Related papers: Information Geometry of Evolution of Neural Networ…

Neural networks have a number of shortcomings. Amongst the severest ones is the sensitivity to distribution shifts which allows models to be easily fooled into wrong predictions by small perturbations to inputs that are often imperceivable…

This paper proposes a new mean-field framework for over-parameterized deep neural networks (DNNs), which can be used to analyze neural network training. In this framework, a DNN is represented by probability measures and functions over its…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

Graph Neural Networks (GNNs) achieve an impressive performance on structured graphs by recursively updating the representation vector of each node based on its neighbors, during which parameterized transformation matrices should be learned…

We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…

In the last decade, motivated by the success of Deep Learning, the scientific community proposed several approaches to make the learning procedure of Neural Networks more effective. When focussing on the way in which the training data are…

We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly…

Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Graphs neural networks (GNNs) learn node features by aggregating and combining neighbor information, which have achieved promising performance on many graph tasks. However, GNNs are mostly treated as black-boxes and lack human intelligible…

Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some…

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…

To overcome the restriction of identical distribution assumption, invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities. In UDA…

Artificial neural networks (ANNs) have become a very powerful tool in the approximation of high-dimensional functions. Especially, deep ANNs, consisting of a large number of hidden layers, have been very successfully used in a series of…

The recent proliferation of 3D content that can be consumed on hand-held devices necessitates efficient tools for transmitting large geometric data, e.g., 3D meshes, over the Internet. Detailed high-resolution assets can pose a challenge to…

Artificial neural networks (ANNs) are popular tools for accomplishing many machine learning tasks, including predicting continuous outcomes. However, the general lack of confidence measures provided with ANN predictions limit their…

Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model…

In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…

(Artificial) neural networks have become increasingly popular in mechanics to accelerate computations with model order reduction techniques and as universal models for a wide variety of materials. However, the major disadvantage of neural…

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…