Related papers: Front Transport Reduction for Complex Moving Front…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The mixed finite element VEF…
Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…
Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…
Moving object detection (MOD) in remote sensing is significantly challenged by low resolution, extremely small object sizes, and complex noise interference. Current deep learning-based MOD methods rely on probability density estimation,…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
This paper presents a multi-scale method for convection-dominated diffusion problems in the regime of large P\'eclet numbers. The application of the solution operator to piecewise constant right-hand sides on some arbitrary coarse mesh…
Popularized by their strong image generation performance, diffusion and related methods for generative modeling have found widespread success in visual media applications. In particular, diffusion methods have enabled new approaches to data…
In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…
In this paper, we consider flow and transport problems in thin domains. The mathematical model considered in the paper is described by a system of equations for velocity, pressure, and concentration, where the flow is described by the…