Modeling Of Dynamic Systems Research Articles

Multiscale model reduction for incompressible flows

We introduce a projection-based model reduction method that systematically accounts for nonlinear interactions between the resolved and unresolved scales of the flow in a low-dimensional dynamical systems model. The proposed method uses a separation of time scales between the resolved and subscale variables to derive a reduced-order model with cubic closure terms for the truncated modes, generalizing the classic Stuart–Landau equation. The leading-order cubic terms are determined by averaging out fast variables through a perturbation series approximation of the action of a stochastic Koopman operator. We show analytically that this multiscale closure model can capture both the effects of mean-flow deformation and the energy cascade before demonstrating improved stability and accuracy in models of chaotic lid-driven cavity flow and vortex pairing in a mixing layer. This approach to closure modelling establishes a general theory for the origin and role of cubic nonlinearities in low-dimensional models of incompressible flows.

Higher-order adaptive dynamical system modeling of the role of epigenetics in anxiety disorders

In this paper, a fifth-order adaptive self-modelling network model is introduced to describe epigenetic involvement in the development of anxiety disorders and its regulation by a possible epigenetics-based therapeutic method. Multiple orders of adaptivity are used in the model to depict the development process, where a higher pathway of any order of adaptivity adapts characteristics of pathways in lower orders and acts as a form of control. These orders of adaptivity and their interlevel interaction were modelled as a higher-order adaptive dynamical system according to the self-modelling network modelling principle. The model was inspired by the structure of the relevant human biological and neurological processes. In addition to modelling the development of an anxiety disorder, also the possibility of an epigenetics-based therapy is suggested and computationally analyzed in this paper.

The Application of the Random Time Transformation Method to Estimate Richards Model for Tree Growth Prediction

To model dynamic systems in various situations results in an ordinary differential equation of the form dydt=g(y,t,θ), where g denotes a function and θ stands for a parameter or vector of unknown parameters that require estimation from observations. In order to consider environmental fluctuations and numerous uncontrollable factors, such as those found in forestry, a stochastic noise process ϵt may be added to the aforementioned equation. Thus, a stochastic differential equation is obtained: dYtdt=f(Yt,t,θ)+ϵt. This paper introduces a method and procedure for parameter estimation in a stochastic differential equation utilising the Richards model, facilitating growth prediction in a forest’s tree population. The fundamental concept of the approach involves assuming that a deterministic differential equation controls the development of a forest stand, and that randomness comes into play at the moment of observation. The technique is utilised in conjunction with the logistic model to examine the progression of an agricultural epidemic induced by a virus. As an alternative estimation method, we present the Random Time Transformation (RTT) method. Thus, this paper’s primary contribution is the application of the RTT method to estimate the Richards model, which has not been conducted previously. The literature often uses the logistic or Gompertz models due to difficulties in estimating the parameter form of the Richards model. Lastly, we assess the effectiveness of the RTT Method applied to the Chapman–Richards model using both simulated and real-life data.

How far neuroscience is from understanding brains.

The cellular biology of brains is relatively well-understood, but neuroscientists have not yet generated a theory explaining how brains work. Explanations of how neurons collectively operate to produce what brains can do are tentative and incomplete. Without prior assumptions about the brain mechanisms, I attempt here to identify major obstacles to progress in neuroscientific understanding of brains and central nervous systems. Most of the obstacles to our understanding are conceptual. Neuroscience lacks concepts and models rooted in experimental results explaining how neurons interact at all scales. The cerebral cortex is thought to control awake activities, which contrasts with recent experimental results. There is ambiguity distinguishing task-related brain activities from spontaneous activities and organized intrinsic activities. Brains are regarded as driven by external and internal stimuli in contrast to their considerable autonomy. Experimental results are explained by sensory inputs, behavior, and psychological concepts. Time and space are regarded as mutually independent variables for spiking, post-synaptic events, and other measured variables, in contrast to experimental results. Dynamical systems theory and models describing evolution of variables with time as the independent variable are insufficient to account for central nervous system activities. Spatial dynamics may be a practical solution. The general hypothesis that measurements of changes in fundamental brain variables, action potentials, transmitter releases, post-synaptic transmembrane currents, etc., propagating in central nervous systems reveal how they work, carries no additional assumptions. Combinations of current techniques could reveal many aspects of spatial dynamics of spiking, post-synaptic processing, and plasticity in insects and rodents to start with. But problems defining baseline and reference conditions hinder interpretations of the results. Furthermore, the facts that pooling and averaging of data destroy their underlying dynamics imply that single-trial designs and statistics are necessary.

