Modeling Of Dynamic Systems Research Articles

Integrating Time-Resolved nrf2 Gene-Expression Data into a Full GUTS Model as a Proxy for Toxicodynamic Damage in Zebrafish Embryo.

The immense production of the chemical industry requires an improved predictive risk assessment that can handle constantly evolving challenges while reducing the dependency of risk assessment on animal testing. Integrating omics data into mechanistic models offers a promising solution by linking cellular processes triggered after chemical exposure with observed effects in the organism. With the emerging availability of time-resolved RNA data, the goal of integrating gene expression data into mechanistic models can be approached. We propose a biologically anchored TKTD model, which describes key processes that link the gene expression level of the stress regulator nrf2 to detoxification and lethality by associating toxicodynamic damage with nrf2 expression. Fitting such a model to complex data sets consisting of multiple endpoints required the combination of methods from molecular biology, mechanistic dynamic systems modeling, and Bayesian inference. In this study, we successfully integrate time-resolved gene expression data into TKTD models and thus provide a method for assessing the influence of molecular markers on survival. This novel method was used to test whether nrf2 can be applied to predict lethality in zebrafish embryos. With the presented approach, we outline a method to successfully approach the goal of a predictive risk assessment based on molecular data.

Developing and Applying Computational Models to Uncover Mechanistic Insights into Complex Biological Processes Across Molecular, Cellular, and Systemic Levels

The complexity of biological processes spans molecular, cellular, and systemic levels, requiring advanced computational models to unravel the intricate mechanisms underlying these phenomena. This research explores the development and application of computational models to gain mechanistic insights into diverse biological systems. By integrating multi-scale data from genomics, proteomics, and cellular imaging, this study leverages machine learning algorithms, dynamical systems modeling, and network analysis to simulate and analyze biological interactions. Key areas of focus include understanding signaling pathways, cellular differentiation, and systemic physiological responses. The research also highlights the role of computational tools in bridging experimental data with theoretical predictions, providing a robust framework for hypothesis generation and testing. Challenges such as data heterogeneity, scalability, and model interpretability are addressed, emphasizing the need for interdisciplinary approaches. This study aims to advance the field of computational biology by offering novel insights into complex biological systems and fostering applications in personalized medicine, drug development, and synthetic biology.

A dynamical systems model for the total fission rate in Drp1-dependent mitochondrial fission.

Mitochondrial hyperfission in response to cellular insult is associated with reduced energy production and programmed cell death. Thus, there is a critical need to understand the molecular mechanisms coordinating and regulating the complex process of mitochondrial fission. We develop a nonlinear dynamical systems model of dynamin related protein one (Drp1)-dependent mitochondrial fission and use it to identify parameters which can regulate the total fission rate (TFR) as a function of time. The TFR defined from a nondimensionalization of the model undergoes a Hopf bifurcation with bifurcation parameter [Formula: see text] where [Formula: see text] is the total concentration of mitochondrial fission factor (Mff) and k+ and k- are the association and dissociation rate constants between oligomers on the outer mitochondrial membrane. The variable μ can be thought of as the maximum build rate over the disassembling rate of oligomers. Though the nondimensionalization of the system results in four dimensionless parameters, we found the TFR and the cumulative total fission (TF) depend strongly on only one, μ. Interestingly, the cumulative TF does not monotonically increase as μ increases. Instead it increases with μ to a certain point and then begins to decrease as μ continues to increase. This non-monotone dependence on μ suggests interventions targeting k+, k-, or [Formula: see text] may have a non-intuitive impact on the fission mechanism. Thus understanding the impact of regulatory parameters, such as μ, may assist future therapeutic target selection.

