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Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a…

Mesoscale eddies are of utmost importance in understanding ocean dynamics and the transport of heat, salt, and nutrients. Accurate representation of these eddies in ocean models is essential for improving model predictions. However,…

Here we propose a technique that successfully reconstructs ocean bathymetry from the free surface velocity and elevation data. This technique is based on the principles of open-channel hydraulics, according to which a sub-critical flow over…

In many experimental contexts, it is necessary to statistically remove the impact of instrumental effects in order to physically interpret measurements. This task has been extensively studied in particle physics, where the deconvolution…

We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom…

Topography on a wet rocky exoplanet could raise land above its sea level. Although land elevation is the product of many complex processes, the large-scale topographic features on any geodynamically-active planet are the expression of the…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

In recent years, deep learning (DL) has emerged as a promising alternative approach for various seismic processing tasks, including primary estimation (or multiple elimination), a crucial step for accurate subsurface imaging. In geophysics,…

Newtonian machine learning (NML) is a wave-equation inversion method that inverts single-dimensional latent space (LS) features of the seismic data for retrieving the subsurface background velocity model. The single-dimensional LS features…

Underwater images suffer from color casts and low contrast due to wavelength- and distance-dependent attenuation and scattering. To solve these two degradation issues, we present an underwater image enhancement network via medium…

We present a new seismic inversion method that uses deep learning (DL) features for the subsurface velocity model estimation. The DL feature is a low-dimensional representation of the high-dimensional seismic data, which is automatically…

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…

Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…

A common setting for scientific inference is the ability to sample from a high-fidelity forward model (simulation) without having an explicit probability density of the data. We propose a simulation-based maximum likelihood deconvolution…

Deep Convolutional Neural Networks (DCNNs) commonly use generic `max-pooling' (MP) layers to extract deformation-invariant features, but we argue in favor of a more refined treatment. First, we introduce epitomic convolution as a building…

In a previous paper, we had shown that because of varying angles of incidence there is a varying degree of convolution down a trace and across a gather, necessitating deconvolution operators varying with time and offset. This idea is…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…

Having been studied since long by statisticians, multivariate median concepts found their way into the image processing literature in the course of the last decades, being used to construct robust and efficient denoising filters for…

We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…