Parameter estimation and modeling of nonlinear dynamical systems based on Runge–Kutta physics-informed neural network

Parameter estimation and modeling of nonlinear dynamical systems based on Runge–Kutta physics-informed neural network

Order reduction of matrix exponentials by proper orthogonal decomposition

Many applications of the matrix exponential exp(At) of a real matrix A and a real parameter t require repeated evaluation of it for different values of t. Such evaluations are time consuming and encounter the curse of dimensionality, especially in the large scale cases. Therefore, reduced order versions of the matrix exponential will be of great use and ease in these situations. The proper orthogonal decomposition (POD) method has wide applications in the reduced order modeling of dynamical systems. The matrix exponential can be considered as the solution of an initial value problem (IVP) as a dynamical system and the reduced order approximations to it be obtained by utilizing the POD method. Following this approach, the matrix exponential exp(At) is viewed as a scalar to matrix function and the optimal subspace(s) of its range space for the order reduction is computed by the POD method. Next, the IVP defining the matrix exponential is projected on the obtained optimal subspace(s). Then the solution of projected IVP is adopted as the desired reduced order approximation of the matrix exponential. An upper estimate for the error of the reduced order approximation is obtained thorough an error analysis. Numerical experiments illustrating efficiency of the method and quality of the obtained approximations is provided.

Complex Systems Modeling of Community Inclusion Currencies

This interdisciplinary paper blends knowledge from computer science and economics in proposing a complex dynamic system subpopulation model for a blockchain form of local complementary currency, generic to the Grassroots Economics Foundation’s Community Inclusion Currency (CIC) implemented in Kenya. Our contribution to the emerging economics literature is five-fold: (i) we take a novel meso-economic approach to elicit utility from actual transactions data and reveal an ‘optimal’ disaggregation number of typical community subgroups; (ii) we relate the local CIC functioning to a nation-wide currency board monetary regime to argue that such a credible CIC implementation ensures trust in the CIC and makes it a valuable market-based channel to alleviate poverty, in addition to humanitarian or government aid channels. However, (iii) we also find evidence in our data that substitutes for real-world money such as CICs are perceived as inferior, and hence CIC systems can only be transitional. Then, (iv) we reveal that, for a poor population, saving dominates as a use of a cluster’s CIC balance, accounting for 47%, followed by purchase of food and water, 25%. Despite these dominant patterns, (v) we uncover a considerable heterogeneity in CIC spending behavior. Our contribution to the related computer-science and Tokenomics literature is two-fold: (i) we provide an open-source scaffold for modeling CIC viability and net flows; (ii) to simulate a subpopulation mixing process, we employ a network-based dynamical system modeling approach that is better grounded in economic principles and monetary theory.

Progress in modeling dynamic systems for sustainable development

This Perspective evaluates recent progress in modeling nature–society systems to inform sustainable development. We argue that recent work has begun to address longstanding and often-cited challenges in bringing modeling to bear on problems of sustainable development. For each of four stages of modeling practice—defining purpose, selecting components, analyzing interactions, and assessing interventions—we highlight examples of dynamical modeling methods and advances in their application that have improved understanding and begun to inform action. Because many of these methods and associated advances have focused on particular sectors and places, their potential to inform key open questions in the field of sustainability science is often underappreciated. We discuss how application of such methods helps researchers interested in harnessing insights into specific sectors and locations to address human well-being, focus on sustainability-relevant timescales, and attend to power differentials among actors. In parallel, application of these modeling methods is helping to advance theory of nature–society systems by enhancing the uptake and utility of frameworks, clarifying key concepts through more rigorous definitions, and informing development of archetypes that can assist hypothesis development and testing. We conclude by suggesting ways to further leverage emerging modeling methods in the context of sustainability science.

Likelihood-ratio test statistic for the finite-sample case in nonlinear ordinary differential equation models.

