Related papers: A Unified Framework for Multiscale Modeling using …
Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response.…
Although Lattice Boltzmann Method (LBM) is relatively straightforward, it demands a well-crafted framework to handle the complex partial differential equations involved in multiphase flow simulations. For the first time to our knowledge,…
The monogenic signal (MS) was introduced by Felsberg and Sommer, and independently by Larkin under the name vortex operator. It is a two-dimensional (2D) analog of the well-known analytic signal, and allows for direct amplitude and phase…
The method of fundamental solution (MFS) is an efficient meshless method for solving a boundary value problem in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
Visual memory schema (VMS) maps show which regions of an image cause that image to be remembered or falsely remembered. Previous work has succeeded in generating low resolution VMS maps using convolutional neural networks. We instead…
The purpose of this paper is to present new classes of function systems as part of multiresolution analyses. Our approach is representation theoretic, and it makes use of generalized multiresolution function systems (MRSs). It further…
Multimodal language models (MLLMs) require large parameter capacity to align high-dimensional visual features with linguistic representations, making them computationally heavy and difficult to deploy efficiently. We introduce a progressive…
An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell…
The Non-Markovian Stochastic Schrodinger Equation (NMSSE) offers a promising approach for open quantum simulations, especially in large systems, owing to its low scaling complexity and suitability for parallel computing. However, its…
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then…
The aim of this work is to propose a new multiphysics mode synthesis (MMS) for the thermomechanical vibration problem. The present thermomechanical model is based on a state-space formulation, which consists of displacement, velocity, and…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
Video diffusion models have recently shown promise for world modeling through autoregressive frame prediction conditioned on actions. However, they struggle to maintain long-term memory due to the high computational cost associated with…
Nonlinear unsteady vortex lattice-vortex particle methods (NL-UVLM-VPM) provide medium-fidelity predictions of rotorcraft aerodynamics with explicit three-dimensional wake representations at a moderate computational cost. This study…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…
An introduction to the Zwanzig-Mori-G\"{o}tze-W\"{o}lfle memory function formalism (or generalized Drude formalism) is presented. This formalism is used extensively in analyzing the experimentally obtained optical conductivity of strongly…