Modeling Of Dynamic Systems Research Articles

Waveformer for modeling dynamical systems

Neural operators have gained recognition as potent tools for learning solutions of a family of partial differential equations. The state-of-the-art neural operators excel at approximating the functional relationship between input functions and the solution space, potentially reducing computational costs and enabling real-time applications. However, they often fall short when tackling time-dependent problems, particularly in delivering accurate long-term predictions. In this work, we propose “waveformer”, a novel operator learning approach for learning solutions of dynamical systems. The proposed waveformer exploits wavelet transform to capture the spatial multi-scale behavior of the solution field and transformers for capturing the long horizon dynamics. We present four numerical examples involving Burgers’s equation, KS-equation, Allen–Cahn equation, and Navier–Stokes equation to illustrate the efficacy of the proposed approach. Results obtained indicate the capability of the proposed waveformer in learning the solution operator and show that the proposed Waveformer can learn the solution operator with high accuracy, outperforming existing state-of-the-art operator learning algorithms by up to an order, with its advantage particularly visible in the extrapolation region.

Research of nonstationary dynamic models of the organizational and technological process of railway transport technical vehicles repair

The problems of analytical and computer research of dynamic models of repair and operation of technical vehicles used in railway transport are among the urgent problems related to ensuring safety and stability of traffic, with the development of digital twins and the improvement of monitoring and diagnostic systems. The analysis of models described by various types of multidimensional nonlinear differential equations requires the use of modern methods of dynamical systems theory, numerical optimization and computer algebra. The purpose of the article is to conduct a qualitative and numerical analysis of mathematical models of organizational and technological processes (OTP) in railway transport, as well as the synthesis of new controlled OTP models. Nonstationary generalizations of a two-dimensional dynamic model describing the repair process of railway transport equipment are proposed. Various cases of using constant and time-dependent parameters are considered. The case of linear and exponential dependences of parameters on time is studied. For the studied models, trajectories are obtained taking into account the variation of constant parameters and taking into account the choice of parametric dependencies, a comparative analysis of the results is presented. The formulation of the problem of optimal control of the number of repaired and repaired railway wagons is proposed. Promising methods for solving this problem using numerical optimization methods, including those inspired by nature, are described. The results can be used in the tasks of constructing and analyzing mathematical models of dynamic systems, in the tasks of numerical modeling of transport systems and technological processes, in the tasks of optimizing the number of vehicles and improving the transportation process, as well as in the tasks of creating digital counterparts in the transport industry.

Possibilities and limits of modelling of long-range economic consequences of air pollution – A case study

Air pollution is the biggest environmental problem in modern societies, causing considerable health damage and requiring substantial financial resources for health care. The goal of the study is to demonstrate the adverse economic consequences of air pollution on example of a small, open Central European country, Hungary, and to provide quantified financial arguments for macroeconomic decision-making for the development of a long-term energy strategy. On the basis of the Cobb-Douglas production function and Solow-Swann model of dynamic economic systems a simple and robust model was constructed to estimate and predict economic losses, caused by the pollution. On base of results it is obvious, that on base of macroeconomic theory and combination of various, publicly available, quality-controlled statistical resources quantifiable models can be constructed to characterise the economic consequences of air pollution, but it should be taken into consideration, that the reliability of economic models considerably depends on their initial parameters and practical validity of assumptions, based on which the underlying economic theories were built. The most important economic burden of air pollution is caused by the loss of working–age population, resulting in a decrease of 4.1–9.4 % a year in Gross Domestic Product (GDP) in the next fifty years. The additional burden of health care costs amounts to 0.1 % of GDP. Reducing air pollution is not only a quality of life improvement but also an investment into the economic development. Notwithstanding of statistical biases it could be proven the importance of combination health economic and econometric methods in preparation of more efficient environmental-related socio-economic decisions.

Nonlinear causal network learning via Granger causality based on extreme support vector regression.

