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The configuration of latent representations plays a critical role in determining the performance of deep neural network classifiers. In particular, the emergence of well-separated class embeddings in the latent space has been shown to…
Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this…
With the edge computing becoming an increasingly adopted concept in system architectures, it is expected its utilization will be additionally heightened when combined with deep learning (DL) techniques. The idea behind integrating demanding…
Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately…
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order…
In this paper, we consider a deep learning approach to the limited aperture inverse obstacle scattering problem. It is well known that traditional deep learning relies solely on data, which may limit its performance for the inverse problem…
Semantic image segmentation is one of the most important tasks in medical image analysis. Most state-of-the-art deep learning methods require a large number of accurately annotated examples for model training. However, accurate annotation…
This work focuses on the development of a super-penalty strategy based on the $L^2$-projection of suitable coupling terms to achieve $C^1$-continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the…
Automated brain lesions detection is an important and very challenging clinical diagnostic task because the lesions have different sizes, shapes, contrasts, and locations. Deep Learning recently has shown promising progress in many…
Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such…
Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…
CANDECOMP/PARAFAC (CP) decomposition is the mostly used model to formulate the received tensor signal in a massive MIMO system, as the receiver generally sums the components from different paths or users. To achieve accurate and low-latency…
Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
Density-equalizing map (DEM) serves as a powerful technique for creating shape deformations with the area changes reflecting an underlying density function. In recent decades, DEM has found widespread applications in fields such as data…
An exact arithmetic, memory efficient direct solution method for finite element method (FEM) computations is outlined. Unlike conventional black-box or low-rank direct solvers that are opaque to the underlying physical problem, the proposed…
Using a Deep Neuronal Network model (DNN) trained on the large ANI-1 data set of small organic molecules, we propose a transferable density-free many-body dispersion model (DNN-MBD). The DNN strategy bypasses the explicit Hirshfeld…
Block discrete diffusion language models factorize a sequence autoregressively over fixed-size positional blocks, decoupling within-block parallel denoising from across-block conditioning. We argue that this rigid partition wastes structure…
We extend the analysis and discretization of the Kirchhoff-Love plate bending problem from [T. F\"uhrer, N. Heuer, A.H. Niemi, An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation, arXiv:1805.07835, 2018]…
In this paper, we introduce the Deep Finite Volume Method (DFVM), an innovative deep learning framework tailored for solving high-order (order \(\geq 2\)) partial differential equations (PDEs). Our approach centers on a novel loss function…