Data-driven balancing of linear dynamical systems

数据驱动平衡的推广：不同基于平衡的简化模型应采样什么

Generalizations of data-driven balancing: What to sample for different balancing-based reduced models

本研究推广QuadBT框架至多种平衡截断模型降阶，明确计算数据驱动降阶模型所需的传递函数数据为目标系统特定谱因子的评估值，奠定相关BT变体数据驱动重构的理论基础并通过合成数据验证模型有效性。

Model Reduction of Linear Dynamical Systems via Balancing for Bayesian Inference

We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large dimension of the dynamical system state poses a computational obstacle to computing the exact posterior distribution. Model reduction offers a variety of computational tools that seek to reduce this computational burden. In particular, balanced truncation is a system-theoretic approach to model reduction which obtains an efficient reduced-dimension dynamical sy…

线性高斯逆问题中先验驱动平衡的后验误差界

Posterior error bounds for prior-driven balancing in linear Gaussian inverse problems

针对线性高斯逆问题，利用逆的摄动理论推导近似后验均值和协方差的误差界，并应用于线性时不变动力系统的平滑问题，建立系统理论与逆问题的新联系，给出基于平衡截断的模型降阶方法的先验误差界。

快速多极方法的数据驱动执行

Data-Driven Execution of Fast Multipole Methods

针对快速多极方法在非规则粒子分布下的负载均衡难题，提出将最耗时阶段分解为任务，利用QUARK运行时环境异步调度任务，实现数据驱动的无序执行，在四路四核Intel Xeon系统上获得线性加速。

Gramians, Energy Functionals and Balanced Truncation for Linear Dynamical Systems with Quadratic Outputs

Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear dynamical equation and a quadratic output function. To this aim, we propose a new algebraic observability Gramian for the system based on Hilbert space adjoint theory. We then show the proposed Gramians satisfy a particular type of generalized Lyapunov equations and we investigate their connections to energy functionals, namely, the controllability and observabil…

A time domain a posteriori error bound for balancing-related model order reduction

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of methods, only a few of them allow for rigorous error control. In this paper, we propose a rigorous error bound for the reduction of linear systems with balancing-related reduction methods. More specifically, we consider the simulation over a finite time interval and provide an a posteriori adaption of the standard a priori bound for Balanced Truncation and Balanc…