Related papers: A DeepParticle method for learning and generating …

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces…

Achievement of solutions in Navier-Stokes equation is one of challenging quests, especially for its closure problem. For achievement of particular solutions, there are variety of numerical simulations including Direct Numerical Simulation…

Extracting scientific results from high-energy collider data involves the comparison of data collected from the experiments with synthetic data produced from computationally-intensive simulations. Comparisons of experimental data and…

Objective: Estimation of the global optima of multiple model parameters is valuable in imaging to form a reliable diagnostic image. Given non convexity of the objective function, it is challenging to avoid from different local minima.…

We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…

In this paper, we present a deep learning-based (DL-based) algorithm, as a purely mathematical platform, for providing intuitive understanding of the properties of electromagnetic (EM) wave-matter interaction in nanostructures. This…

This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…

We study a system of interacting diffusions that models chemotaxis of biological cells or microorganisms (referred to as particles) in a chemical field that is dynamically modified through the collective contributions from the particles.…

We develop novel neural network-based implicit particle methods to compute high-dimensional Wasserstein-type gradient flows with linear and nonlinear mobility functions. The main idea is to use the Lagrangian formulation in the…

We derive the divergence-kernel formula for the linear response of random dynamical systems. Specifically, the pathwise expression is for the parameter-derivative of the marginal or stationary density, not an averaged observable. Our…

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…

The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and…

Recent studies revealed the mathematical connection of deep neural network (DNN) and dynamic system. However, the fundamental principle of DNN has not been fully characterized with dynamic system in terms of optimization and generalization.…

In this study, we propose a high-performance disparity (depth) estimation method using dual-pixel (DP) images with few parameters. Conventional end-to-end deep-learning methods have many parameters but do not fully exploit disparity…

This paper presents a convolutional neural network (CNN)-based deep learning model, inspired from UNet with series of encoder and decoder units with skip connections, for the simulation of microwave-plasma interaction. The microwave…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

We develop and analyze a stochastic genetic interacting particle method (SGIP) for reaction-diffusion-advection (RDA) equations. The SGIP method employs operator splitting to approximate the advection-diffusion and reaction processes,…

An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials.…

``$\Delta$-machine learning" refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) density functional theory (DFT) energies and gradients to close to a coupled cluster…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…