Related papers: Simplifying FFT-based methods for solid mechanics …
Predicting effective thermal conductivity by solving a Partial Differential Equation (PDE) defined on a high-resolution Representative Volume Element (RVE) is a computationally intensive task. In this paper, we tackle the task by proposing…
The computational efficiency and rapid convergence of fast Fourier transform (FFT)-based solvers render them a powerful numerical tool for periodic cell problems in multiscale modeling. On regular grids, they tend to outperform traditional…
We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain,…
Traditional vision-based autonomous driving systems often face difficulties in navigating complex environments when relying solely on single-image inputs. To overcome this limitation, incorporating temporal data such as past image frames or…
A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…
In wave propagation problems, finite difference methods implemented on staggered grids are commonly used to avoid checkerboard patterns and to improve accuracy in the approximation of short-wavelength components of the solutions. In this…
We discuss an effective field theory (EFT) approach to the computation of fluctuation-induced interactions between particles bound to a thermally fluctuating fluid surface controlled by surface tension. By describing particles as points,…
The density functional theory (DFT) is used to investigate the mechanical properties of pure, fully hydrogenated, semi-hydrogenated, fully fluorinated, and semi-fluorinated germanene sheets, including Young's and bulk moduli, and plastic…
Foundation models encode rich representations that can be adapted to downstream tasks by fine-tuning. However, fine-tuning a model on one data distribution often degrades performance under distribution shifts. Current approaches to robust…
For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid…
In order to accelerate implementation of hyperelastic materials for finite element analysis, we developed an automatic numerical algorithm that only requires the strain energy function. This saves the effort on analytical derivation and…
Energy-based finite-element formulations provide a unified framework for describing complex physical systems in computational mechanics. In these energy-based methods, the governing equations can be obtained directly by considering the…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Recent advancements have illuminated the efficacy of some tensorization-decomposition Parameter-Efficient Fine-Tuning methods like LoRA and FacT in the context of Vision Transformers (ViT). However, these methods grapple with the challenges…
The transformer model is known to be computationally demanding, and prohibitively costly for long sequences, as the self-attention module uses a quadratic time and space complexity with respect to sequence length. Many researchers have…
Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids…
We introduce Attention Free Transformer (AFT), an efficient variant of Transformers that eliminates the need for dot product self attention. In an AFT layer, the key and value are first combined with a set of learned position biases, the…
The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used approach for solving the former is the so-called…