Modeling Of Dynamic Systems Research Articles

Unlocking Interpretable Prediction of Battery Random Discharge Capacity With Domain Adaptative Physics Constraint

AbstractTracking the battery discharge capacity is significant, yet challenging due to complicated degradation patterns as well as varying or even random usage scenarios. This work proposes a physics‐constrained domain adaptation framework to predict the capacities during random discharge with non‐destructive mechanism diagnosis using early or random discharging information. By imposing the impedance as physical constraints in a domain adaptative layer, the interpretability and generalization of the model can be improved as the physics‐constrained layer provides physical insights into the battery mechanism characteristics, enabling onboard and non‐destructive diagnosis without complex tests. The learned impedances in the physics‐constrained layer are well‐fitted to the real ones, suggesting accurate physical insights and, therefore, good interpretability of the trained model. Furthermore, apart from capacity prediction, the aging mechanisms of the cell can be interpreted through the learned physics from this deep learning framework without impedance measurement. Such interpretation has also been validated experimentally through post‐mortem analysis. This work provides an example of grey‐box modeling of complex dynamic systems where deep learning models can provide certain physical details to increase the model's interpretability.

Dynamical models reveal anatomically reliable attractor landscapes embedded in resting-state brain networks

Abstract Analyses of functional connectivity (FC) in resting-state brain networks (RSNs) have generated many insights into cognition. However, the mechanistic underpinnings of FC and RSNs are still not well-understood. It remains debated whether resting-state activity is best characterized as reflecting noise-driven fluctuations around a single stable state, or instead, as a nonlinear dynamical system with nontrivial attractors embedded in the RSNs. Here, we provide evidence for the latter, by constructing whole-brain dynamical systems models from individual resting-state fMRI (rfMRI) recordings, using the Mesoscale Individualized NeuroDynamic (MINDy) framework. The MINDy models consist of hundreds of neural masses representing brain parcels, connected by fully trainable, individualized weights. We found that our models manifested a diverse taxonomy of nontrivial attractor landscapes including multiple equilibria and limit cycles. However, when projected into anatomical space, these attractors mapped onto a limited set of canonical RSNs, including the default mode network (DMN) and frontoparietal control network (FPN), which were reliable at the individual level. Further, by creating convex combinations of models, bifurcations were induced that recapitulated the full spectrum of dynamics found via fitting. These findings suggest that the resting brain traverses a diverse set of dynamics, which generate several distinct but anatomically overlapping attractor landscapes. Treating rfMRI as a unimodal stationary process (i.e., conventional FC) may miss critical attractor properties and structure within the resting brain. Instead, these may be better captured through neural dynamical modeling and analytic approaches. The results provide new insights into the generative mechanisms and intrinsic spatiotemporal organization of brain networks.

Computational Fluid Dynamic Modeling of Pack-Level Battery Thermal Management Systems in Electric Vehicles

In electric vehicles (EVs), the batteries are arranged in the battery pack (BP), which has a small layout space and difficulty in dissipating heat. Therefore, in EVs, the battery thermal management systems (BTMSs) are critical to managing heat to ensure safety and performance, particularly under higher operating temperatures and longer discharge conditions. To solve this problem, in this article, the thermal analysis models of a 3-battery-cell BP were created, including scenarios (1) natural air cooling without a BTMS; (2) natural air cooling with water cooling hybrid BTMS; and (3) forced air cooling plus water cooling composite BTMS. The thermal performances of the pack-level BPs were simulated and analyzed based on computational fluid dynamics (CFD). A variety of boundary conditions and working parameters, such as ambient temperature, inlet coolant flow rate and initial temperature, discharge rate, air flow rate, and initial temperature, were considered. The results show that without a BTMS (Scenario 1), the maximum temperature in the BP rises rapidly and continuously to reach 63.8 °C, much higher than the upper bound of the recommended operating temperature range (ROTR between +20 °C to +35 °C) under the extreme discharge rate of 3 C and even if the discharge rate is 2 C. With a hybrid BTMS (Scenario 2), the maximum temperature in BP rises to about 38.7 °C, slightly above the upper bound of the ROTR. Lowering the coolant (water) initial temperature can effectively lower the temperature up to 5.7 °C in BP, but the water flow rate cannot since the turbulence model. While with a composite BTMS (Scenario 3), the temperature can be further lowered up to 1.5 °C under the extreme discharge rate of 3C, just reaching the upper bound of the ROTR. In addition, lowering the initial coolant temperature or air temperature can effectively decrease the temperatures up to 5.1 and 1.0 °C, respectively, in BP, but the coolant flow rate (due to the turbulence model) and the air flow rate cannot. Finally, the thermal performances of the different battery cells in the BP with different cooling systems and at the different positions of the BP were compared and analyzed. The present work may contribute to the design of BTMSs in the EV industry.

