Related papers: Deep Learning Moment Closure Approximations using …
Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space…
We propose effective scheme of deep learning method for high-order nonlinear soliton equation and compare the activation function for high-order soliton equation. The neural network approximates the solution of the equation under the…
We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…
This paper describes deep learning models based on convolutional neural networks applied to the problem of predicting EM wave propagation over rural terrain. A surface integral equation formulation, solved with the method of moments and…
Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control…
Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
This paper presents a novel probabilistic approach to deep robot learning from demonstrations (LfD). Deep movement primitives (DMPs) are deterministic LfD model that maps visual information directly into a robot trajectory. This paper…
Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo…
Datasets in the real world are often complex and to some degree hierarchical, with groups and sub-groups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these…
Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…
We present the first top-down ansatz for constructing lattice Boltzmann methods (LBM) in d dimensions. In particular, we construct a relaxation system (RS) for a given scalar, linear, d-dimensional advection-diffusion equation.…
In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then…
The aim of this paper is twofold: the first is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow…
Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…
A dynamic Boltzmann machine (DyBM) has been proposed as a model of a spiking neural network, and its learning rule of maximizing the log-likelihood of given time-series has been shown to exhibit key properties of spike-timing dependent…
In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order…
Deep neural networks (DNNs) for supervised learning can be viewed as a pipeline of a feature extractor (i.e. last hidden layer) and a linear classifier (i.e. output layer) that is trained jointly with stochastic gradient descent (SGD). In…
Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications…