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Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Convolutional neural networks have recently demonstrated high-quality reconstruction for single-image super-resolution. In this paper, we propose the Laplacian Pyramid Super-Resolution Network (LapSRN) to progressively reconstruct the…

The quality of inverse problem solutions obtained through deep learning [Barbastathis et al, 2019] is limited by the nature of the priors learned from examples presented during the training phase. In the case of quantitative phase retrieval…

In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…

Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing…

The Local Learning Coefficient (LLC) is introduced as a novel complexity measure for deep neural networks (DNNs). Recognizing the limitations of traditional complexity measures, the LLC leverages Singular Learning Theory (SLT), which has…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

Training deep neural networks on large datasets containing high-dimensional data requires a large amount of computation. A solution to this problem is data-parallel distributed training, where a model is replicated into several…

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…

Deep neural networks (DNNs) are widely used as surrogate models in geophysical applications; incorporating theoretical guidance into DNNs has improved the generalizability. However, most of such approaches define the loss function based on…

The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e. physics based) or data-driven (i.e. machine-learning based) origins. In order to combine the strengths of these two…

In this paper we address the problem of representing 3D visual data with parameterized volumetric shape primitives. Specifically, we present a (two-stage) approach built around convolutional neural networks (CNNs) capable of segmenting…

Inferring the exact parameters of a neural network with only query access is an NP-Hard problem, with few practical existing algorithms. Solutions would have major implications for security, verification, interpretability, and understanding…

For image super-resolution (SR), bridging the gap between the performance on synthetic datasets and real-world degradation scenarios remains a challenge. This work introduces a novel "Low-Res Leads the Way" (LWay) training framework,…

We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…

A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of…

In this article, our goal is to solve two-parameter singular perturbation problems (SPPs) in one- and two-dimensions using an adapted Physics-Informed Neural Networks (PINNs) approach. Such problems are of major importance in engineering…

Deep unfolding networks (DUNs) have achieved remarkable success and become the mainstream paradigm for spectral compressive imaging (SCI) reconstruction. Existing DUNs are derived from full-HSI imaging models, where each stage operates…

In this paper, we investigate the use of single hidden-layer neural networks as a family of ansatz functions for the resolution of partial differential equations (PDEs). In particular, we train the network via Extreme Learning Machines…

The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…