Related papers: ANN-MoC Method for Inverse Transient Transport Pro…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
Most unsupervised anomaly detection methods based on representations of normal samples to distinguish anomalies have recently made remarkable progress. However, existing methods only learn a single decision boundary for distinguishing the…
An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an…
With the improvement of the pattern recognition and feature extraction of Deep Neural Networks (DPNNs), image-based design and optimization have been widely used in multidisciplinary researches. Recently, a Reconstructive Neural Network…
Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…
The current practice of manually processing features for high-dimensional and heterogeneous aviation data is labor-intensive, does not scale well to new problems, and is prone to information loss, affecting the effectiveness and…
Inverse design of transport equations can be addressed by using a gradient-adjoint methodology. In this methodology numerical schemes used for the adjoint resolution determine the direction of descent in its iterative algorithm, and…
We show that the inverse problems for a class of kinetic equations can be solved by classical tools in PDE analysis including energy estimates and the celebrated averaging lemma. Using these tools, we give a unified framework for the…
IoT devices are increasingly the source of data for machine learning (ML) applications running on edge servers. Data transmissions from devices to servers are often over local wireless networks whose bandwidth is not just limited but, more…
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…
Artificial neural networks (ANN) have been shown to be flexible and effective function estimators for identification of nonlinear state-space models. However, if the resulting models are used directly for nonlinear model predictive control…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The…
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…
The problem of optimal mass transport arises in numerous applications including image registration, mesh generation, reflector design, and astrophysics. One approach to solving this problem is via the Monge-Amp\`ere equation. While recent…
In this paper, we propose an online path planning architecture that extends the model predictive control (MPC) formulation to consider future location uncertainties for safer navigation through cluttered environments. Our algorithm combines…
Accurately and efficiently simulating complex fluid dynamics is a challenging task that has traditionally relied on computationally intensive methods. Neural network-based approaches, such as convolutional and graph neural networks, have…