Precision data-driven modeling of cortical dynamics reveals person-specific mechanisms underpinning brain electrophysiology

Task-free brain activity affords unique insight into the functional structure of brain network dynamics and has been used to identify neural markers of individual differences. In this work, we present an algorithmic optimization framework that directly inverts and parameterizes brain-wide dynamical-systems models involving hundreds of interacting neural populations, from single-subject M/EEG time-series recordings. This technique provides a powerful neurocomputational tool for interrogating mechanisms underlying individual brain dynamics ("precision brain models") and making quantitative predictions. We extensively validate the models' performance in forecasting future brain activity and predicting individual variability in key M/EEG metrics. Last, we demonstrate the power of our technique in resolving individual differences in the generation of alpha and beta-frequency oscillations. We characterize subjects based upon model attractor topology and a dynamical-systems mechanism by which these topologies generate individual variation in the expression of alpha vs. beta rhythms. We trace these phenomena back to global variation in excitatory-inhibitory balance, highlighting the explanatory power of our framework to generate mechanistic insights.

DynPy—Python Library for Mechanical and Electrical Engineering: An Assessment with Coupled Electro-Mechanical Direct Current Motor Model

DynPy is an open-source library implemented in Python (version 3.10.12) programming language which aims to provide a versatile set of functionalities for mechanical and electrical engineers. It enables the user to model, solve, simulate, and report analysis of dynamic systems with the use of a single environment. The DynPy library comes with a predefined collection of ready-to-use mechanical and electrical systems. A proprietary approach to creating new systems by combining independent elements defined as classes, such as masses, springs, dampers, resistors, capacitors, inductors, and more, allows for the quick creation of new, or the modification of existing systems. In the paper examples for obtaining analytical and numerical solutions of the systems described with ordinary differential equations were presented. The assessment of solver accuracy was conducted utilising a coupled electro-mechanical model of a direct current motor, with MATLAB/Simulink (R2022b) used as a reference tool. The model was solved in DynPy with the hybrid analytical–numerical method and fully analytically, while in MATLAB/Simulink strictly numerical simulations were run. The comparison of the results obtained from both tools not only proved the credibility of the developed library but also showed its superiority in specific conditions.

From Serendipity to Precision: Integrating AI, Multi-Omics, and Human-Specific Models for Personalized Neuropsychiatric Care.

Background/Objectives: The dual forces of structured inquiry and serendipitous discovery have long shaped neuropsychiatric research, with groundbreaking treatments such as lithium and ketamine resulting from unexpected discoveries. However, relying on chance is becoming increasingly insufficient to address the rising prevalence of mental health disorders like depression and schizophrenia, which necessitate precise, innovative approaches. Emerging technologies like artificial intelligence, induced pluripotent stem cells, and multi-omics have the potential to transform this field by allowing for predictive, patient-specific interventions. Despite these advancements, traditional methodologies such as animal models and single-variable analyses continue to be used, frequently failing to capture the complexities of human neuropsychiatric conditions. Summary: This review critically evaluates the transition from serendipity to precision-based methodologies in neuropsychiatric research. It focuses on key innovations such as dynamic systems modeling and network-based approaches that use genetic, molecular, and environmental data to identify new therapeutic targets. Furthermore, it emphasizes the importance of interdisciplinary collaboration and human-specific models in overcoming the limitations of traditional approaches. Conclusions: We highlight precision psychiatry's transformative potential for revolutionizing mental health care. This paradigm shift, which combines cutting-edge technologies with systematic frameworks, promises increased diagnostic accuracy, reproducibility, and efficiency, paving the way for tailored treatments and better patient outcomes in neuropsychiatric care.

A physics-aware neural network for effective refractive index prediction of photonic waveguides

Neural network (NN)—based surrogates have been effectively used for modeling dynamic systems, including photonic devices. However, black-box data-driven modeling approaches significantly suffer from performance reduction in high-dimensional spaces.As a remedy, we propose a novel physics-aware NN architecture for the effective index prediction of photonic strip waveguides. The model learns a translation between the strip waveguide and an equivalent infinite slab waveguide by employing physical loss terms in the loss function. The proposed method exhibits significantly lower error, with more than 50% reduction, compared to a black-box NN and a variational method. Because of its physical basis, the proposed NN can predict field distributions in rectangular waveguides and the effective indices of higher-order modes.

