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In this paper, we present a NURBS-enhanced finite element method that integrates the NURBS-based boundary representation of a geometric domain into a standard finite element framework for hexahedral meshes. We decompose an open, bounded,…

This work presents a methodology to predict a near-optimal spacing function, which defines the element sizes, suitable to perform steady RANS turbulent viscous flow simulations. The strategy aims at utilising existing high fidelity…

Capsules are the multidimensional analogue to scalar neurons in neural networks, and because they are multidimensional, much more complex routing schemes can be used to pass information forward through the network than what can be used in…

Simulating large proteins using traditional molecular dynamics (MD) is computationally demanding. To address this challenge, we propose a novel tree-structured coarse-grained model that efficiently captures protein dynamics. By leveraging a…

Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic…

Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…

Recently, adversarial deception becomes one of the most considerable threats to deep neural networks. However, compared to extensive research in new designs of various adversarial attacks and defenses, the neural networks' intrinsic…

Microstructural materials design is one of the most important applications of inverse modeling in materials science. Generally speaking, there are two broad modeling paradigms in scientific applications: forward and inverse. While the…

We propose a neural network-based computational framework for the simultaneous optimization of structural topology, curved layers, and path orientations to achieve strong anisotropic strength in fiber-reinforced thermoplastic composites…

Designing composite materials as per the application requirements is fundamentally a challenging and time consuming task. Here we report the development of a deep neural network based computational framework capable of solving the forward…

We propose a new framework for image classification with deep neural networks. The framework introduces intermediate outputs to the computational graph of a network. This enables flexible control of the computational load and balances the…

Nanoindentation is vital for probing mechanical properties, yet traditional grid-based workflows are inefficient for targeting specific microstructural features. We present an automated nanoindentation framework that integrates machine…

Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…

Neural networks (NNs) lack measures of "reliability" estimation that would enable reasoning over their predictions. Despite the vital importance, especially in areas of human well-being and health, state-of-the-art uncertainty estimation…

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…

A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be…

This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…