Related papers: Geometric deep learning for computational mechanic…

Deep learning applications are drastically progressing in seismic processing and interpretation tasks. However, the majority of approaches subsample data volumes and restrict model sizes to minimise computational requirements. Subsampling…

In the last decade, deep learning has become a major component of artificial intelligence. The workhorse of deep learning is the optimization of loss functions by stochastic gradient descent (SGD). Traditionally in deep learning, neural…

Plastic anisotropy in metals remains challenging to model. This is partly because conventional phenomenological yield criteria struggle to combine a highly descriptive, flexible representation with constraints, such as convexity, dictated…

Despite Graph neural networks' significant performance gain over many classic techniques in various graph-related downstream tasks, their successes are restricted in shallow models due to over-smoothness and the difficulties of…

Deep learning in molecular and materials sciences is limited by the lack of integration between applied science, artificial intelligence, and high-performance computing. Bottlenecks with respect to the amount of training data, the size and…

With the recent advance of geometric deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of…

We introduce a de novo elastography method to learn the elasticity of solids from measured strains. The deep neural network in our new method is supervised by the theory of elasticity and does not require labeled data for training. Results…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

We provide a series of results for unsupervised learning with autoencoders. Specifically, we study shallow two-layer autoencoder architectures with shared weights. We focus on three generative models for data that are common in statistical…

Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…

Predicting metro passenger flow precisely is of great importance for dynamic traffic planning. Deep learning algorithms have been widely applied due to their robust performance in modelling non-linear systems. However, traditional deep…

Recently, deep learning approaches have been extensively investigated to reconstruct images from accelerated magnetic resonance image (MRI) acquisition. Although these approaches provide significant performance gain compared to compressed…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…

In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…

We present a novel geometric deep learning layer that leverages the varifold gradient (VariGrad) to compute feature vector representations of 3D geometric data. These feature vectors can be used in a variety of downstream learning tasks…

The microstructure is an essential part of materials, storing the genes of materials and having a decisive influence on materials' physical and chemical properties. The material genetic engineering program aims to establish the relationship…

Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…