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A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…

A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…

In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the…

Deep metric learning aims to learn a function mapping image pixels to embedding feature vectors that model the similarity between images. Two major applications of metric learning are content-based image retrieval and face verification. For…

We present a minimalistic but effective neural network that computes dense facial correspondences in highly unconstrained RGB images. Our network learns a per-pixel flow and a matchability mask between 2D input photographs of a person and…

Despite the remarkable success of deep neural networks in a myriad of settings, several works have demonstrated their overwhelming sensitivity to near-imperceptible perturbations, known as adversarial attacks. On the other hand, prior works…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer…

We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…

Deep neural networks need a big amount of training data, while in the real world there is a scarcity of data available for training purposes. To resolve this issue unsupervised methods are used for training with limited data. In this…

We present a neural network based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models…

Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…

As deep learning models and datasets rapidly scale up, network training is extremely time-consuming and resource-costly. Instead of training on the entire dataset, learning with a small synthetic dataset becomes an efficient solution.…

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local…

Learning to learn is a powerful paradigm for enabling models to learn from data more effectively and efficiently. A popular approach to meta-learning is to train a recurrent model to read in a training dataset as input and output the…

Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning…

The efficient fusion of depth maps is a key part of most state-of-the-art 3D reconstruction methods. Besides requiring high accuracy, these depth fusion methods need to be scalable and real-time capable. To this end, we present a novel…

Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such…

This paper proposes a novel image segmentation approachthat integrates fully convolutional networks (FCNs) with a level setmodel. Compared with a FCN, the integrated method can incorporatesmoothing and prior information to achieve an…