Related papers: A numerical study of heat source reconstruction fo…
We consider the steady heat transfer between a collection of impermeable obstacles immersed in an incompressible 2D potential flow, when each obstacle has a prescribed boundary temperature distribution. Inside the fluid, the temperature…
The accurate robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. We present a novel method that combines rescaled localized Radial Basis…
We present a new method for introducing stable non-equilibrium concentration gradients in molecular dynamics simulations of mixtures. This method extends earlier Reverse Non-Equilibrium Molecular Dynamics (RNEMD) methods which use kinetic…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations…
We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…
We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…
"Generalized Hydrodynamics" (GHD) stands for a model that describes one-dimensional \textit{integrable} systems in quantum physics, such as ultra-cold atoms or spin chains. Mathematically, GHD corresponds to nonlinear equations of kinetic…
In medical imaging, the diffusion models have shown great potential for synthetic image generation tasks. However, these approaches often lack the interpretable connections between the generated and real images and can create anatomically…
This article applies low-cost singular value decomposition (lcSVD) for the first time, to the authors knowledge, on combustion reactive flow databases. The lcSVD algorithm is a novel approach to SVD, suitable for calculating high-resolution…
This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on…
Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems. We stabilize the method via residual minimization. We discretize the problem using…
This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the…
We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code {\small GADGET}. It is based on a fast, robust and photon-conserving integration scheme where the…
We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an…
In this paper, we propose a time-marching multi-level Variational Multiscale-Tensor Decomposition (VMS-TD) algorithm to solve the heat equation with a moving heat source model that arises from additive manufacturing. First, we take a…