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Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function…

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known…

We propose a novel deep learning approach to nonparametric statistical inference for the conditional hazard function of survival time with right-censored data. We use a deep neural network (DNN) to approximate the logarithm of a conditional…

Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be…

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the…

Recurrent and deep neural networks (RNNs/DNNs) are cornerstone architectures in machine learning. Remarkably, RNNs differ from DNNs only by weight sharing, as can be shown through unrolling in time. How does this structural similarity fit…

Deep learning (DL) is transforming industry as decision-making processes are being automated by deep neural networks (DNNs) trained on real-world data. Driven partly by rapidly-expanding literature on DNN approximation theory showing they…

Over the last few years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a wide variety of computational problems including computer vision, image classification, speech recognition,…

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that…

We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

We develop a deep convolutional neural network (DCNN) based framework for model-free prediction of the occurrence of extreme events both in time ("when") and in space ("where") in nonlinear physical systems of spatial dimension two. 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,…

Within the family of explainable machine-learning, we present Fredholm neural networks (Fredholm NNs): deep neural networks (DNNs) architectures motivated by fixed-point iteration schemes for the solution of linear and nonlinear Fredholm…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

Dense pixel matching problems such as optical flow and disparity estimation are among the most challenging tasks in computer vision. Recently, several deep learning methods designed for these problems have been successful. A sufficiently…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…