Likelihood ratios are frequently utilized as basis for statistical tests, for model selection criteria and for assessing parameter and prediction uncertainties, e.g. using the profile likelihood. However, translating these likelihood ratios into p-values or confidence intervals requires the exact form of the test statistic's distribution. The lack of knowledge about this distribution for nonlinear ordinary differential equation (ODE) models requires an approximation which assumes the so-called asymptotic setting, i.e. a sufficiently large amount of data. Since the amount of data from quantitative molecular biology is typically limited in applications, this finite-sample case regularly occurs for mechanistic models of dynamical systems, e.g. biochemical reaction networks or infectious disease models. Thus, it is unclear whether the standard approach of using statistical thresholds derived for the asymptotic large-sample setting in realistic applications results in valid conclusions. In this study, empirical likelihood ratios for parameters from 19 published nonlinear ODE benchmark models are investigated using a resampling approach for the original data designs. Their distributions are compared to the asymptotic approximation and statistical thresholds are checked for conservativeness. It turns out, that corrections of the likelihood ratios in such finite-sample applications are required in order to avoid anti-conservative results.

The Dynamics of Pasture-Herbivores-Carnivores with Sigmoidal Density Dependent Harvesting.

We investigate biomass-herbivore-carnivore (top predator) interactions in terms of a tritrophic dynamical systems model. The harvesting rates of the herbivores and the top predators are described by means of a sigmoidal function of the herbivores density and the top predator density, respectively. The main focus in this study is on the dynamics as a function of the natural mortality and the maximal harvesting rate of the top predators. We identify parameter regimes for which we have non-existence of equilibrium points as well as necessary conditions for the existence of such states of the modelling framework. The system does not possess any finite equilibrium states in the regime of high herbivore mortality. In the regime of a high consumption rate of the herbivores and low mortality rates of the top predator, an asymptotically stable finite equilibrium state exists. For this positive equilibrium to exist the mortality of the top predator should not exceed a certain threshold level. We also detect regimes producing coexistence of equilibrium states and their respective stability properties. In the regime of negligible harvesting of the top predator level, we observe a finite window of the natural top predator mortality rates for which oscillations in the top predator-, the herbivore- and the biomass level take place. The lower and upper bound of this window correspond to two Hopf bifurcation points. We also identify a bifurcation diagram using the top predator harvesting rate as a control variable. Using this diagram we detect several saddle node- and Hopf bifurcation points as well as regimes for which we have coexistence of interior equilibrium states, bistability and relaxation type of oscillations.

A tangential interpolation framework for the AAA algorithm

AbstractInterpolation‐based data‐driven methods, such as the Loewner framework or the Adaptive Antoulas‐Anderson (AAA) algorithm, are established and effective approaches to find a realization of a dynamical system from frequency response data (measurements of the system's transfer function). If a system‐theoretic representation of the original model is not available or unfeasible to evaluate efficiently, such reduced realizations enable effective analysis and simulation. This is especially relevant for models of interconnected dynamical systems, which typically have a high number of inputs and outputs to model their coupling conditions correctly.Tangential interpolation is an established strategy to construct accurate reduced‐order models while ensuring a reasonably small size even if many inputs and/or outputs have to be considered. In this contribution, we evaluate the applicability and effectiveness of data‐driven interpolation methods to compute reduced‐order models of dynamical systems with many inputs and outputs. Additionally, we extend AAA to a tangential interpolation setting and thus enable the use of AAA‐like methods in the context of transfer function interpolation for systems with many inputs and outputs.

Catalog of Dynamical System Models with Semantic Metadata

AbstractThis contribution presents the concept and implementation of a catalog (i.e., a structured collection) of dynamical system models, relevant to control theory. The key features of the catalog are: (a) a combination of human‐readable model documentation with executable code; (b) semantic metadata for each model plus a web platform to provide SPARQL search interface; and (c) model data and supporting software based on open source repositories and open for extension and improvement.

Using Deep Learning Models to Predict Prosthetic Ankle Torque.

