Related papers: Simplifying FFT-based methods for solid mechanics …
FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green…
As FMs drive progress toward Artificial General Intelligence (AGI), fine-tuning them under privacy and resource constraints has become increasingly critical particularly when highquality training data resides on distributed edge devices.…
Feature Transformation is crucial for classic machine learning that aims to generate feature combinations to enhance the performance of downstream tasks from a data-centric perspective. Current methodologies, such as manual expert-driven…
An improved approach to updating the electric field in simulations of Coulomb gases using the local lattice technique introduced by Maggs and Rossetto, is described and tested. Using the Fast Fourier Transform (FFT) an independent…
Topology Optimization (TO) holds the promise of designing next-generation compact and efficient fluidic devices. However, the inherent complexity of fluid-based TO systems, characterized by multiphysics nonlinear interactions, poses…
This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…
The convergence to the self-consistency in the dynamical-mean-field-theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are…
Edge devices are being deployed at increasing volumes to sense and act on information from the physical world. The discrete Fourier transform (DFT) is often necessary to make this sensed data suitable for further processing -- such as by…
Understanding how structural flexibility affects the properties of metal-organic frameworks (MOFs) is crucial for the design of better MOFs for targeted applications. Flexible MOFs can be studied with molecular dynamics simulations, whose…
The versatility of self-attention mechanism earned transformers great success in almost all data modalities, with limitations on the quadratic complexity and difficulty of training. To apply transformers across different data modalities,…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic…
In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…
Robust fine-tuning aims to achieve competitive in-distribution (ID) performance while maintaining the out-of-distribution (OOD) robustness of a pre-trained model when transferring it to a downstream task. Recently, projected gradient…
We modify the Green operator involved in Fourier-based computational schemes in elasticity, in 2D and 3D. The new operator is derived by expressing continuum mechanics in terms of centered differences on a rotated grid. Use of the modified…
Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…
The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the…
Classical density functional theory (DFT) is a powerful framework to study inhomogeneous fluids. Its standard form is based on the knowledge of a generating free energy functional. If this is known exactly, then the results obtained by…
Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at…
Density Functional Theory (DFT) allows for predicting all the chemical and physical properties of molecular systems from first principles by finding an approximate solution to the many-body Schr\"odinger equation. However, the cost of these…