Related papers: Discrete models of force chain networks

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. To understand the response of such a network as a function of the prestrain, we consider…

The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials. It uses tangential components of the displacement…

Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by…

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…

Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…

Convolutional Neural Networks (CNNs) are well-known for their vulnerability to adversarial attacks, posing significant security concerns. In response to these threats, various defense methods have emerged to bolster the model's robustness.…

Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…

Composite materials like syntactic foams have complex internal microstructures that manifest high-stress concentrations due to material discontinuities occurring from hollow regions and thin walls of hollow particles or microballoons…

A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…

Several deep learning models have been proposed for question answering. However, due to their single-pass nature, they have no way to recover from local maxima corresponding to incorrect answers. To address this problem, we introduce the…

The concept of SCN offers a fast framework with universal approximation guarantee for lifelong learning of non-stationary data streams. Its adaptive scope selection property enables for proper random generation of hidden unit parameters…

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of…

Stress transmission in planar open-cell cellular solids is analysed using a recent theory developed for marginally rigid granular assemblies. This is made possible by constructing a one-to-one mapping between the two systems. General…

The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…

Generative design problems often encompass complex action spaces that may be divergent over time, contain state-dependent constraints, or involve hybrid (discrete and continuous) domains. To address those challenges, this work introduces…

Object detection in challenging situations such as scale variation, occlusion, and truncation depends not only on feature details but also on contextual information. Most previous networks emphasize too much on detailed feature extraction…

Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the…