Inverse dynamics from motion capture is the most common technique for acquiring biomechanical kinetic data. However, this method is time-intensive, limited to a gait laboratory setting, and requires a large array of reflective markers to be attached to the body. A practical alternative must be developed to provide biomechanical information to high-bandwidth prosthesis control systems to enable predictive controllers. In this study, we applied deep learning to build dynamical system models capable of accurately estimating and predicting prosthetic ankle torque from inverse dynamics using only six input signals. We performed a hyperparameter optimization protocol that automatically selected the model architectures and learning parameters that resulted in the most accurate predictions. We show that the trained deep neural networks predict ankle torques one sample into the future with an average RMSE of 0.04 ± 0.02 Nm/kg, corresponding to 2.9 ± 1.6% of the ankle torque's dynamic range. Comparatively, a manually derived analytical regression model predicted ankle torques with a RMSE of 0.35 ± 0.53 Nm/kg, corresponding to 26.6 ± 40.9% of the ankle torque's dynamic range. In addition, the deep neural networks predicted ankle torque values half a gait cycle into the future with an average decrease in performance of 1.7% of the ankle torque's dynamic range when compared to the one-sample-ahead prediction. This application of deep learning provides an avenue towards the development of predictive control systems for powered limbs aimed at optimizing prosthetic ankle torque.

Leader Identity on the Fly: Intra-personal Leader Identity Dynamics in Response to Strong Events

Recent theorizing challenges the notion that leadership, and especially leader identities, is static. Yet, we know little about the dynamics that characterize how leader identities change within individuals across short periods of time. The current work integrates theorizing on temporal dynamics in leadership research with event systems theory to describe and predict day-to-day shifts (i.e., unidirectional, sudden changes) and dynamic ebb and flow patterns (i.e., multidirectional, potentially nonlinear changes over multiple days) of individuals’ leader identities. Specifically, we argue that the experience of strong (i.e., novel, disruptive, extraordinary) daily events facilitates positive leader identity shifts, and that over time, the resulting identity ebb and flows are more pronounced in unfamiliar compared to familiar contexts. We collected experience sampling data from 69 young adults at a university in the UK across seven-day periods at three different time points during the academic year (1159 data points). Using dynamical systems modeling, we analyze the velocity (i.e., rate of change) and the acceleration (i.e., change in velocity) parameters of individuals’ leader identity dynamics. We find that (a) on a daily level, strong events prompt positive shifts in leader identity, and that (b) over time, chains of stronger and weaker events provoke similar patterns of leader identity ebb and flows. However, these relationships are not stronger in unfamiliar compared to familiar contexts. Our research informs the theoretical understanding of events and short-term leader identity dynamics. We discuss implications for theory and research, in particular how events can trigger leader identity formation.

Dynamic modeling and analysis of high-speed flexible planetary gear transmission systems

Modern planetary gear transmissions are often made with flexible components and operated at high or varying speed. Despite advances in understanding their dynamic performance, they remain vulnerable to problems leading—in some cases—to subsequent system failure. In this study, using angular and translational displacements as generalized coordinates, we establish lumped-parameter dynamic sub-models of the sun and planet gears that accurately consider gear-tooth dynamic behavior; we also develop reduced-order finite-element sub-models that fully consider the flexibility of the housing and carrier. Investigating the coupling between these sub-models in depth enables us to construct a complete hybrid dynamic model that can be used for coupling-dynamics analysis of flexible planetary gears under high- and variable-speed conditions. The accuracy of our planetary-gear-dynamics model is verified by comparing simulation data in the time and frequency domains to the results of experiments conducted on a planetary gear transmission system test bench specially built for this purpose. Finally, the dynamic characteristics of high-speed flexible planetary gears are studied at low speed, high speed, and high acceleration.

Modeling of truncated normal distribution for estimating hydraulic parameters in water distribution systems: taking nodal water demand as an example.

The normal probability density function (PDF) is widely used in parameter estimation in the modeling of dynamic systems, assuming that the random variables are distributed at infinite intervals. However, in practice, these random variables are usually distributed in a finite region confined by the physical process and engineering practice. In this study, we address this issue through the application of truncated normal PDF. This method avoids a non-differentiable problem inherited in the truncated normal PDF at the truncation points, a limitation that can limit the use of analytical methods (e.g., Gaussian approximation). A data assimilation method with the derived formula is proposed to describe the probability of parameter and measurement noise in the truncated space. In application to a water distribution system (WDS), the proposed method leads to estimating nodal water demand and hydraulic pressure key to hydraulic and water quality model simulations. Application results to a hypothetical and a large field WDS clearly show the superiority of the proposed method in parameter estimation for WDS simulations. This improvement is essential for developing real-time hydraulic and water quality simulation and process control in field applications when the parameter and measurement noise are distributed in the finite region.

