Related papers: Eulerian-Lagrangian particle-based model for diffu…
We develop a 3D Eulerian model to study the transport and distribution of microplastics in the global ocean. Among other benefits that will be discussed in the paper, one unique feature of our model is that it takes into consideration the…
We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…
Downscaling, or super-resolution, provides decision-makers with detailed, high-resolution information about the potential risks and impacts of climate change, based on climate model output. Machine learning algorithms are proving themselves…
Analytical solutions are derived for the steady-state size distributions of precipitating rain and snow particles assuming growth via collection of suspended cloud particles. Application of the Liouville equation to the transfer of…
Data-driven weather prediction models exhibit promising performance and advance continuously. In particular, diffusion models represent fine-scale details without spatial smoothing, which is crucial for mesoscale predictions, such as heavy…
We study parameter estimation for interacting particle systems (IPSs) consisting of $N$ weakly interacting multivariate hypoelliptic SDEs. We propose a locally Gaussian approximation of the transition dynamics, carefully designed to address…
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These…
The evolution and release of fission gas impacts the performance of UO2 nuclear fuel. We have created a Bayesian framework to calibrate a novel model for fission gas transport that predicts diffusion rates of uranium and xenon in UO2 under…
We study diffusion-controlled growth of a spherical droplet with a moving boundary using a physics-informed neural network (PINN) formulation. The governing diffusion equation is coupled to the interfacial mass balance, with the droplet…
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…
The conditional diffusion model has been demonstrated as an efficient tool for learning robot policies, owing to its advancement to accurately model the conditional distribution of policies. The intricate nature of real-world scenarios,…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…
Assessing the availability of rainfall water plays a crucial role in rainfed agriculture. Given the substantial proportion of agricultural practices in India being rainfed and considering the potential trends in rainfall amounts across…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…
Vegetation patterns are a characteristic feature of semi-arid regions. On hillsides these patterns occur as stripes running parallel to the contours. The Klausmeier model, a coupled reaction-advection-diffusion system, is a deliberately…
Accurate prediction of atmospheric optical turbulence in localized environments is essential for estimating the performance of free-space optical systems. Macro-meteorological models developed to predict turbulent effects in one environment…
Latent diffusion models (LDMs) have demonstrated remarkable generative capabilities across various low-level vision tasks. However, their potential for point cloud completion remains underexplored due to the unstructured and irregular…