Related papers: A Unified Framework for Multiscale Modeling using …
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
State-space models (SSMs) have recently attention as an efficient alternative to computationally expensive attention-based models for sequence modeling. They rely on linear recurrences to integrate information over time, enabling fast…
This paper proposes a novel way to solve transient linear, and non-linear solid dynamics for compressible, nearly incompressible, and incompressible material in the updated Lagrangian framework for tetrahedral unstructured finite elements.…
This paper presents a goal-oriented a posteriori error estimation framework for linear functionals in the stabilized finite element discretization of the stationary convection-diffusion-reaction (CDR) equation. The theoretical framework for…
We derive a completely positive post-Markovian master equation (PMME) from a microscopic Markovian collisional model framework, incorporating bath memory effects via a probabilistic single-shot measurement approach. This phenomenological…
We propose an overlapping Schwarz space-time refinement framework for the material point method (OS-MPM) to improve computational efficiency in problems with strongly localized deformation, contact, and large geometric nonlinearity. The…
Learning from multimodal datasets can leverage complementary information and improve performance in prediction tasks. A commonly used strategy to account for feature correlations in high-dimensional datasets is the latent variable approach.…
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
Multimodal Large Models (MLLMs) have achieved remarkable progress in vision-language understanding and generation tasks. However, existing MLLMs typically rely on static modality fusion strategies, which treat all modalities equally…
Mathematical approaches from dynamical systems theory are used in a range of fields. This includes biology where they are used to describe processes such as protein-protein interaction and gene regulatory networks. As such networks increase…
Standard projection-based model reduction for dynamical systems incurs closure error because it only accounts for instantaneous dependence on the resolved state. From the Mori-Zwanzig (MZ) perspective, projecting the full dynamics onto a…
Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
In multiscale modelling, multiple models are used simultaneously to describe scale-dependent phenomena in a system of interest. Here we introduce a machine learning (ML)-based multiscale modelling framework for modelling hierarchical…
Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different…
We present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to…
We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…
We present an energy-conserving numerical scheme to solve the Vlasov-Maxwell (VM) system based on the regularized moment method proposed in [Z. Cai, Y. Fan, and R. Li. CPAM, 2014]. The globally hyperbolic moment system is deduced for the…