ANÁLISE MATEMÁTICA E SIMULAÇÃO DO SISTEMA DE AMORTECIMENTO VEICULAR COM MATLAB

Abstract: In modern control theory, the concept of state variables plays a crucial role in the modeling and analysis of dynamic systems. These variables provide a comprehensive description of the system’s future behavior over time. The organization into a state vector enables a compact and complete representation of the system’s internal state. The state-space function describes the temporal evolution of these variables in response to system inputs, offering an efficient mathematical approach for the design and analysis of control systems. Applications range from industrial process control to autonomous vehicle control and robotics. By understanding and applying these concepts, control engineers develop effective solutions for challenges in complex systems, ensuring performance, stability, and efficiency in dynamic environments. Keywords: state variables; dynamic systems; state-space; control; stability.

Enhancing dynamical system modeling through interpretable machine-learning augmentations: a case study in cathodic electrophoretic deposition

Abstract We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine-learning enhancements. As a demonstrative application, we pursue the modeling of cathodic electrophoretic deposition, commonly known as e-coating. Our approach illustrates a systematic procedure for enhancing physical models by identifying their limitations through inference on experimental data and introducing adaptable model enhancements to address these shortcomings. We begin by tackling the issue of model parameter identifiability, which reveals aspects of the model that require improvement. To address generalizability, we introduce modifications, which also enhance identifiability. However, these modifications do not fully capture essential experimental behaviors. To overcome this limitation, we incorporate interpretable yet flexible augmentations into the baseline model. These augmentations are parameterized by simple fully-connected neural networks, and we leverage machine-learning tools, particularly neural ordinary differential equations, to learn these augmentations. Our simulations demonstrate that the machine-learning-augmented model more accurately captures observed behaviors and improves predictive accuracy. Nevertheless, we contend that while the model updates offer superior performance and capture the relevant physics, we can reduce off-line computational costs by eliminating certain dynamics without compromising accuracy or interpretability in downstream predictions of quantities of interest, particularly film thickness predictions. The entire process outlined here provides a structured approach to leverage data-driven methods by helping us comprehend the root causes of model inaccuracies and by offering a principled method for enhancing model performance.

Collaborative Problem-Solving for the ‘Polycrisis’

The paper focuses on the “Polycrisis,” which is first defined and then positioned as the context for a subsequent discussion about both the formal and social conditions for effective collaborative problem-solving. It then highlights the potential for diagrammatic reasoning to contribute to solving what some commentators choose to call ‘wicked-problems’ including those associated natural, economic, and social forms of fragility. This discussion is informed by pertinent advances in applied category theory, which has a wide range of application-domains including cyber-physical systems, scientific systems, dynamical systems, software engineering, and machine learning. The formal constructs and techniques to be surveyed include optics and parametric lenses, as well as David Spivak’s organisational categories. Optics and lenses have not only been applied to software engineering but also to the modelling of dynamical systems and machine learning. They possess a diagrammatic representation (as string diagrams), which serves as an aid in their deployment (e.g. AlgebraicJulia, Symbolica AI, Haskell applications). The paper argues that these developments should assist users in their collaborative modelling of the Polycrisis by: (i) integrating machine learning, differential programming, and calibration and simulation of dynamical systems; (ii) accounting for subsystem interactions within a larger system that features different stock-flow rates; (iii) accommodating non-linear mappings and weight-sharing; (iv) formally supporting a variety of stochastic influences over the systems that are being modelled; and, (iv) imposing on the whole, the internal logic associated with a topos.

Beyond Acceleration: Exploring Higher-Order Time Derivatives of Position in Physical and Engineering Systems

This article investigates the higher-order derivatives of position concerning time, including jerk, snap, and extending up to the tenth-order derivative. A mathematical model that accurately describes the motion of an object with high precision and smooth control is presented, along with an analysis of its series convergence. Additionally, the article explores the applications of these higher-order derivatives across various fields of physics. Key areas include advanced robotics and mechanical systems, vibration control, aerospace engineering, and seismology, where these derivatives are particularly relevant. Furthermore, the modeling of complex dynamic systems with high precision is discussed, providing extensive insights into the behavior of these systems.

Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics

Two rheological Burgers–Faraday models and rheological dynamical systems were created by using two new rheological models: Kelvin–Voigt–Faraday fractional-type model and Maxwell–Faraday fractional-type model. The Burgers–Faraday models described in the paper are new models that examine the dynamical behavior of materials with coupled fields: mechanical stress and strain and the electric field of polarization through the Faraday element. The analysis of the constitutive relation of the fractional order for Burgers–Faraday models is given. Two Burgers–Faraday fractional-type dynamical systems were created under certain approximations. Both rheological Burgers-Faraday dynamic systems have two internal degrees of freedom, which are introduced into the system by each standard light Burgers-Faraday bonding element. It is shown that the sequence of bonding elements in the structure of the standard light Burgers-Faraday bonding element changes the dynamic properties of the rheological dynamic system, so that in one case the system behaves as a fractional-type oscillator, while in the other case, it exhibits a creeping or pulsating behavior under the influence of an external periodic force. These models of rheological dynamic systems can be used to model new natural and synthetic biomaterials that possess both viscoelastic/viscoplastic and piezoelectric properties and have dynamical properties of stress relaxation.