Development Strategy For The Sabang Area With The Logistics Port Concept In The Malaka Strait

Sabang area is part of the Republic of Indonesia (NKRI) territory, which passed by shipping lines in the Strait of Malacca. Geographic layout of the strategic area, so it is considered a potential to be developed into a maritime area. In the year of 2000, Sabang set to be a free trade area and free port. But until now, this region did not show significant development. In this paper, Sabang area will be assessed the potential and direction of development using the method of TOWS and two step AHP. The direction of development constructed by logistics support concept and simulated using the method of dynamical systems to get the model of the system. The results obtained that Sabang area is potential for development. Simulation of dynamical systems models provides scenarios in anticipation of situations that may happen in the future by increase tank investment and fuel supply so can fulfill fuel needs. In addition, there are a several trickle effects of this system such as the improvement of region economics, the development of docking facilities and service and awareness of regional security.

Thermal design and heat transfer optimisation of a liquid organic hydrogen carrier batch reactor for hydrogen storage

Liquid organic hydrogen carriers (LOHCs) are considered a promising hydrogen storage technology. Heat must be exchanged with an external medium, such as a heat transfer fluid, for the required chemical reactions to occur. Batch reactors are simple but useful solutions for small-scale storage applications, which can be modelled with a lumped-parameter approach, adequately reproducing their dynamic performance. For such reactors, power is consumed to circulate the external heat transfer fluid and stir the organic liquid inside the reactor, and heat transfer performance and power consumption are two key parameters in reactor optimisation. Therefore, with reference to the hydrogen release phase, this paper describes a procedure to optimise the reactor thermal design, based on a lumped-parameter model, in terms of heat transfer performance and minimum power consumption. Two batch reactors are analysed: a conventional jacketed reactor with agitation nozzles and a half-pipe coil reactor. Heat transfer performance is evaluated by introducing a newly defined dimensionless parameter, the Heat Transfer Ratio (HTR), whose value directly correlates to the heat rate required by the carrier's dehydrogenation reaction. The resulting model is a valid tool for adequately reproducing the hydrogen storage behaviour within dynamic models of complex and detailed energy systems.

The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control

The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors, from simple harmonic motion in the single pendulum to chaotic dynamics in multi-arm pendulums. Under forcing, even the single pendulum may exhibit chaos, providing a simple example of a damped-driven system. All multi-armed pendulums are characterized by the existence of index-one saddle points, which mediate the transport of trajectories in the system, providing a simple mechanical analog of various complex transport phenomena, from biolocomotion to transport within the solar system. Further, pendulum systems have long been used to design and test both linear and nonlinear control strategies, with the addition of more arms making the problem more challenging. In this work, we provide extensive designs for the construction and operation of a high-performance, multi-link pendulum on a cart system. Although many experimental setups have been built to study the behavior of pendulum systems, such an extensive documentation on the design, construction, and operation is missing from the literature. The resulting experimental system is highly flexible, enabling a wide range of benchmark problems in dynamical systems modeling, system identification and learning, and control. To promote reproducible research, we have made our entire system open-source, including 3D CAD drawings, basic tutorial code, and data. Moreover, we discuss the possibility of extending our system capability to be operated remotely, enabling researchers all around the world to use it, thus increasing access.

Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles

Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do not provide uncertainty estimates, which are crucial for establishing the trustworthiness of these techniques in downstream decision making tasks and scenarios. In recent years, ensemble-based methods have achieved significant success for the uncertainty quantification in DNNs on a number of benchmark problems. However, their performance on real-world applications remains under-explored. In this work, we present an automated approach to DNN discovery and demonstrate how this may also be utilized for ensemble-based uncertainty quantification. Specifically, we propose the use of a scalable neural and hyperparameter architecture search for discovering an ensemble of DNN models for complex dynamical systems. We highlight how the proposed method not only discovers high-performing neural network ensembles for our tasks, but also quantifies uncertainty seamlessly. This is achieved by using genetic algorithms and Bayesian optimization for sampling the search space of neural network architectures and hyperparameters. Subsequently, a model selection approach is used to identify candidate models for an ensemble set construction. Afterwards, a variance decomposition approach is used to estimate the uncertainty of the predictions from the ensemble. We demonstrate the feasibility of this framework for two tasks — forecasting from historical data and flow reconstruction from sparse sensors for the sea-surface temperature. We demonstrate superior performance from the ensemble in contrast with individual high-performing models and other benchmarks.