A novel controllability method on temporal networks based on tree model

Temporal networks have become instrumental in modeling dynamic systems across various disciplines, presenting unique challenges and opportunities in understanding and influencing their behavior. Controllability, a fundamental aspect of network dynamics, plays a pivotal role in manipulating these systems towards desired states. In this paper, we embark on a comprehensive exploration of controllability within the realm of temporal networks. A new method for controlling temporal networks is proposed, in which the intervention of all the dynamics of temporal networks can provide the possibility to speed up the network controllability processes. In the proposed method, the network dynamics are stored in the tree data structure to reduce the computational complexity of the algorithm for finding control nodes while maintaining essential information in controllable processes. Results show that the proposed algorithm with linear complexity of O(N2logNΔt4)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{O}}({{\\varvec{N}}}^{2}{\\varvec{l}}{\\varvec{o}}{\\varvec{g}}{\\varvec{N}}{\\Delta {\\varvec{t}}}^{4})$$\\end{document}. Evaluation against conventional methods on experimental datasets reveals notable improvements: a 41.8% reduction in the minimum number of control nodes, a 36.37% decrease in time of receiving fully control network, and a 38.5% reduction in control algorithm execution time compared to layered model-based control methods.

Differential Equations: The Mathematical Framework for Modelling Dynamic Systems

Differential equations are essential tools in the mathematical Modelling of dynamic systems, providing a framework for describing phenomena that evolve over time or space. These equations are used across diverse fields, including physics, engineering, biology, economics, and social sciences, to capture the behavior of systems governed by rates of change. This paper explores the role of differential equations in Modelling dynamic systems, presents different types of differential equations, discusses solution methods, and examines the applicability and challenges associated with their use. Through this discussion, we aim to highlight the fundamental importance of differential equations in understanding and predicting the behavior of real-world systems.

Multilevel modeling and control of dynamic systems

The underlying changes of complex dynamic systems are affected by numerous highly interdependent components with nonlinear interactions and cannot be suitably predicted by merely analyzing their individual parts. Recent technological developments (reducing the size of actuators and sensors, increasing speed and productivity) make it possible to monitor and handle systems on time, even during transient processes. In many practical applications, to effectively study rapidly evolving systems, their structure has to be examined at three levels: Micro-Scale (Short-Term), Meso-Scale (Intermediate-Term), and Macro-Scale (Long-Term). This multiscale framework provides a powerful tool for understanding and managing the intricate dynamics of complex systems. Macro-scale and micro-scale approaches are conventionally utilized in general system modeling and control theory, especially within the fields of networked control and multi-agent systems. By leveraging the meso-scale perspective, it is possible to balance detailed component analysis with overarching system behaviors, thereby enhancing the efficiency and effectiveness of operational strategies in complex systems. This paper presents and discusses a formal meso-level depiction of dynamics and control, assuming a finite number of attractors form and remain stable over time progress. Integral characteristics and dynamics of clusters are defined, simplifying control synthesis while maintaining problem formulation. A significant challenge is the model error due to changing cluster structures linked to randomized estimation and optimization algorithms valid under unknown disturbances. To demonstrate the practicality of this framework, the approach is applied to control tasks of a group of robots, leading to scalable and effective control strategies.

Stochastic Processes with Expected Stopping Time

Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.

Abstract 4145826: Atrial Fibrillation Screening During Sinus Rhythm Periods by Interrelated Systems Dynamics Analysis

Background: Previous studies have shown that AF screening in at-risk populations can reduce stroke incidence. However, non-targeted screening approaches often result in high false positive rates, placing an unnecessary burden on the healthcare system. In contrast, artificial intelligence-guided screening has been demonstrated to increase diagnostic yield in large prospective clinical trials. This approach, however, requires recording an ECG and a large-scale dataset for model training. Heart rate variability (HRV) analysis has proven effective in deciphering key heart dynamics. By analyzing HRV as interrelated dynamic systems, it may be possible to facilitate targeted AF screening using wearable devices that measure heart rate. The Koopman operator, used for data-driven modeling of interrelated dynamic systems, has been shown to accurately predict complex phenomena in chaotic systems such as climate forecasting and drug adverse reaction prediction. This is achieved by utilizing common characteristics of the systems for most model parameters, with only a small fraction of the parameters being specific to a certain system. Methods: Long (>10 hour) records from 361 individuals (AFDB, LTAFDB) and healthy individuals' datasets from PhysioNet and THEW were analyzed for inter-beat intervals. The unified dataset was then split into 94 training, 17 validation, and 250 test set patients. Recordings from the training set were used to train both the common and specific parts of the interrelated dynamic systems model for each patient, along with a shared small neural network classifying patients into low and high risk for AF based on the unique (not shared between patients) singular values of the dynamic system model. Patient-specific dynamic system models were then fitted for the validation and test sets to calculate the patient dynamic singular values, which were used to classify patients into low and high risk for AF groups. Results: Atrial fibrillation occurred in 48 of 202 (23%) patients classified as low risk and 35 of 48 (72.9%) patients classified as high risk (odds ratio 8.63, 95% CI 4.23-17.64), yielding 72.9% sensitivity with 76.2% specificity. Conclusion: In this retrospective analysis, classification of the dynamic system model singular values identified patients at high risk for atrial fibrillation from sinus rhythm period.

