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The Keller-Segel-Navier-Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid velocity and pressure. It is known that if the total initial cell…

In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep Bayesian Neural Network (BNN). We do so by incorporating a KL divergence penalty term into the…

Stochastic gradient descent (SGD) now acts as a fundamental part of optimization in current machine learning. Meanwhile, deep learning architectures have shown outstanding performance in a wide range of fields, such as natural language…

Neural networks have achieved state of the art results in many areas, supposedly due to parameter sharing, locality, and depth. Tensor networks (TNs) are linear algebraic representations of quantum many-body states based on their…

High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…

Deep learning (DL) is an emerging analysis tool across sciences and engineering. Encouraged by the successes of DL in revealing quantitative trends in massive imaging data, we applied this approach to nano-scale deeply sub-diffractional…

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only…

We introduce a novel approach to the three-dimensional reconstruction of superfluid vortex filaments using deep convolutional neural networks. Superfluid vortices, quantum mechanical phenomena of immense scientific interest, are challenging…

In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented here has broad applications in determining large time…

In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such…

We introduce a novel method for identifying the mass composition of ultra-high-energy cosmic rays using deep learning. The key idea of the method is to use a chain of two neural networks. The first network predicts the type of a primary…

There has been recent interest in developing scalable Bayesian sampling methods such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) for big-data analysis. A standard SG-MCMC algorithm simulates samples…

In this paper, we develop a systematic deep learning approach to solve two-dimensional (2D) stationary quantum droplets (QDs) and investigate their wave propagation in the 2D amended Gross-Pitaevskii equation with Lee-Huang-Yang correction…

Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…

A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…

Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for…

We introduce a method to reconstruct the kinematics of neutral-current deep inelastic scattering (DIS) using a deep neural network (DNN). Unlike traditional methods, it exploits the full kinematic information of both the scattered electron…

On the forefront of scientific computing, Deep Learning (DL), i.e., machine learning with Deep Neural Networks (DNNs), has emerged a powerful new tool for solving Partial Differential Equations (PDEs). It has been observed that DNNs are…

Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…