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Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…
Some fractals -- for instance those associated with the Mandelbrot and quadratic Julia sets -- are computed by iterating a function, and identifying the boundary between hyperparameters for which the resulting series diverges or remains…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
Materials property predictions have improved from advances in machine learning algorithms, delivering materials discoveries and novel insights through data-driven models of structure-property relationships. Nearly all available models rely…
In this paper, we present an application of 2-D convolutional neural networks (2-D CNNs) designed to perform both feature extraction and classification stages as a single organism to solve the highlighted problems. The method uses a network…
Soft tissue simulation in virtual environments is becoming increasingly important for medical applications. However, the high deformability of soft tissue poses significant challenges. Existing methods rely on segmentation, meshing and…
Despite an artificial intelligence-assisted modeling of disordered crystals is a widely used and well-tried method of new materials design, the issues of its robustness, reliability, and stability are still not resolved and even not…
Direct prediction of material properties from microstructures through statistical models has shown to be a potential approach to accelerating computational material design with large design spaces. However, statistical modeling of highly…
Accurate estimation of production times is critical for effective manufacturing scheduling, yet traditional methods relying on expert analysis or historical data often fall short in dynamic or customized production environments. This paper…
We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In…
The revolution in materials in the past century was built on a knowledge of the atomic arrangements and the structure-property relationship. The sine qua non for obtaining quantitative structural information is single crystal…
Molecular property calculations are the bedrock of chemical physics. High-fidelity \textit{ab initio} modeling techniques for computing the molecular properties can be prohibitively expensive, and motivate the development of…
Predicting fracture load in laminated composites with stress raisers is challenging due to complex failure mechanisms such as delamination, fibre breakage, and matrix cracking, which are heavily influenced by fibre orientation, layup…
The macroscopic response of short fiber reinforced composites is dependent on an extensive range of microstructural parameters. Thus, micromechanical modeling of these materials is challenging and in some cases, computationally expensive.…
This paper proposes a Fast Graph Convolutional Neural Network (FGRNN) architecture to predict sequences with an underlying graph structure. The proposed architecture addresses the limitations of the standard recurrent neural network (RNN),…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
We propose a novel deep learning framework for predicting permeability of porous media from their digital images. Unlike convolutional neural networks, instead of feeding the whole image volume as inputs to the network, we model the…
Catastrophic forgetting is a major problem in continual learning, and lots of approaches arise to reduce it. However, most of them are evaluated through task accuracy, which ignores the internal model structure. Recent research suggests…
Bone fractures present a major global health challenge, often resulting in pain, reduced mobility, and productivity loss, particularly in low-resource settings where access to expert radiology services is limited. Conventional imaging…
Graph neural networks (GNNs) have emerged as powerful surrogates for mesh-based computational fluid dynamics (CFD), but training them on high-resolution unstructured meshes with hundreds of thousands of nodes remains prohibitively…