Approximation Properties of Chlodovsky-Type Two-Dimensional Bernstein Operators Based on (p, q)-Integers

In the present study, we introduce the two-dimensional Chlodovsky-type Bernstein operators based on the (p,q)-integer. By leveraging the inherent symmetry properties of (p,q)-integers, we examine the approximation properties of our new operator with the help of a Korovkin-type theorem. Further, we present the local approximation properties and establish the rates of convergence utilizing the modulus of continuity and the Lipschitz-type maximal function. Additionally, a Voronovskaja-type theorem is provided for these operators. We also investigate the weighted approximation properties and estimate the rate of convergence in the same space. Finally, illustrative graphics generated with Maple demonstrate the convergence rate of these operators to certain functions. The optimization of approximation speeds by these symmetric operators during system control provides significant improvements in stability and performance. Consequently, the control and modeling of dynamic systems become more efficient and effective through these symmetry-oriented innovative methods. These advancements in the fields of modeling fractional differential equations and control theory offer substantial benefits to both modeling and optimization processes, expanding the range of applications within these areas.

Loss Function for Deep Learning to Model Dynamical Systems

Loss Function for Deep Learning to Model Dynamical Systems

Higher-order interactions lead to ‘reluctant’ synchrony breaking

To model dynamical systems on networks with higher-order (non-pairwise) interactions, we recently introduced a new class of ordinary differential equations (ODEs) on hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady-state branch.

Modeling and control of dynamical biomechanical arm systems with elastic joints sensitive to the effect of an external load

In this study, a biomechanical model mimicking the human hand-arm system under heavy disk excitation is developed to define the stability threshold between the preload vibration and the stress of the human hand-arm system. The fully electromechanical system, consisting of a DC motor, a transmission system, and three discrete masses representing the upper arm, forearm, and hand lifting a heavy disk, is connected by shock absorbers and various springs. The challenge of mimicking the angular activity of the elbow joint in torsion and flexion was also included to assess its contribution to system stability and to study the absorption of mechanical energy in the human hand-arm system. Finally, the movements of the model were described by a differential matrix equation, and its analysis facilitates the understanding of the threshold of the chaotic behaviors observed in an oscillating arms system. Specifically, it explores how the motion of a DC motor can be regulated using a single controller parameter within the context of a multi-degree-of-freedom human hand-arm system. The study uses numerical integrations to analyze system behaviors, with an emphasis on the use of frequency spectra, Poincaré maps, and bifurcation diagrams for visualization and interpretation. The results indicate that the system exhibits chaotic behavior when subjected to certain conditions, particularly when the mass load exceeds 35 kg. Imposing motion on the mass block further intensifies the chaos, leading to manifestations such as strong oscillations and frequency-synchronization effects. These characteristics, exhibited by the idealized model, which imitates the human body through a mechanical model and computation of the motions of the body, play a vital role in various fields of ergonomics and sports biomechanics. Understanding the dynamic behaviors of such systems, especially in response to varying conditions, has significant implications for engineering applications.

Integrating machine learning with causal inference for enhanced system dynamics modeling: A framework for predicting complex interactions

Approaches and methods like System Dynamics Modelling (SDM) have been significant for assessing the behavior of many systems. However, classical methodologies applied in traditional approaches to SDM fail to identify nonlinear feedback and power dependencies, revealing hidden temporal casual relationships. In this paper, I present a novel approach that combines ML and causal inference methods to improve the forecast capability and semantics of system dynamics models. Incorporating ML algorithms for predictions and Causal Inference techniques for explanation, this combined strategy presents a new era for understanding the system interaction and quantifying the hidden causes within various systems. We illustrate the advantages of the suggested framework over traditional SDM and purely ML approaches by employing it to analyze a genuine circumstance for both prognosis and discovering causal relationships. Our findings indicate that such integration is effective in enhancing the comprehension of system interactions and deriving a reliable method for estimating subsequent state conditions in complex contexts. The results are relevant for various disciplines, starting with economics and ending with environmental protection sciences, where interactions and changes vary. As a result, it will give a foundation for further studies of integrating future computerized methods in the dynamical system modeling of the next generation.

