Related papers: Disordered auxetic networks with no re-entrant pol…
Auxetic metamaterials are commonly thought to exhibit favorable mechanical properties, notably high energy absorption. Here we investigate disordered metamaterials obtained from random beam networks by optimizing simultaneously auxeticity…
This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…
In this paper, the average density of states (ADOS) with a binary alloy disorder in disordered graphene systems are calculated based on the recursion method. We observe an obvious resonant peak caused by interactions with surrounding…
Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints…
We consider how to connect a set of disjoint networks to optimize the performance of the resulting composite network. We quantify this performance by the coherence of the composite network, which is defined by an $H_2$ norm of the system.…
The rapid increment of morbidity of brain stroke in the last few years have been a driving force towards fast and accurate segmentation of stroke lesions from brain MRI images. With the recent development of deep-learning, computer-aided…
Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the…
As a generalization of Postnikov's construction (see arXiv: math/0609764), we define a map from the space of edge weights of a directed network in an annulus into a space of loops in the Grassmannian. We then show that universal Poisson…
In this paper we discuss non-commutative and non-associative geometries that emerge in the context of non-geometric closed string backgrounds. T-duality and doubled field theory plays an important role in formulating the corresponding…
We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…
We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded…
Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural…
This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…
We study the distributed stochastic compositional optimization problems over directed communication networks in which agents privately own a stochastic compositional objective function and collaborate to minimize the sum of all objective…
Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In…
A method to construct integrable deformations of Hamiltonian systems of ODEs endowed with Lie-Poisson symmetries is proposed by considering Poisson-Lie groups as deformations of Lie-Poisson (co)algebras. Moreover, the underlying Lie-Poisson…
We analyze the effect of adding quenched disorder along a defect line in the 2D conformal minimal models using replicas. The disorder is realized by a random applied magnetic field in the Ising model, by fluctuations in the ferromagnetic…
Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity equations deteriorates as the Lam\'e coefficient $\lambda\to\infty$, or equivalently as the Poisson ratio…
By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…
Lattice-based mechanical metamaterials are known to exhibit quite a unique mechanical behavior owing to their rational internal architecture. This includes unusual properties such as a negative Poisson's ratio, which can be easily tuned in…