Related papers: The E$\Delta$-MHC-Geo Transformer: Adaptive Geodes…
Currently, prominent Transformer architectures applied on graphs and meshes for shape analysis tasks employ traditional attention layers that heavily utilize spectral features requiring costly eigenvalue decomposition-based methods. To…
Recently, compressible magnetohydrodynamics (MHD) has been elegantly formulated in terms of Lie derivatives. This paper exploits the geometrical properties of the Lie bracket to give new insights into the properties of compressible MHD…
Given sparse depths and the corresponding RGB images, depth completion aims at spatially propagating the sparse measurements throughout the whole image to get a dense depth prediction. Despite the tremendous progress of deep-learning-based…
We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients $\sigma(x)$ in dimension two. We show that conductivity coefficients are…
This paper introduces a new grid-forming control for power converters, termed hybrid angle control (HAC) that ensures the almost global closed-loop stability. HAC combines the recently proposed matching control with a novel nonlinear angle…
We address the inverse problem for the mean-field Ising model with two- and three-body interactions using a Bayesian framework. Parameter recovery in this setting is notoriously difficult, particularly near phase transitions, at…
We revisit the Hahm-Kulsrud-Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian,…
We consider height functions on symmetric spaces $M\cong G/K$ embedded in the associated matrix Lie group $G$. In particular we study the relationship between the critical sets of the height function on $G$ and its restriction to $M$. Also…
Identifying the heterogeneous conductivity field and reconstructing the contaminant release history are key aspects of subsurface remediation. Achieving these two goals with limited and noisy hydraulic head and concentration measurements is…
This research presents a novel depth estimation algorithm based on a Transformer-encoder architecture, tailored for the NYU and KITTI Depth Dataset. This research adopts a transformer model, initially renowned for its success in natural…
Recent Transformer-based methods have achieved advanced performance in point cloud registration by utilizing advantages of the Transformer in order-invariance and modeling dependency to aggregate information. However, they still suffer from…
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of…
Fully adaptive computations of the resistive magnetohydrodynamic (MHD) equations are presented in two and three space dimensions using a finite volume discretization on locally refined dyadic grids. Divergence cleaning is used to control…
Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…
The metriplectic framework, which permits to formulate an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The…
Accurate residential load forecasting is critical for power system reliability with rising renewable integration and demand-side flexibility. However, most statistical and machine learning models treat external factors, such as weather,…
It has been discovered that latent-Euclidean variational autoencoders (VAEs) admit, in various capacities, Riemannian structure. We adapt these arguments but for complex VAEs with a complex latent stage. We show that complex VAEs reveal to…
Recent studies have applied variational calculus, conformal mapping, and point transformations to extend the one-dimensional SCLC from planar gaps to more complicated geometries. However, introducing a magnetic field orthogonal to the…
Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets.…
A locally metric connection on a smooth manifold $M$ is a torsion-free connection $D$ on $TM$ with compact restricted holonomy group $\mathrm{Hol}_0(D)$. If the holonomy representation of such a connection is irreducible, then $D$ preserves…