For complex networked systems, based on the consideration of nonlinearity and causality, a novel general method of nonlinear causal network learning, termed extreme support vector regression Granger causality (ESVRGC), is proposed. The nonuniform time-delayed influence of the driving nodes on the target node is particularly considered. Then, the restricted model and the unrestricted model of Granger causality are, respectively, formulated based on extreme support vector regression, which uses the selected time-delayed components of system variables as the inputs of kernel functions. The nonlinear conditional Granger causality index is finally calculated to confirm the strength of a causal interaction. Generally, based on the simulation of a nonlinear vector autoregressive model and nonlinear discrete time-delayed dynamic systems, ESVRGC demonstrates better performance than other popular methods. Also, the validity and robustness of ESVRGC are also verified by the different cases of network types, sample sizes, noise intensities, and coupling strengths. Finally, the superiority of ESVRGC is successful verified by the experimental study on real benchmark datasets.

Some methodological aspects of mathematical modeling in dynamic systems

This paper is devoted to methodologies in the field of mathematical foundations of information technology and computer sciences. The theoretical foundations of mathematical modeling of dynamic systems are briefly presented. Various aspects of the concept of a model are considered. The division into types of models is presented. The steps of the mathematical modeling process are detailed. Basic requirements for mathematical models are formulated. The main approaches used in the process of mathematical modeling are described.

Mathematical modelling with computational fractional order for the unfolding dynamics of the communicable diseases

Mathematical models based on computational fractional orders, employed for accurate modelling of complex dynamic systems, can ensure the implementation of various analytical, numerical and computing methods encompassing their applications to emerging and ever-varying real-world problems. Tracking, managing and controlling communicable diseases, one being monkeypox with different features, virological and taxonomic attributes, are oriented towards high-risk groups concerning global public health. This study, accordingly, is devoted to the presentation of the piecewise global derivative model of the monkeypox virus by applying the Caputo and Atangana Baleanu fractional-order derivatives in the partitioned two sub-intervals. The model includes eight compartments with two categories of human and rodent populations. The cases which take part in some sense for the said infection are investigated along with connection in this format. The existence and uniqueness of the solution in the framework of the piecewise global derivative are analyzed for both sub-intervals using fixed point theory. The detailed investigation of the dynamics of fractional-order systems and among many other dynamic features, stability is addressed. The stability of the solution is, thus, examined using the idea of Ulam Hyers concept. For the best fitting values of the parameters, the results are simulated using the monkeypox data. Using the method of Newton polynomial, different piecewise dynamics of each compartment are simulated on different fractional orders and time durations. This kind of a proposed approach is thought to lay a foundation where the transmission takes place to control epidemic events and other infectious medical conditions through vaccines or taking preventive measures to maintain and advance global public health while fully optimizing the clinical care of the diseases to manage complications, alleviate symptoms as well as prevent the long-term sequelae. This analysis also deals with sudden variation in monkeypox dynamics and also for crossover dynamics along with removal of discontinuity through modification of piecewise global analysis.

Data-driven analysis and prediction of dynamic postprandial metabolic response to multiple dietary challenges using dynamic mode decomposition.

In the field of precision nutrition, predicting metabolic response to diet and identifying groups of differential responders are two highly desirable steps toward developing tailored dietary strategies. However, data analysis tools are currently lacking, especially for complex settings such as crossover studies with repeated measures.Current methods of analysis often rely on matrix or tensor decompositions, which are well suited for identifying differential responders but lacking in predictive power, or on dynamical systems modeling, which may be used for prediction but typically requires detailed mechanistic knowledge of the system under study. To remedy these shortcomings, we explored dynamic mode decomposition (DMD), which is a recent, data-driven method for deriving low-rank linear dynamical systems from high dimensional data.Combining the two recent developments "parametric DMD" (pDMD) and "DMD with control" (DMDc) enabled us to (i) integrate multiple dietary challenges, (ii) predict the dynamic response in all measured metabolites to new diets from only the metabolite baseline and dietary input, and (iii) identify inter-individual metabolic differences, i.e., metabotypes. To our knowledge, this is the first time DMD has been applied to analyze time-resolved metabolomics data. We demonstrate the potential of pDMDc in a crossover study setting. We could predict the metabolite response to unseen dietary exposures on both measured (R2 = 0.40) and simulated data of increasing size (= 0.65), as well as recover clusters of dynamic metabolite responses. We conclude that this method has potential for applications in personalized nutrition and could be useful in guiding metabolite response to target levels. The measured data analyzed in this study can be provided upon reasonable request. The simulated data along with a MATLAB implementation of pDMDc is available at https://github.com/FraunhoferChalmersCentre/pDMDc.

