Fractional Laplacian Pyramids

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The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a ch ...

Effective Prognostics and Health Management (PHM) relies on accurate prediction of the Remaining Useful Life (RUL). Data-driven RUL prediction techniques rely heavily on the representativeness of the available time-to-failure trajectories. Therefore, these ...

The capabilities of deep learning systems have advanced much faster than our ability to understand them. Whilst the gains from deep neural networks (DNNs) are significant, they are accompanied by a growing risk and gravity of a bad outcome. This is troubli ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

The way biological brains carry out advanced yet extremely energy efficient signal processing remains both fascinating and unintelligible. It is known however that at least some areas of the brain perform fast and low-cost processing relying only on a smal ...

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...

Most recent 6D object pose estimation methods first use object detection to obtain 2D bounding boxes before actually regressing the pose. However, the general object detection methods they use are ill-suited to handle cluttered scenes, thus producing poor ...

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Deep neural networks trained on physical losses are emerging as promising surrogates for nonlinear numerical solvers. These tools can predict solutions to Maxwell's equations and compute gradients of output fields with respect to the material and geometric ...

A central question of machine learning is how deep nets manage to learn tasks in high dimensions. An appealing hypothesis is that they achieve this feat by building a representation of the data where information irrelevant to the task is lost. For image da ...

We prove non-uniqueness for a class of weak solutions to the Navier???Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1. ...

Fault diagnosis plays an essential role in reducing the maintenance costs of rotating machinery manufacturing systems. In many real applications of fault detection and diagnosis, data tend to be imbalanced, meaning that the number of samples for some fault ...

Fetal brain diffusion magnetic resonance images (MRI) are often acquired with a lower through-plane than in-plane resolution. This anisotropy is often overcome by classical upsampling methods such as linear or cubic interpolation. In this work, we employ a ...

We present an image-based pipeline for generating geometrical digital twins (GDTs) of stone masonry elements with detail down to the stone level. For this purpose, we acquire RGB images of the individual stones and of the wall during the construction phase ...

Neural Architecture Search (NAS) has fostered the automatic discovery of stateof- the-art neural architectures. Despite the progress achieved with NAS, so far there is little attention to theoretical guarantees on NAS. In this work, we study the generaliza ...

During the Artificial Intelligence (AI) revolution of the past decades, deep neural networks have been widely used and have achieved tremendous success in visual recognition. Unfortunately, deploying deep models is challenging because of their huge model s ...

In this study, we present the deep learning image segmentation model for drone-based grain size analysis of gravel bars called GALET. The objectives are to quantify the performance of the code and to test its applicability in river research and management. ...

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...

Fractional Laplacian Pyramids

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The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation

Domain adaptation via alignment of operation profile for Remaining Useful Lifetime prediction

Safe Deep Neural Networks

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Benign Overfitting in Deep Neural Networks under Lazy Training

Supervised learning and inference of spiking neural networks with temporal coding

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Rigidity-Aware Detection for 6D Object Pose Estimation

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Predicting nonlinear optical scattering with physics-driven neural networks

How deep convolutional neural networks lose spatial information with training

Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Fault Detection and Diagnosis with Imbalanced and Noisy Data: A Hybrid Framework for Rotating Machinery

Through-Plane Super-Resolution With Autoencoders in Diffusion Magnetic Resonance Imaging of the Developing Human Brain

Image-based geometric digital twinning for stone masonry elements

Generalization Properties of NAS under Activation and Skip Connection Search

Improving the Training of Compact Neural Networks for Visual Recognition

GALET: A deep learning image segmentation model for drone-based grain size analysis of gravel bars

Robust numerical integration on curved polyhedra based on folded decompositions