Generalization of neural network models for complex network dynamics

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph. Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems, especially in complex systems that lack explicit first principles. A recently employed machine learning tool for studying dynamics is neural networks, which can be used for solution finding or discovery of differential equations. However, deploying deep learning models in unfamiliar settings-such as predicting dynamics in unobserved state space regions or on novel graphs-can lead to spurious results. Focusing on complex systems whose dynamics are described with a system of first-order differential equations coupled through a graph, we study generalization of neural network predictions in settings where statistical properties of test data and training data are different. We find that neural networks can accurately predict dynamics beyond the immediate training setting within the domain of the training data. To identify when a model is unable to generalize to novel settings, we propose a statistical significance test.

Use of Deep-Learning-Accelerated Gradient Approximation for Reservoir Geological Parameter Estimation

The estimation of space-varying geological parameters is often not computationally affordable for high-dimensional subsurface reservoir modeling systems. The adjoint method is generally regarded as an efficient approach for obtaining analytical gradient and, thus, proceeding with the gradient-based iteration algorithm; however, the infeasible memory requirement and computational demands strictly prohibit its generic implementation, especially for high-dimensional problems. The autoregressive neural network (aNN) model, as a nonlinear surrogate approximation, has gradually received increasing popularity due to significant reduction of computational cost, but one prominent limitation is that the generic application of aNN to large-scale reservoir models inevitably poses challenges in the training procedure, which remains unresolved. To address this issue, model-order reduction could be a promising strategy, which enables us to train the neural network in a very efficient manner. A very popular projection-based linear reduction method, i.e., propel orthogonal decomposition (POD), is adopted to achieve dimensionality reduction. This paper presents an architecture of a projection-based autoregressive neural network that efficiently derives an easy-to-use adjoint model by the use of an auto-differentiation module inside the popular deep learning frameworks. This hybrid neural network proxy, referred to as POD-aNN, is capable of speeding up derivation of reduced-order adjoint models. The performance of POD-aNN is validated through a synthetic 2D subsurface transport model. The use of POD-aNN significantly reduces the computation cost while the accuracy remains. In addition, our proposed POD-aNN can easily obtain multiple posterior realizations for uncertainty evaluation. The developed POD-aNN emulator is a data-driven approach for reduced-order modeling of nonlinear dynamic systems and, thus, should be a very efficient modeling tool to address many engineering applications related to intensive simulation-based optimization.

Dynamic Modeling of Distribution Power Systems with Renewable Generation for Stability Analysis

This paper presents a comprehensive study on the dynamic modeling of distribution power systems with a focus on the integration of renewable energy sources (RESs) for stability analysis. Our research delves into the static and dynamic behavior of distribution systems, emphasizing the need for enhanced load modeling to mitigate planning and operational uncertainties. Using MATLAB/Simulink®, we simulate four distinct study cases characterized by varying load types and levels of distributed generation (DG), particularly solar PV, under both balanced and unbalanced conditions. Our findings highlight the critical role of DG in influencing voltage stability, revealing that deviations in voltage and current during grid imbalances remain within acceptable limits. The study underscores the importance of DG-based inverters in maintaining grid stability through reactive power support and sets the stage for future research on microgrid simulations and battery storage integration to further enhance system stability and performance.

Expanding and improving analyses of nucleotide recoding RNA-seq experiments with the EZbakR suite.

