Sample‐based robust model reduction for non‐linear systems biology models

We discuss methods for model order reduction (MOR) of linear systems with many input and output variables, arising in the modeling of linear (sub) circuits with a huge number of nodes and a large number of terminals, like power grids. Our work is based on the approaches SVDMOR and ESVDMOR proposed in recent publications (1; 2; 3; 4; 5). In particular, we discuss efficient numerical algorithms for their implementation. Only by using efficient tools from numerical linear algebra, these methods become applicable for truly large-scale problems.

The main part of the computational cost required for solving the problem of optimal material design with extreme properties using a topology optimization formulation is devoted to solving the equilibrium system of equations derived through the implementation of the finite element method (FEM). To reduce this computational cost, among other methodologies, various model order reduction (MOR) approaches can be utilized. In this work, a simple Matlab code for solving the topology optimization for the design of materials combined with three different model order reduction approaches is presented. The three MOR approaches presented in the code implementation are the proper orthogonal decomposition (POD), the on-the-fly reduced order model construction and the approximate reanalysis (AR) following the combined approximations approach. The complete code, containing all participating functions (including the changes made to the original ones), is provided.

A new method for model order reduction for an important class of non-linear dynamical systems is proposed. The reduction technique is based on the frequency balanced reduction method within a desired frequency band and a developed Trajectory Piecewise-Linear (TPWL) model order reduction approach. Both the methods are recently developed techniques and they can increase the accuracy and efficiency of the reduction method. The computational load and memory are significantly reduced when the method is used in the hybrid reduction method. The accuracy enhanced hybrid method is applicable to very large scale non-linear models efficiently and accurately. The numerical results show the accuracy and efficiency enhancement of the proposed method.

Sensitivity analysis of random linear differential–algebraic equations using system norms

Neglecting the armature inductance, La, is a common approach for model order reduction for a class of brush DC motors. Some authors, however, make a partial or incomplete interpretation for neglecting La, leading students to wrong results and misunderstandings. The existing conditions in the literature and in introductory control systems textbooks are either based on the time constant of the mechanical system being greatly larger than that of the electrical system, or La ≈ 0. These conditions are not supported analytically and no corresponding error analysis of any kind is provided. This paper analyzes and criticizes the eligibility of these conditions and provides an error model that corresponds to the model order reduction associated with neglecting La, and another that corresponds to neglecting the non-dominant pole. Experimental results are included to illustrate the suitability of the proposed error models and the suitability of employing such models in basic control designs.

In this paper the Routh Approximation method is explored for getting the reduced order model of a higher order model. The reduced order modeling of a large system is necessary to ease the analysis of the system. The approach is examined and compared to single-input single-output (SISO) and multi-input multi-output (MIMO) systems. The response comparison is considered in terms of step response parameters and graphical comparisons. It is reported that the reduced order model using proposed Routh Approximation (RA) method is almost similar in behavior to that of with original systems.

The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the Linear Complementarity Programming (LCP) method as basic methodology. It has the advantage of resulting in the much smaller dual problem that is associated with the governing variational principle and that turns out to be beneficial for the model order reduction. Since the shape of the contact zone depends strongly on the acting outer forces, the LCP for the Lagrange multipliers has to be solved in each time step. The model order reduction scheme, on the other hand, is applied to the large linear system for the displacements and computed in advance by means of an Arnoldi process. In terms of computational effort the reduction scheme is very appealing because the contact constraints are fully satisfied while the reduction acts only on the displacements. As an extension of our approach, we furthermore take up the idea of the Craig-Bampton method in order to distinguish between interior nodes and the nodes in the contact zone. A careful performance analysis closes the paper.

This report summarizes fiscal year (FY) 2017 progress towards developing and implementing within the SPARC in-house finite volume flow solver advanced fluid reduced order models (ROMs) for compressible captive-carriage flow problems of interest to Sandia National Laboratories for the design and qualification of nuclear weapons components. The proposed projection-based model order reduction (MOR) approach, known as the Proper Orthogonal Decomposition (POD)/Least- Squares Petrov-Galerkin (LSPG) method, can substantially reduce the CPU-time requirement for these simulations, thereby enabling advanced analyses such as uncertainty quantification and de- sign optimization. Following a description of the project objectives and FY17 targets, we overview briefly the POD/LSPG approach to model reduction implemented within SPARC . We then study the viability of these ROMs for long-time predictive simulations in the context of a two-dimensional viscous laminar cavity problem, and describe some FY17 enhancements to the proposed model reduction methodology that led to ROMs with improved predictive capabilities. Also described in this report are some FY17 efforts pursued in parallel to the primary objective of determining whether the ROMs in SPARC are viable for the targeted application. These include the implemen- tation and verification of some higher-order finite volume discretization methods within SPARC (towards using the code to study the viability of ROMs on three-dimensional cavity problems) and a novel structure-preserving constrained POD/LSPG formulation that can improve the accuracy of projection-based reduced order models. We conclude the report by summarizing the key takeaways from our FY17 findings, and providing some perspectives for future work.

Many new promising model order reduction (MOR) methods and algorithms were developed during the last decade. Industry and academic research institutions intend to test, validate, compare, and use these new promising MOR techniques with their own models. Therefore, an MOR toolbox bridging the gap between theoretical, algorithmic, and numerical developments to an end-user-oriented program, usable by non-experts, was developed called ‘Model Order Reduction of Elastic Multibody Systems’ (Morembs). A C++ implementation as well as a Matlab implementation including an intuitive graphical user interface is available. Import from various FE programs is possible, and the reduced elastic bodies can be exported to a variety of programs to simulate the compact models. In the course of the various projects, many improvements on the algorithmic side were added. As we learned over the years, there is not one ‘optimal’ MOR method. ‘Optimal’ MOR depends on circumstances, like boundary conditions, excitation spectra, further model usage. The toolbox is now used, e.g., in solid mechanics, biomechanics, vehicle dynamics, control of flexible structures, or crash simulations. In all these use cases, the toolbox allows the user to facilitate their well-known modeling and simulation environment. Only the critical MOR process during preprocessing is performed with Morembs, which helps to compare the various MOR techniques to find the most suited one.

Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order reduction approaches are available in the existing literature that alleviate this issue by approximating the solution at a coarse scale preserving fine scale features. We attempt to present a comparison between two such model order reduction techniques, namely (1) adaptive numerical homogenization and (2) generalized multiscale basis functions. We rely upon a non-linear, multi-phase, black-oil model formulation, commonly encountered in the oil and gas industry, as the basis for comparing the aforementioned two approaches. An expanded mixed finite element formulation is used to separate the spatial scales between non-linear, flow, and transport problems. A numerical benchmark is setup using fine scale property information from the 10th SPE comparative project dataset for the purpose of comparing accuracies of these two schemes. An adaptive criterion is employed by both the schemes for local enrichment that allows us to preserve solution accuracy compared to the fine scale benchmark problem. The numerical results indicate that both schemes are able to adequately capture the fine scale features of the model problem at hand.

This paper presents a framework for model order reduction based on Balanced Truncation (BT) method and Artificial Neural Networks (ANN). As social, architectural and technical models are witnessing rapid complexity increase, it has become essential to find solutions to obtain a lower complex version of models while still preserving the model integrity. The main idea of the proposed framework is to reduce uncertainty by cascading two different Model Order Reduction (MOR) approaches, the BT technique and the Jordan Recurrent Neural Network (JRNN). The reduced model obtained by the JRNN network is estimated using the Instrument Variable (IV) estimation approach. Finally, the BT reduced model and the estimated JRNN reduced model are cascaded to obtain the final reduced order version of the original plant. The cascading procedure takes the powerfulness of both techniques and present them in a single system capable to compensate for possible errors and uncertainties. Simulation results prove the efficiency of the proposed framework in terms of the deduction strength and the integrity level.