Koopman-based surrogate models for multi-objective optimization of agent-based systems

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.

Data-Driven Modeling of the Nonlinear Dynamics of Passive Lower-Limb Prosthetic Systems

Abstract Modeling the nonlinear dynamics of prosthetic feet is an important tool for linking prosthesis mechanical properties to end-user outcomes. There has been a renewed interest in data-driven modeling of dynamical systems, with the development of the Extended Dynamic Mode Decomposition with control (eDMDc) and the Sparse Identification of Nonlinear Dynamics with Control (SINDYc). These algorithms do not require prior information about the system, including mechanical configuration, and are data-driven. The aim of this study was to assess the feasibility and accuracy of applying these data-driven algorithms to model prosthesis nonlinear load response dynamics. Different combinations of a dynamic response foot, a hydraulic ankle unit, and three shock-absorbing pylons of varying resistance were tested loaded and unloaded at three orientations reflecting critical positions during the stance phase of walking. We tested two different data-driven algorithms, the eDMDc, with two different kernels, and the SINDYc, which regresses the coefficients for a nonlinear ordinary differential equation. Each algorithm was able to model the nonlinear prosthesis dynamics, but the SINDYc outperformed the eDMDc methods with a root mean square error across orientations < 1.50 mm and a maximum error in peak displacement of 1.28 mm or 4% relative error. From the estimated SINDYc governing equation of the system dynamics, we were able to simulate different mechanical behavior by systematically varying parameter values, which offers a novel foundation for designing, controlling, and classifying prosthetic systems ultimately aimed at improving prosthesis user outcomes.

Volterra Black-Box Models Identification Methods: Direct Collocation vs. Least Squares

The Volterra integral-functional series is the classic approach for nonlinear black box dynamical system modeling. It is widely employed in many domains including radiophysics, aerodynamics, electronic and electrical engineering and many others. Identifying the time-varying functional parameters, also known as Volterra kernels, poses a difficulty due to the curse of dimensionality. This refers to the exponential growth in the number of model parameters as the complexity of the input-output response increases. The least squares method (LSM) is widely acknowledged as the standard approach for tackling the issue of identifying parameters. Unfortunately, the LSM suffers with many drawbacks such as the sensitivity to outliers causing biased estimation, multicollinearity, overfitting and inefficiency with large datasets. This paper presents an alternative approach based on direct estimation of the Volterra kernels using the collocation method. Two model examples are studied. It is found that the collocation method presents a promising alternative for optimization, surpassing the traditional least squares method when it comes to the Volterra kernels identification including the case when input and output signals suffer from considerable measurement errors.

BioModME for building and simulating dynamic computational models of complex biological systems.

Molecular mechanisms of biological functions and disease processes are exceptionally complex, and our ability to interrogate and understand relationships is becoming increasingly dependent on the use of computational modeling. We have developed "BioModME," a standalone R-based web application package, providing an intuitive and comprehensive graphical user interface to help investigators build, solve, visualize, and analyze computational models of complex biological systems. Some important features of the application package include multi-region system modeling, custom reaction rate laws and equations, unit conversion, model parameter estimation utilizing experimental data, and import and export of model information in the Systems Biology Matkup Language format. The users can also export models to MATLAB, R, and Python languages and the equations to LaTeX and Mathematical Markup Language formats. Other important features include an online model development platform, multi-modality visualization tool, and efficient numerical solvers for differential-algebraic equations and optimization. All relevant software information including documentation and tutorials can be found at https://mcw.marquette.edu/biomedical-engineering/computational-systems-biology-lab/biomodme.php. Deployed software can be accessed at https://biomodme.ctsi.mcw.edu/. Source code is freely available for download at https://github.com/MCWComputationalBiologyLab/BioModME.

