BUSLAEV NETS, KAC MODEL AND INFORMATION ENTROPY OF DYNAMICAL SYSTEMS

This paper discusses the possibility of using a Jordan neural network as a model of dynamic systems and it presents a Model Predictive Control (MPC) algorithm in which such a network is used for prediction. The Jordan network is a simple recurrent neural structure in which only one value of the process input signal (from the previous sampling instant) and only one value of the delayed output signal of the model (from the previous sampling instant) are used as the inputs of the network. In order to obtain a computationally simple MPC algorithm, the nonlinear Jordan neural model is repeatedly linearised on-line around an operating point, which leads to a quadratic optimisation problem. Effectiveness of the described MPC algorithm is compared with that of the truly nonlinear MPC scheme with on-line nonlinear optimisation performed at each sampling instant.

Storing metadata about models of dynamical systems in a machine readable form is one of the key steps towards their accessibility and reusability. In the domain of process-based modeling of dynamical systems, the task is to construct an explanatory model of a dynamical system from domain knowledge and data. In this paper, we present a workflow for annotation, storage and querying of process-based models specifically in the domain of aquatic ecosystems. To provide the vocabulary of key terms about the process-based modeling paradigm, we use the Ontology for Process-Based Modeling of Dynamical Systems (OntoPBM). Next, to capture the domain-specific characteristics, we extend OntoPBM with terms specific for aquatic ecosystems. The annotations for each process-based model are stored in an RDF triple store. This enables us to execute SPARQL queries on facts asserted in the annotations, as well as facts inferred from the domain knowledge encoded in the ontology. Finally, by following the proposed workflow, we generate the minimal information about a model, which takes us one step closer towards reusable research.

The paper proposes a new method for identifying orders of input-output models for unknown nonlinear dynamic systems. The approach is based on the continuity property of the nonlinear functions which represent input-output models of continuous dynamic systems. The approach does not depend on any nonlinear function approximation methods and solely depends on the system's input-output data measured in experiments. By evaluating the modification of an index which is defined as Lipschitz number with the successive modification of model orders, the appropriate model orders can be determined simply and reliably. Theoretical background of the present approach is discussed. Several examples from chaotic dynamic systems, nonlinear plant models are presented to demonstrate the effectiveness of the present method.

Ensembles are a well established machine learning paradigm, leading to accurate and robust models, predominantly applied to predictive modeling tasks. Ensemble models comprise a finite set of diverse predictive models whose combined output is expected to yield an improved predictive performance as compared to an individual model. In this paper, we propose a new method for learning ensembles of process-based models of dynamic systems. The process-based modeling paradigm employs domain-specific knowledge to automatically learn models of dynamic systems from time-series observational data. Previous work has shown that ensembles based on sampling observational data (i.e., bagging and boosting), significantly improve predictive performance of process-based models. However, this improvement comes at the cost of a substantial increase of the computational time needed for learning. To address this problem, the paper proposes a method that aims at efficiently learning ensembles of process-based models, while maintaining their accurate long-term predictive performance. This is achieved by constructing ensembles with sampling domain-specific knowledge instead of sampling data. We apply the proposed method to and evaluate its performance on a set of problems of automated predictive modeling in three lake ecosystems using a library of process-based knowledge for modeling population dynamics. The experimental results identify the optimal design decisions regarding the learning algorithm. The results also show that the proposed ensembles yield significantly more accurate predictions of population dynamics as compared to individual process-based models. Finally, while their predictive performance is comparable to the one of ensembles obtained with the state-of-the-art methods of bagging and boosting, they are substantially more efficient.

BackgroundIdentifying a proper model structure, using methods that address both structural and parameter uncertainty, is a crucial problem within the systems approach to biology. And yet, it has a marginal presence in the recent literature. While many existing approaches integrate methods for simulation and parameter estimation of a single model to address parameter uncertainty, only few of them address structural uncertainty at the same time. The methods for handling structure uncertainty often oversimplify the problem by allowing the human modeler to explicitly enumerate a relatively small number of alternative model structures. On the other hand, process-based modeling methods provide flexible modular formalisms for specifying large classes of plausible model structures, but their scope is limited to deterministic models. Here, we aim at extending the scope of process-based modeling methods to inductively learn stochastic models from knowledge and data.ResultsWe combine the flexibility of process-based modeling in terms of addressing structural uncertainty with the benefits of stochastic modeling. The proposed method combines search trough the space of plausible model structures, the parsimony principle and parameter estimation to identify a model with optimal structure and parameters. We illustrate the utility of the proposed method on four stochastic modeling tasks in two domains: gene regulatory networks and epidemiology. Within the first domain, using synthetically generated data, the method successfully recovers the structure and parameters of known regulatory networks from simulations. In the epidemiology domain, the method successfully reconstructs previously established models of epidemic outbreaks from real, sparse and noisy measurement data.ConclusionsThe method represents a unified approach to modeling dynamical systems that allows for flexible formalization of the space of candidate model structures, deterministic and stochastic interpretation of model dynamics, and automated induction of model structure and parameters from data. The method is able to reconstruct models of dynamical systems from synthetic and real data.

