Symplectic Model Reduction of Hamiltonian Systems

In this paper, a symplectic model reduction technique, proper symplectic decomposition (PSD) with symplectic Galerkin projection, is proposed to save the computational cost for the simplification of large-scale Hamiltonian systems while preserving the symplectic structure. As an analogy to the classical proper orthogonal decomposition (POD)-Galerkin approach, PSD is designed to build a symplectic subspace to fit empirical data, while the symplectic Galerkin projection constructs a reduced Hamiltonian system on the symplectic subspace. For practical use, we introduce three algorithms for PSD, which are based upon: the cotangent lift, complex singular value decomposition, and nonlinear programming. The proposed technique has been proven to preserve system energy and stability. Moreover, PSD can be combined with the discrete empirical interpolation method to reduce the computational cost for nonlinear Hamiltonian systems. Owing to these properties, the proposed technique is better suited than the classical POD-Galerkin approach for model reduction of Hamiltonian systems, especially when long-time integration is required. The stability, accuracy, and efficiency of the proposed technique are illustrated through numerical simulations of linear and nonlinear wave equations.Comment: 25 pages, 13 figure

A DDDAS Plume Monitoring System with Reduced Kalman Filter1

AbstractA new dynamic data-driven application system (DDDAS) is proposed in this article to dynamically estimate a concentration plume and to plan optimal paths for unmanned aerial vehicles (UAVs) equipped with environmental sensors. The proposed DDDAS dynamically incorporates measured data from UAVs into an environmental simulation while simultaneously steering measurement processes. The main idea is to employ a few time-evolving proper orthogonal decomposition (POD) modes to simulate a coupled linear system, and to simultaneously measure plume concentration and plume source distribution via a reduced Kalman filter. In order to maximize the information gain, UAVs are dynamically driven to hot spots chosen based on the POD modes using a greedy algorithm. We demonstrate the efficacy of the data assimilation and control strategies in a numerical simulation and a field test

Consensus of self-driven agents with avoidance of collisions

In recent years, many efforts have been addressed on collision avoidance of collectively moving agents. In this paper, we propose a modified version of the Vicsek model with adaptive speed, which can guarantee the absence of collisions. However, this strategy leads to an aggregated state with slowly moving agents. We therefore further introduce a certain repulsion, which results in both faster consensus and longer safe distance among agents, and thus provides a powerful mechanism for collective motions in biological and technological multi-agent systems.Comment: 8 figures, and 7 page

Human Microbe-Disease Association Prediction Based on Adaptive Boosting

There are countless microbes in the human body, and they play various roles in the physiological process. There is growing evidence that microbes are closely associated with human diseases. Researching disease-related microbes helps us understand the mechanisms of diseases and provides new strategies for diseases diagnosis and treatment. Many computational models have been proposed to predict disease-related microbes, in this paper, we developed a model of Adaptive Boosting for Human Microbe-Disease Association prediction (ABHMDA) to reveal the associations between diseases and microbes by calculating the relation probability of disease-microbe pair using a strong classifier. Our model could be applied to new diseases without any known related microbes. In order to assess the prediction power of the model, global and local leave-one-out cross validation (LOOCV) were implemented. As shown in the results, the global and local LOOCV values reached 0.8869 and 0.7910, respectively. What’s more, 10, 10, and 8 out of the top 10 microbes predicted to be most likely to be associated with Asthma, Colorectal carcinoma and Type 1 diabetes were all verified by relevant literatures or database HMDAD, respectively. The above results verify the superior predictive performance of ABHMDA

Accelerating consensus of self-driven swarm via adaptive speed

In resent years, Vicsek model has attracted more and more attention and been well developed. However, the in-depth analysis on the convergence time are scarce thus far. In this paper, we study some certain factors that mainly govern the convergence time of Vicsek model. By extensively numerical simulations, we find the convergence time scales in a power law with $r^2\ln N$ in the noise-free case, where $r$ and $N$ are horizon radius and the number of particles. Furthermore, to accelerate the convergence, we propose a new model in which the speed of each particle is variable. The convergence time can be remarkably shortened compared with the standard Vicsek model.Comment: 11 pages, 6 figure

Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters as this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $1000\times$ reduction in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs