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We propose a novel data-driven approach for high-resolution bathymetric reconstruction from sidescan. Sidescan sonar (SSS) intensities as a function of range do contain some information about the slope of the seabed. However, that…

Background: Floods are the most common natural disaster in the world, affecting the lives of hundreds of millions. Flood forecasting is therefore a vitally important endeavor, typically achieved using physical water flow simulations, which…

When a fluid flows over a solid surface, it creates a thin boundary layer where the flow velocity is influenced by the surface through viscosity, and can transition from laminar to turbulent at sufficiently high speeds. Understanding and…

Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

In a desired environmental protection system, groundwater may not be excluded. In addition to the problem of over-exploitation, in total disagreement with the concept of sustainable development, another not negligible issue concerns the…

Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…

The paper surveys recent progresses in understanding the dynamics and loss landscape of the gradient flow equations associated to deep linear neural networks, i.e., the gradient descent training dynamics (in the limit when the step size…

The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…

The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of…

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for…

Real depth super-resolution (DSR), unlike synthetic settings, is a challenging task due to the structural distortion and the edge noise caused by the natural degradation in real-world low-resolution (LR) depth maps. These defeats result in…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Inferring seabed topography from wave height observations is fundamental to tsunami hazard assessment, coastal planning, and large scale ocean circulation modeling. Classical inversion models typically rely on direct sensing or optimization…

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the…

Recent RGB-guided depth super-resolution methods have achieved impressive performance under the assumption of fixed and known degradation (e.g., bicubic downsampling). However, in real-world scenarios, captured depth data often suffer from…

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the…

In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy…