Related papers: A versatile FEM framework with native GPU scalabil…
Statistical heterogeneity is a root cause of tension among accuracy, fairness, and robustness of federated learning (FL), and is key in paving a path forward. Personalized FL (PFL) is an approach that aims to reduce the impact of…
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
Differentiable simulators represent an environment's dynamics as a differentiable function. Within robotics and autonomous driving, this property is used in Analytic Policy Gradients (APG), which relies on backpropagating through the…
Molecule generation using generative AI is vital for drug discovery, yet class-specific datasets often contain fewer than 100 training examples. While fragment-based models handle limited data better than atom-based approaches, existing…
Recent researches on unsupervised domain adaptation (UDA) have demonstrated that end-to-end ensemble learning frameworks serve as a compelling option for UDA tasks. Nevertheless, these end-to-end ensemble learning methods often lack…
In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control variables. We develop an…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
Modern graphics processing units (GPUs) provide an unprecedented level of computing power. In this study, we present a high-performance, multi-GPU implementation of the analytical nuclear gradient for Kohn-Sham time-dependent density…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
Modern GPUs feature specialized hardware units that enable high-performance, asynchronous dataflow execution. However, the conventional SIMT programming model is fundamentally misaligned with this task-parallel hardware, creating a…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
Ptychography is a lensless imaging method that allows for wavefront sensing and phase-sensitive microscopy from a set of diffraction patterns. Recently, it has been shown that the optimization task in ptychography can be achieved via…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
Many equilibrated flux recovery methods for finite element solutions rely on ad hoc or method-specific techniques, limiting their generalizability and efficiency. In this work, we introduce the Equilibrated Averaging Residual Method (EARM),…
Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains…
When translating UI design prototypes to code in industry, automatically generating code from design prototypes can expedite the development of applications and GUI iterations. However, in design prototypes without strict design…
Attention-based Transformers have demonstrated strong adaptability across a wide range of tasks and have become the backbone of modern Large Language Models (LLMs). However, their underlying mechanisms remain open for further exploration.…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…