Related papers: Multiscale Structural Reliability Analysis in high…

High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the…

Deep neural networks (DNNs) have become integral to a wide range of scientific and practical applications due to their flexibility and strong predictive performance. Despite their accuracy, however, DNNs frequently exhibit poor calibration,…

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable density, compressible turbulent mixing. Though models of this kind (Reynolds Averaged Navier…

Herein, we present a new data-driven multiscale framework called FE${}^\text{ANN}$ which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous…

Accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows rely on effective closures, but currently available closures are notoriously unreliable. Kassinos et al. (J. Fluid Mechanics, 428, pp. 213-248,…

Deep Neural Networks (DNNs) enable a wide series of technological advancements, ranging from clinical imaging, to predictive industrial maintenance and autonomous driving. However, recent findings indicate that transient hardware faults may…

Network reliability assessment is pivotal for ensuring the robustness of modern infrastructure systems, from power grids to communication networks. While exact reliability computation for binary-state networks is NP-hard, existing…

To improve the uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon…

A major challenge in studying robustness in deep learning is defining the set of ``meaningless'' perturbations to which a given Neural Network (NN) should be invariant. Most work on robustness implicitly uses a human as the reference model…

We propose a globally convergent multilevel training method for deep residual networks (ResNets). The devised method can be seen as a novel variant of the recursive multilevel trust-region (RMTR) method, which operates in hybrid…

We propose a spectrally normalized surrogate for forward and inverse mechanical homogenization with hard physical guarantees. Leveraging the Voigt-Reuss bounds, we factor their difference via a Cholesky-like operator and learn a…

This study investigates whether Physically Recurrent Neural Networks (PRNNs), a recent surrogate model for heterogeneous materials, trained on a micromodel with fixed material parameters, can maintain accuracy for varying material…

For multilayer structures, interfacial failure is one of the most important elements related to device reliability. For cohesive zone modelling, traction-separation relations represent the adhesive interactions across interfaces. However,…

Machine learning techniques often lack formal correctness guarantees, evidenced by the widespread adversarial examples that plague most deep-learning applications. This lack of formal guarantees resulted in several research efforts that aim…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional…

Characterization and modeling of path-dependent behaviors of complex materials by phenomenological models remains challenging due to difficulties in formulating mathematical expressions and internal state variables (ISVs) governing…

A fundamental issue in multiscale materials modeling and design is the consideration of traction-separation behavior at the interface. By enriching the deep material network (DMN) with cohesive layers, the paper presents a novel data-driven…

As a surrogate for computationally intensive meso-scale simulation of woven composites, this article presents Recurrent Neural Network (RNN) models. Leveraging the power of transfer learning, the initialization challenges and sparse data…