An approach to logical-mathematical computer modeling of linear and nonlinear dynamical systems

The paper deals with the problem of modeling linear and nonlinear dynamical systems using information technologies and programming. The processes of modeling, synthesis and inference of solutions to problems are considered, and the possibility of their integration within the described approach is shown. The substantive aspects of the development of special mathematical and algorithmic support for the construction of a software system for the analysis and processing of expert information for the purposes of automated synthesis and inference of solutions are briefly outlined. The aim of the work is to create a new approach of logical-mathematical computer modeling of linear and nonlinear dynamical systems and to develop a prototype of a software computational expert system based on it. As a result of the research, a universal approach of logical-mathematical computer modeling of linear and nonlinear dynamical systems has been developed and proposed. The proposed approach can be used to organize the process of computer modeling and automated synthesis of task solutions with the output of their results. The mathematical model of the knowledge base and process of its construction for the selected subject area, as well as the algorithm for outputting solutions to problems with its software implementation in the Python programming language, are shown. Examples of solution output for various linear and nonlinear problems are given. The developed prototype of the software computational expert system using the proposed logical- mathematical approach will significantly simplify the process of modeling dynamical systems and make the solution of problems' simpler and more understandable.

D3NN: Data-Driven Dual-level Neural Network Tool for Dynamical System Modeling and Abstraction

This paper presents D3NN, a neural network learning tool for dual-level dynamic system modeling. This tool aims to model the dynamic system under a dual-level modeling framework, i.e., modeling the system dynamics through a computationally efficient and precise low-level neural hybrid system and an interpretable high-level transition system abstraction. Given samples of the dynamic system and user specifications, the proposed tool can generate a low-level distributive learning framework consisting of shallow neural network approximations for local dynamics and its high-level transition system abstraction that allows Computational Tree Logic (CTL) formulae verification.

Property Tax in Indonesia: A Proposal for Increasing Land and Building Tax Revenue Using the System Dynamics Simulation Method

The current hottest issue in Indonesia is the small amount of Land and Building Tax (LBT) revenue at the national and local levels. This research aims to find a valuable model for increasing LBT revenue for the government by formulating ideal clauses and determining what policies should be implemented. This research aims to reveal the practice of tax avoidance and evasion on LBT tax objects, which causes LBT income to stagnate yearly, and find a solution by mapping actual conditions and forecasting the next ten years using a system dynamics model. The research question is why LBT makes a small contribution to total state revenue, even though the object and what are the solutions to increase LBT income in the future. The research methodology uses quantitative methods supported by qualitative analysis using dynamical system modeling. This modeling makes it possible to predict increases in tax revenues by considering several variables that cause LBT revenues to stagnate. The findings of this study show that LBT revenues will proliferate compared to revenues in the initial year of the simulation if intervention is carried out by reducing tax avoidance and tax evasion, increasing tax compliance, and the value of the income growth ratio per tax object. This study found nine actors essential in increasing property taxes in Indonesia: civil officials, tax officials, tax authorities, notaries, large companies, state and regional-owned enterprises, sellers, and buyers of property. In conclusion, the government needs to improve the tax collection system and implement various strategies, including increasing the role of notaries to prevent tax evasion in housing.

CoDBench: a critical evaluation of data-driven models for continuous dynamical systems

We introduce CoDBench, an exhaustive benchmarking suite comprising 12 state-of-the-art data-driven models for solving differential equations, including 4 distinct categories of models, against 10 widely applicable benchmark datasets encompassing challenges from fluid and solid mechanics.