Nucleotide recoding RNA sequencing methods (NR-seq; TimeLapse-seq, SLAM-seq, TUC-seq, etc.) are powerful approaches for assaying transcript population dynamics. In addition, these methods have been extended to probe a host of regulated steps in the RNA life cycle. Current bioinformatic tools significantly constrain analyses of NR-seq data. To address this limitation, we developed EZbakR, an R package to facilitate a more comprehensive set of NR-seq analyses, and fastq2EZbakR, a Snakemake pipeline for flexible preprocessing of NR-seq datasets, collectively referred to as the EZbakR suite. Together, these tools generalize many aspects of the NR-seq analysis workflow. The fastq2EZbakR pipeline can assign reads to a diverse set of genomic features (e.g., genes, exons, splice junctions, etc.), and EZbakR can perform analyses on any combination of these features. EZbakR extends standard NR-seq mutational modeling to support multi-label analyses (e.g., s4U and s6G dual labeling), and implements an improved hierarchical model to better account for transcript-to-transcript variance in metabolic label incorporation. EZbakR also generalizes dynamical systems modeling of NR-seq data to support analyses of premature mRNA processing and flow between subcellular compartments. Finally, EZbakR implements flexible and well-powered comparative analyses of all estimated parameters via design matrix-specified generalized linear modeling. The EZbakR suite will thus allow researchers to make full, effective use of NR-seq data.

Conformal symplectic and constraint-preserving model order reduction of constrained conformal Hamiltonian systems

Dissipative and constrained dynamical systems model various physical phenomena comprising damping and constraining forces. These forces give rise to specific geometric properties of the dynamical system's governing equations. In this paper, we reduce and solve high-dimensional parameterized constrained and damped nonlinear differential equations with structure-preserving algorithms. These algorithms preserve the constrained equation's geometric properties, such as conformal symplecticness and phase-space, through model order reduction and numerical integration. We develop a reduced model based on an orthosymplectic reduced basis and establish the well-posedness and conformal symplecticness of the reduced model. Moreover, we derive a priori error bounds for state space and constraints errors. Subsequently, we utilize two RATTLE-based integrators to simulate the full and reduced models while preserving their geometric properties. Numerical experiments on constrained damped oscillators and a constrained lattice grid justify theoretical results and demonstrate the advantages of the structure-preserving computational methods for constrained dynamical systems.

Data-driven predictor of control-affine nonlinear dynamics: Finite discrete-time bilinear approximation of koopman operator

This paper introduces a novel and efficient data-driven approach for approximating a finite discrete-time bilinear model of control affine nonlinear dynamical systems with a tunable parameter that balances model dimension and prediction accuracy. An approximation of the Koopman operator based on the evolutions of the nonlinear system measurements used to lift a control-affine nonlinear system to a higher dimensional model. However, higher dimensional spaces can result in a long learning time and the curse of dimensionality in control analysis. The proposed approach addresses these challenges by introducing a convex optimization which identifies informative observable functions. This technique allows for the adjustment of a parameter to strike a balance between model dimension and accuracy in prediction. The main contribution of this study is to introduce a reduced dimensional bilinear model for a nonlinear complex system. This achievement is made possible by implementing convex sparse optimization, enabling the exploration of informative estimated Koopman eigenfunctions while minimizing the number of system measurements required. The optimization problem is solved using the alternating direction method of multipliers. The effectiveness of the proposed method is evaluated on three different nonlinear systems: a numerical nonlinear system, a Van der Pol oscillator, and a Duffing oscillator. In the last simulation, an estimation of the Koopman linear model is considered as a special case, and the policy iteration algorithm is employed to evaluate optimal control designed for different reduced-dimensional models.

Neural dynamical operator: Continuous spatial-temporal model with gradient-based and derivative-free optimization methods

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different types of data, e.g., with different spatial and temporal resolutions, and the combined use of short-term trajectories and long-term statistics. In this work, we build on the recent progress of neural operator and present a data-driven modeling framework called neural dynamical operator that is continuous in both space and time. A key feature of the neural dynamical operator is the resolution-invariance with respect to both spatial and temporal discretizations, without demanding abundant training data in different temporal resolutions. To improve the long-term performance of the calibrated model, we further propose a hybrid optimization scheme that leverages both gradient-based and derivative-free optimization methods and efficiently trains on both short-term time series and long-term statistics. We investigate the performance of the neural dynamical operator with three numerical examples, including the viscous Burgers' equation, the Navier–Stokes equations, and the Kuramoto–Sivashinsky equation. The results confirm the resolution-invariance of the proposed modeling framework and also demonstrate stable long-term simulations with only short-term time series data. In addition, we show that the proposed model can better predict long-term statistics via the hybrid optimization scheme with a combined use of short-term and long-term data.