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Representation learning, i.e. the generation of representations useful for downstream applications, is a task of fundamental importance that underlies much of the success of deep neural networks (DNNs). Recently, robustness to adversarial…

Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here we present a minimalist model of such co-evolving networks in a spatially continuous domain, where…

In the past decade, significant strides in deep learning have led to numerous groundbreaking applications. Despite these advancements, the understanding of the high generalizability of deep learning, especially in such an over-parametrized…

In this paper, a micro-mechanical model is introduce to characterize the stress softening phenomenon in double network hydrogels. Damage in polymer matrices under deformation, which appears as the rupture of cross-linking, is assumed to…

Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up…

A nuclear fuel cycle contains several facilities with different purposes such as mining, conversion, enrichment, and fuel rod fabrication. These facilities form a network, which is naturally sparse in the number of connections (i.e., edges)…

Adversarial attacks have been proven to be potential threats to Deep Neural Networks (DNNs), and many methods are proposed to defend against adversarial attacks. However, while enhancing the robustness, the clean accuracy will decline to a…

Solving for globally optimal line switching decisions in AC transmission grids can be intractability slow. Machine learning (ML) models, meanwhile, can be trained to predict near-optimal decisions at a fraction of the speed. Verifying the…

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure.…

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…

In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the…

The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective behavior of dislocation dynamics at the mesoscale leads to…

Studying the invertibility of deep neural networks (DNNs) provides a principled approach to better understand the behavior of these powerful models. Despite being a promising diagnostic tool, a consistent theory on their invertibility is…

A plethora of natural and industrial shear-driven granular flows exhibit particle-size segregation. Its occurrence is commonly attributed to two primary mechanisms: kinetic sieving and squeeze expulsion. While kinetic sieving is relatively…

Adversarial attack transferability is well-recognized in deep learning. Prior work has partially explained transferability by recognizing common adversarial subspaces and correlations between decision boundaries, but little is known beyond…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

Deep Graph Networks (DGNs) currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in…

Multi-phase materials, such as composite materials, exhibit multiple competing failure mechanisms during the growth of a macroscopic defect. For the simulation of the overall fracture process in such materials, we develop a two-phase spring…

Gravity-induced buoyancy, inevitable in most solidification processes, substantially alters the dynamics of crystal growth, such that incorporating fluid flow in solidification models is crucial to understand and predict key aspects of…

Physical computing has the potential to enable widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction. While individual devices provide basic data…