The increasing deployment of communication services is urging microwave filter industry to satisfy stringent electrical specifications in microwave devices and, in addition, in rather short delivery times. These electromagnetic devices require time-consuming full-wave simulations, by means of commercial software. However, there is plenty of room for improvement in this strategy to satisfy industrial needs. Instead of using engineering brute force, which can be expensive and computer-demanding, we can use the so-called model order reduction techniques.A reduced-order model is a mathematically equivalent model to a more complicated full-order model, still maintaining the same behavior of the original one within a specific parameter range, but in a much simpler setting.This work introduces what model order reduction can do for you in microwave filter full-wave design. Traditionally, fast frequency sweeps have been provided by these reduced-order models. However, there are plenty of more options available. The electromagnetic system matrix is compressed to its minimum size, i.e., the order of the microwave filter plus a few more, say, three or four more. This reduced-size system matrix captures all the physics in the 3D model of your electromagnetic device. As a result, a more in-depth zero-pole diagram can be obtained with ease, where the dominant electromagnetic poles, reflection and transmission zeros are clearly identified. The experienced eyes of the microwave engineer no longer need to guess where these poles and zeros are located by looking at the S-parameter response. This model order reduction approach detail their position on the complex plane, in the Laplace domain.In addition, this reduced-order model, i.e., the reduced-size system matrix, can be arranged to identify the electromagnetic couplings among the resonators in the microwave device under study. This allows the microwave engineer to know which couplings are actually present in the full-wave simulation of the electromagnetic device, including the leakage ones. As a result, the tuning process of the device turns into a simple task, adjusting only the right couplings to target the electrical specifications.Several examples will show the capabilities and possibilities of model order reduction approaches in microwave filter design.

Pharmacotherapy is the mainstay in the treatment of Parkinson's disease and the armamentarium of drugs available for the therapy of this disease is still expanding. Anti-Parkinson's disease drugs are effective in reducing the physical symptoms, such as hypokinesia, bradykinesia, rigidity and tremor. However, there is a large interindividual variability in response to anti-Parkinson's disease drugs with respect to both drug efficacy and toxicity. It is thought that genetic variability in genes encoding drug-metabolizing enzymes, drug receptors and proteins involved in pathway signaling is an important factor in determining interindividual variability in drug response. Pharmacogenetics aims at identifying genetic markers associated with drug response. Ideally, knowledge of these genetic markers will enable us to predict an individual's drug response in terms of both efficacy and toxicity. The role of pharmacogenetics in the treatment of Parkinson's disease is relatively unexplored. Therefore, we aim to present a systematic review of the published pharmacogenetic studies in Parkinson's disease and to describe polymorphic genes of interest for future research.

Investigations of small-signal stability of electrical power systems are usually performed by modal and time-domain analysis using descriptive differential equations of machines. Thereby, the modal analysis enables the identification of all dominant states of the linearized power system model, which are associated with electromechanical interactions and power oscillations. For reasons of simplification and due to computation capabilities, a reduction of the model order is often advantageous. This can be done by neglecting different physical effects within the machines, retaining the topology and the modal characteristics of the power system regarding its electromechanical behavior. This paper presents a modal analysis based approach for power system model order reduction. In order to reproduce the small-signal behavior of power systems accurately, damping and synchronizing parameters are introduced within the reduced-order model. Subsequently, each coefficient is determined analytically for a single machine infinite bus system and using the particle swarm optimization method for a multi-machine system. The deviation to the electromechanical reference modes of the higherorder power system model constitutes the objective function to be minimized. The results confirm that the approach is suitable for the aspired goals and fulfills the accuracy requirements.

Three-dimensional electromagnetic methods are fundamental tools for the analysis and design of high-speed systems. These methods often generate large systems of equations, and model order reduction (MOR) methods are used to reduce such a high complexity. When the geometric dimensions become electrically large or signal waveform rise times decrease, time delays must be included in the modeling. Design space optimization and exploration are usually performed during a typical design process that consequently requires repeated simulations for different design parameter values. Efficient performing of these design activities calls for parameterized model order reduction (PMOR) methods, which are able to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as layout or substrate features. We propose a novel PMOR method for neutral delayed differential systems, which is based on an efficient and reliable combination of univariate model order reduction methods, a procedure to find scaling and frequency shifting coefficients and positive interpolation schemes. The proposed scaling and frequency shifting coefficients enhance and improve the modeling capability of standard positive interpolation schemes and allow accurate modeling of highly dynamic systems with a limited amount of initial univariate models in the design space. The proposed method is able to provide parameterized reduced order models passive by construction over the design space of interest. Pertinent numerical examples validate the proposed PMOR approach.