A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solutions. At the same time, depending on parameter values, different dynamic regimes—stationary or oscillatory, established as a result of transient modes of various types—can be observed in the modeled system. Predicting changes in the solution dynamics type depending on changes in model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computational experiments, i.e., solving a series of direct problems with various sets of parameters followed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allowing the obtainment and analysis of information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for the visualization and classification of various dynamic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method enables qualitative visualization of the results of the set of solutions of a mathematical model and the performance of the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka–Volterra model and artificial sets of various dynamics.

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Conventional reliability analysis of load-sharing parallel systems is mainly based on failure rate of components, in which failure dependence of components and load redistribution are also characterized by specified failure rates. However, the failure rate of mechanical components always varies with time, which is difficult to measure. Therefore, in this paper, quantitative dynamic reliability models of mechanical load-sharing parallel systems are developed in terms of stress parameters and strength parameters rather than failure rate of components, which consider the degradation mechanism of mechanical components. The proposed models take into account the strength degradation path dependence (SDPD) of a component, the strength degradation process dependence between different components in a system, and the random load redistribution. In addition, Monte Carlo simulation is carried out to verify the proposed models. The results show that SDPD and the load-sharing effect have considerable influences on dynamic reliability of mechanical load-sharing parallel systems.

Precise dynamic mathematical models of complex systems are important in control and diagnostic systems design and allow testing a complex system in virtual environment at a low cost. They can be also utilized in rapid prototyping using a concept of hardware in the loop. Ever improving methods of experimental identification and using approaches in non-linear approximation can considerably increase the precision of dynamic models of complex systems. The article deals with non-linear approximation of transfer gains of a complex system and evaluates the influence of operational point selection on precision of the resulting model using methods of experimental data driven identification. The object of control is represented by two similar small turbojet engines at the Departments of the authors, the iSTC-21v and TKT-1, both based on the same power section having two degrees of freedom: fuel mass flow rate and variable convergent nozzle position.

System identification deals with the problem of building the mathematical models of dynamical systems according to the input and output data. The open-loop system identification (Observer/Kalman Filter SystemIdentification, OKID) for stable systems without requiring feedback control is introduced first. For identifying marginally stable or unstable system, however, feedback control is required to ensure the overall system stability. The algorithm of closed-loop system identification (CLID) with known feedback dynamics is shown next.

Social-ecological systems research aims to understand the nature of social-ecological phenomena, to find ways to foster or manage conditions under which desired phenomena occur or to reduce the negative consequences of undesirable phenomena. Such challenges are often addressed using dynamical systems models (DSM) or agent-based models (ABM). Here we develop an iterative procedure for combining DSM and ABM to leverage their strengths and gain insights that surpass insights obtained by each approach separately. The procedure uses results of an ABM as inputs for a DSM development. In the following steps, results of the DSM analyses guide future analysis of the ABM and vice versa. This dialogue, more than having a tight connection between the models, enables pushing the research frontier, expanding the set of research questions and insights. We illustrate our method with the example of poverty traps and innovation in agricultural systems, but our conclusions are general and can be applied to other DSM-ABM combinations.

The archive contains all libraries of domain knowledge, the incomplete models and the data used in the experiments described in the manuscript titled "Learning stochastic process-based models of dynamical systems from knowledge and data" pubilshed in BMC Systems Biology

This paper presents a new method for modelling of dynamic systems by using specially designed orthogonal polynomial neural networks. These networks utilize the feature that the basis made of orthogonal functions can be used for approximation of arbitrary function, while their property of orthogonality enables optimal performances in the sense of both convergence time and approximation error. In this regard, generalized quasi-orthogonal polynomials, specifically tailored for the application in the modelling of complex dynamic systems with time-varying behaviour, are considered. Adaptivity of the designed model is achieved by using variable factors inside the orthogonal basis. The designed orthogonal neural network is applied in modelling of laboratory twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems. Detailed comparative analysis is performed for a different number of polynomials in expansion with the purpose of finding the optimal model in the sense of trade-off between model accuracy and complexity.

The use of genetic algorithms (GAs) and other evolutionary optimization methods to design fuzzy rules for systems modeling and data classification have received much attention in recent literature. Authors have focused on various aspects of these randomized techniques, and a whole scale of algorithms have been proposed. We comment on some recent work and describe a new and efficient two-step approach that leads to good results for function approximation, dynamic systems modeling and data classification problems. First, fuzzy clustering is applied to obtain a compact initial rule-based model. Then this model is optimized by a real-coded GA subjected to constraints that maintain the semantic properties of the rules. We consider four examples from the literature: a synthetic nonlinear dynamic systems model, the iris data classification problem, the wine data classification problem, and the dynamic modeling of a diesel engine turbocharger. The obtained results are compared to other recently proposed methods.