General Model Reduction Research Articles

Interpolatory Methods for Model Reduction [Bookshelf

The surge of interest in machine learning has led to increased emphasis on the value of accurate, efficient surrogate models. The book is divided into four parts. Part 1, consisting of Chapters 1 and 2, introduces the reader to the basic ideas underlying general model reduction and provides the relevant system-theoretic background needed for the remainder of the book. Part 2, consisting of Chapters 3–5, covers core concepts of interpolatory model reduction where wellknown results and state-of-the-art implementations are presented in a compact yet deep way. Part 3, consisting of Chapters 6 and 7, provides the first comprehensive textbook exposition of recent developments in parameter dependent dynamical systems and nonlinear interpolatory model reduction. This book is a timely reminder that before we reach for black-box approximation functions (which often require prohibitive amounts of data to train), there is a long and rigorous history (and many recent advances) in system-theoretic model-reduction methods that can deliver structured, reduced-order models in a broad range of scientific and engineering settings.

A Review of the Accuracy of Primal Assembly Model Order Reduction Techniques

Model order reduction (MOR) techniques have been used in structural dynamics for over sixty years as a quick and effective way to examine the dynamic behavior of complex finite element (FE) models. Various macroscopic phenomena arise from the physics and mechanics of the underlying microstructure, and MOR approaches can be employed in conjunction with the multiscale computational homogenization approach, which is deriving local macroscopic constitutive responses from underlying microstructure; to predict the dynamic behavior of heterogeneous macrostructures. The accuracy and efficiency of the most representative approaches from dynamic condensation, component mode synthesis (CMS), and general model reduction (GMR) methods are compared in this paper. The techniques considered are Guyan and the improved reduced system (IRS) from classical dynamic condensation, Craig-Bampton (CB) and enhanced Craig-Bampton (ECB) from CMS, IRS-based substructuring, GMR, and GMRPlus. All the substructuring methods employ primal assembly at the boundary interface of the substructures. The accuracy and computing efficiency of the techniques are compared in-depth using real-world engineering problems, and the effect of the number of substructures on the accuracy and computational cost is also examined.

A general model reduction with primal assembly in structural dynamics

A new formulation of general model reduction in structural dynamics is presented. The proposed method consists of four attributes: a hybrid method combining dynamic condensation and component mode synthesis that are arguably the most popular model reduction techniques, a precise model reduction taking the inertia effect into consideration, primal assembly at the boundary interface of substructures and general formulations of model reduction with primal assembly. Comparisons of the proposed model reduction method with the conventional methods are provided as well as an efficient model reduction procedure of the proposed method. In particular, its advantages and performance of the proposed method are thoroughly investigated with various numerical examples.

An Improved Model Reduction Method and its Application in Similar Simulation of Complex Systems

The model reduction methods aim at simplifying system model while retaining system dynamic behaviors. In this study, an improved high-order system model reduction method based on modal aggregation is proposed, and which is applied to a typical complex mechanical system. Compared with general model reduction methods based on aggregation method, this method derived from the modal matrix can get more accurate aggregation matrix. The research on natural characteristic of gas turbine blade-disk shows that the reduced-order model obtained by modal aggregation method retains the dynamics of original complex system, which verified feasibility and effectiveness of the modal aggregation reduction method and also provided an easy method for similar simulation modeling and dynamic characteristic analysis of high-order complex systems.

Probability Distance Based Compression of Hidden Markov Models

Large-scale stochastic models are relevant in many different fields such as computational biology, finance, social sciences, communication, and traffic networks. In order to both efficiently simulate and analyze such models and to understand the essential properties of the system, it is desirable to have model reduction techniques that much reduce the dimensionality of the model while at the same time preserving the system's essential dynamical properties. In this paper, a general model reduction technique for the class of discrete space and time hidden Markov models is presented, thereby also including the more special class of discrete Markov chains. The method is illustrated on some model applications.

Robust simplifications of multiscale biochemical networks

BackgroundCellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.ResultsWe propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in [1]. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-κB pathway.ConclusionOur approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.

Positive realness preserving model reduction with H/sub /spl infin norm error bounds

Many physical systems that occur in applications are naturally passive, for example, mechanical systems with dual sensors and actuators, and electrical circuits with passive components. Taking advantage of this property, many controller schemes have been proposed with the property that the controller is strictly positive real. Due to design and implementation considerations, the plant or the controller may need to be approximated by a lower-order system. It is highly desirable for the reduced-order system to also possess the positive realness property to guarantee that the resulting closed-loop system remains stable. Motivated by this problem, this paper considers the general model-reduction problem for a positive real system under the constraint that the reduced system is also positive real. We present a solution based on the balanced stochastic truncation. When the higher-order system is strictly positive real, we derive an H/sub /spl infin norm bound on the approximation error. We also consider alternate approaches of approximating the spectral factors with associated H/sub /spl infin norm error bounds. An example is included to show the efficacy of this method and comparison with other approaches.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Model reduction methods for dynamic analyses of large structures

User-friendly finite element pre-processors permit detailed modelling of engineering structures with complicated topologies, often resulting in a much larger number of degrees of freedom than that motivated by the expected complexity of the structural response. Dynamic analyses of these large-scale models might require a prohibitive amount of CPU time. In particular, the uncoupling of the equations of motion for linear systems with non-proportional damping by means of a complex eigenvector basis is computationally very demanding. We present general model reduction procedures, applicable to whole structures or substructures, that produce a series of reduced models each spanning appropriate subspaces (general Krylov spaces) of the solution space. Crucial steps in such procedures are the selection of basis vectors for the (sub)structures and the control of reduction errors. The set of basis vectors is generated by using a simple physical approach for successively reducing the residual error in the governing equilibrium equations. A frequency window method (shifting) is used to capture the relevant frequency content. The residuals of the equilibrium equations, computed on fully expanded level, are used as reliable measures of the reduction errors. The efficiency of the techniques is demonstrated in some numerical experiments and on a large engineering problem, using a program based on SAP IV.