures similar to those presented in the high-resolution solution. Although there are various underlying physical reasons for this,…

Travelling wavepackets are key coherent features contributing to the dynamics of several advective flows. This work introduces the Hilbert proper orthogonal decomposition (HPOD) to distil these features from flow field data, leveraging…

Recently, the degenerate preconditioned proximal point (PPP) method provides a unified and flexible framework for designing and analyzing operator-splitting algorithms such as Douglas-Rachford (DR). However, the degenerate PPP method…

This paper presents an improved and modified partial differential equation (PDE)-based de-hazing algorithm. The proposed method combines logarithmic image processing models in a PDE formulation refined with linear filter-based operators in…

We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible…

Remote sensing of oceanographic data often yields incomplete coverage of the measurement domain. This can limit interpretability of the data and identification of coherent features informative of ocean dynamics. Several methods exist to…

Estimating time-resolved velocity and pressure fields from Particle Image Velocimetry (PIV) remains challenging due to its limited temporal resolution in many applications. Data-driven approaches that combine snapshot PIV with…

The characteristic decomposition for GRMHD is not known in a form useful for current numerical simulations. This prevents us from using the most accurate known computational methods, such as full-wave Riemann solvers. In this paper, we…

Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…

Constructing high-definition (HD) maps from sensory input requires accurately mapping the road elements in image space to the Bird's Eye View (BEV) space. The precision of this mapping directly impacts the quality of the final vectorized HD…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to…

Computing the dispersion relation for two-dimensional photonic crystals is a notoriously challenging task: It involves solving parameterized Helmholtz eigenvalue problems with high-contrast coefficients. To resolve the challenge, we propose…

The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal fluid velocity. However, numerical simulations can violate these…

Underwater images are often affected by light refraction and absorption, reducing visibility and interfering with subsequent applications. Existing underwater image enhancement methods primarily focus on improving visual quality while…

Image reconstruction in the presence of severe degradation remains a challenging inverse problem, particularly in beam diagnostics for high-energy physics accelerators. As modern facilities demand precise detection of beam halo structures…

With the advent of NASA's lunar reconnaissance orbiter (LRO), a large amount of high-resolution digital elevation maps (DEMs) have been constructed by using narrow-angle cameras (NACs) to characterize the Moon's surface. However, NAC DEMs…

Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic -- primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms…

In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in…

Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…