Негативное влияние гистерезисных явлений на процесс разработки месторождений нефти и газа

It is known that irreversibilities of hysteresis nature of global or local scale, lead to the necessity to revise the methods of solving the main problems of hydrodynamic modelling and analysis of dynamic systems, as they can radically affect the traditional conclusions and practical recommendations. It is assumed that in the steady-state mode of motion or filtration, phase displacements make all sorts of oscillations in the vicinity of the unstable position, due primarily to irreversible hysteresis phenomena and jumps arising from the instability of the front of oil displacement by water, the manifestation of capillary effects, hysteresis of phase transitions, irreversibility of deformations under excessive load at large pressure drops, including hydraulic fracturing. With this purpose in the theory of catastrophes the dynamic models of growth are investigated and control parameters are selected with the calculation and the possibility to predict the expected local irreversibilities and instabilities before the onset of bifurcation. Hysteresis behaviour in the filtration process is generated by lithological differences of geofluidodynamic medium and its geological and physical characteristics and properties of saturating fluids. And as a rule, it is provoked by not always adequate, excessive external load on the tested medium. The proposed solutions are part of a new concept of unsteady waterflooding, which provides for early prediction and taking measures in case of instability of the displacement front and, as a consequence, water breakthrough into production wells. It is of great interest to prevent the consequences of these negative effects on the quantitative components of technological and economic indicators, in the case of oil field development we are talking about the final recovery factor of oil, gas and condensate. System optimisation of oil field development is designed for a certain technological and economic effect, including additional oil production, effective mobilisation and saving of injected and withdrawn water and gas.

Generative agent‐based modeling: an introduction and tutorial

AbstractWe discuss the emerging new opportunity for building feedback‐rich computational models of social systems using generative artificial intelligence. Referred to as generative agent‐based models (GABMs), such individual‐level models utilize large language models to represent human decision‐making in social settings. We provide a GABM case in which human behavior can be incorporated into simulation models by coupling a mechanistic model of human interactions with a pre‐trained large language model. This is achieved by introducing a simple GABM of social norm diffusion in an organization. For educational purposes, the model is intentionally kept simple. We examine a wide range of scenarios and the sensitivity of the results to several changes in the prompt. We hope the article and the model serve as a guide for building useful dynamic models of various social systems that include realistic human reasoning and decision‐making. © 2024 System Dynamics Society.

Active computing experiment in modeling the dynamics of mechatronic systems

In the process of debugging the structure of dynamic models of various technical systems, the need arises for direct intervention in the modeling process. The ability to control the modeling process in real time and, if necessary, change the values of phase variables or the structure of the model, is a flexible way to analyze the adequacy of the model using tool-oriented means. By changing the structure and parameters of the model during the modeling process, you can interactively analyze the influence of a particular parameter (block/macrostructure) on the behavior of a dynamic system. This method of carrying out calculations with the possibility of reconstructing the structure and parameters during the modeling process is called an active computational experiment. In the work, an active computational experiment is demonstrated using the example of a mechatronic system - a drive using simulation software ISMA (Novosibirsk, NSTU NETI) and SimInTech (Moscow, MSTU / 3V-Service LLC).

On Koopman-based surrogate models for non-holonomic robots

Data-driven surrogate models of dynamical systems based on the extended dynamic mode decomposition are nowadays well-established and widely applied. Further, for non-holonomic systems exhibiting a multiplicative coupling between states and controls, the usage of bilinear surrogate models has proven beneficial. However, an analysis of the approximation quality and its dependence on different hyperparameters, including physics-motivated dictionary choices, with real-world experimental data is still missing. To close this gap and due to its high practical relevance and widespread usage in applications such as service robotics, we investigate Koopman-based surrogate modeling for a differential-drive mobile robot, also in hardware.

Exploring the Dynamical System Modeling and Evolutionary Mechanisms for the Integration of AI and Civic Education Management in Colleges and Universities

Abstract With the help of the dynamics model of the integration of AI and the management of college civic education, this paper investigates the integration of artificial intelligence and civic education in three directions: application specification, application design, and application practice. Using differential equations to represent the non-linear dynamics equations of the system and by means of differential solutions, the evolution mechanism of AI education application and integration is projected in this paper. The integration of AI and college civic education is explored through empirical analysis and comparative analysis. The results show that the average value of the comprehensive score of the three directions in the sample colleges and universities is 77.5828, which is in the bare integration stage, and the integration degree in the “formulation” path is the best, which is 85.698, and is in the complete integration stage. The students in the experimental class of the sample universities scored better than the control class without AI integration in civic education. There were no students with scores below 60, and there were 32 more students than the control class in the 90–100 segment.