Related papers: A Mathematical Framework for Quantifying Nonlinear…
In the domain of computer vision, optical flow stands as a cornerstone for unraveling dynamic visual scenes. However, the challenge of accurately estimating optical flow under conditions of large nonlinear motion patterns remains an open…
The two-layer quasigeostrophic model (2LQG) and the Eady model are two idealized systems illustrating the baroclinic instability of atmospheric jets and ocean currents. The two setups share many ingredients -- background vertically sheared…
To detect distribution shifts and improve model safety, many out-of-distribution (OOD) detection methods rely on the predictive uncertainty or features of supervised models trained on in-distribution data. In this paper, we critically…
In the analysis of elastic-scattering experimental data, optical-model parameters (usually, depths of real and imaginary potentials) are fitted and conclusions are drawn analyzing their variations at bombardment energies close to the…
In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
Analyzing the effects of ocean eddies is important in oceanology for gaining insights into transport of energy and biogeochemical particles. We present an application of statistical visualization algorithms for the analysis of the Red Sea…
Quality-Diversity (QD) has demonstrated potential in discovering collections of diverse solutions to optimisation problems. Originally designed for deterministic environments, QD has been extended to noisy, stochastic, or uncertain domains…
The Eady problem of baroclinic instability as applicable to quasi-geostrophic oceanic flows with zero internal PV gradients is revisited by introducing a mild slope and Ekman pumping on the lower boundary. The solution behaviour is…
This work presents EddyNet, a deep learning based architecture for automated eddy detection and classification from Sea Surface Height (SSH) maps provided by the Copernicus Marine and Environment Monitoring Service (CMEMS). EddyNet is a…
In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in…
Brain vessel segmentation of MR scans is a critical step in the diagnosis of cerebrovascular diseases. Due to the fine vessel structure, manual vessel segmentation is time consuming. Therefore, automatic deep learning (DL) based…
The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution moreover correlates with a model's epistemic uncertainty,…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
Unsupervised optical flow methods typically lack reliable uncertainty estimation, limiting their robustness and interpretability. We propose U$^{2}$Flow, the first recurrent unsupervised framework that jointly estimates optical flow and…
The precision of contouring target structures and organs-at-risk (OAR) in radiotherapy planning is crucial for ensuring treatment efficacy and patient safety. Recent advancements in deep learning (DL) have significantly improved OAR…
Uncertainty quantification is a critical yet unsolved challenge for deep learning, especially for the time series imputation with irregularly sampled measurements. To tackle this problem, we propose a novel framework based on the principles…
Sediment transport over wave-induced ripples is a very complex phenomenon where available models fail to provide accurate predictions. For coastal engineering applications, the 1-DV advection-diffusion equation could be used with an…
We present a publicly accessible database designed to aid in the conception, training, demonstration, evaluation, and comparison of reduced-complexity models for fluid mechanics. Availability of high-quality flow data is essential for all…
Conventional training for optical flow and stereo depth models typically employs a uniform loss function across all pixels. However, this one-size-fits-all approach often overlooks the significant variations in learning difficulty among…