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We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a two-mesh technique for the prediction of the stress field associated with such systems. We generalize…

Deep neural networks are powerful learning models that achieve state-of-the-art performance on many computer vision, speech, and language processing tasks. In this paper, we study a fundamental question that arises when designing deep…

An increasing number of electronics are directly embedded on the clothing to monitor human status (e.g., skeletal motion) or provide haptic feedback. A specific challenge to prototype and fabricate such a clothing is to design the wiring…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

Current dynamic networks and dynamic pruning methods have shown their promising capability in reducing theoretical computation complexity. However, dynamic sparse patterns on convolutional filters fail to achieve actual acceleration in…

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…

Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspond to sum-product neural networks with a sparse connectivity…

As 3D models become critical in today's manufacturing and product design, conventional 3D modeling approaches based on Computer-Aided Design (CAD) are labor-intensive, time-consuming, and have high demands on the creators. This work aims to…

Recently there has been a surge of research on improving the communication efficiency of distributed training. However, little work has been done to systematically understand whether the network is the bottleneck and to what extent. In this…

Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices…

Deep neural networks (DNNs) have become the state-of-the-art technique for machine learning tasks in various applications. However, due to their size and the computational complexity, large DNNs are not readily deployable on edge devices in…

We study the problem of comparing a pair of geometric networks that may not be similarly defined, i.e., when they do not have one-to-one correspondences between their nodes and edges. Our motivating application is to compare power…

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…

The pressure strain correlation plays a critical role in the Reynolds stress transport modelling. Accurate modelling of the pressure strain correlation leads to proper prediction of turbulence stresses and subsequently the other terms of…

In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

Recent advances in designing meta-materials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally-efficient…

We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at…

A tunable stiffness bone rod was designed, optimized, and 3D printed to address the common shortcomings of existing bone rods in the healing of long fractured bones. The common deficiencies of existing bone fixations are high stiffness,…