Holistic Dynamic Modeling and Simulation of Alkaline Water Electrolysis Systems Based on Heat Current Method

Hydrogen production technology is becoming increasingly important with the rapid development of hydrogen energy. Among existing hydrogen production technologies, alkaline water electrolysis (AWE) is drawing wide attention due to its advantages such as high maturity and low cost, and its performance analysis and optimization are important for applications. However, the AWE system contains processes with different physical and mathematical properties such as electrochemical reaction and heat transport processes, bringing difficulties to the system modeling. Moreover, the electrical and thermal processes have different characteristic time scales, and the system shows a sophisticated dynamic behavior, which has not been well studied yet. Here, a homomorphic dynamic model of the AWE system in the form of electrical circuit is built to describe the thermal and electrochemical processes uniformly, where the two parts are integrated via the energy conservation seamlessly. The model is verified by comparing with the experimental data and shows a high accuracy. The dynamic simulation analysis is conducted to investigate the dynamic response characteristics of the system under current step changes and fluctuations. The temperature overshoot and oscillation phenomena caused by delays in heat transport processes are studied. Results show that the time delay yields a maximum temperature overshoot of 10 °C, which would reduce the lifespan of the stack. This also highlights the importance of dynamic system analysis.

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.

A computational and multi-brain signature for aberrant social coordination in schizophrenia.

Social functioning impairment is a core symptom of schizophrenia (SCZ). Yet, the computational and neural mechanisms of social coordination in SCZ under real-time and naturalistic settings are poorly understood. Here, we instructed patients with SCZ to coordinate with a healthy control (HC) in a joint finger-tapping task, during which their brain activity was measured by functional near-infrared spectroscopy simultaneously. The results showed that patients with SCZ exhibited poor rhythm control ability and unstable tapping behaviour, which weakened their interpersonal synchronization when coordinating with HCs. Moreover, the dynamical systems modeling revealed disrupted between-participant coupling when SCZ patients coordinated with HCs. Importantly, increased inter-brain synchronization was identified within SCZ-HC dyads, which positively correlated with behavioural synchronization and successfully predicted dimensions of psychopathology. Our study suggests that SCZ individuals may require stronger interpersonal neural alignment to support their deficient coordination performance. This hyperalignment may be relevant for developing inter-personalized treatment strategies.

An Approach for Modeling and Simulation of Virtual Sensors in Automatic Control Systems Using Game Engines and Machine Learning.

We live in an era characterized by Society 4.0 and Industry 4.0 where successive innovations that are more or less disruptive are occurring. Within this context, the modeling and simulation of dynamic supervisory and control systems require dealing with more sophistication and complexity, with effects in terms of development errors and higher costs. One of the most difficult aspects of simulating these systems is the handling of vision sensors. The current tools provide these sensors but in a specific and limited way. This paper describes a six-step approach to sensor virtualization. For testing the approach, a simulation platform based on game engines was developed. As contributions, the platform can simulate dynamic systems, including industrial processes with vision sensors. Furthermore, the proposed virtualization approach allows for the modeling of sensors in a systematic way, reducing the complexity and effort required to simulate this type of system.

Development of an observer of rotor angular velocity and resistance moment on the shaft of an adjustable permanent magnet synchronous motor powered through long cable

Relevance. Currently, when using submersible electric motors in centrifugal electric pump installations in cyclic operation mode, there is a reduction in the inter-repair period of submersible equipment, which is associated with a reduction in oil pumping periods to several minutes. As a result, there is a multiple increase in starting currents and torque, which leads to an increase in mechanical loads on the pump shaft and appearance of resonance phenomena during the electric motor acceleration, reducing the reliability of a seal protection. To solve these problems, it is necessary to synthesize closed-loop vector control systems with current and electromagnetic torque control in transient responses. Open-loop scalar control systems for electric drives of oil well production are used in operation, which is due to the complexity of obtaining feedback signals on the angular velocity of the rotor and the moment of resistance on the shaft by means of submersible telemetry. This problem determines the relevance and necessity of developing observers for rotor speed and load torque estimation, taking into account the features of the technological process of installing centrifugal electric pumps, in particular, the presence of a long cable for powering a submersible electric motor based on a synchronous machine with permanent magnets. Aim. To develop a full-order observer rotor speed and load torque for the dynamic system "long supply cable – synchronous motor with permanent magnets". Methods. System analysis and identification of dynamic systems, synthesis of Luenberger observers, mathematical modeling of dynamic systems, electric drives and electrical machines. Result and conclusions. The authors have proposed the mathematical model of a rotor speed and load torque full-order observer for the dynamic system "long supply cable – synchronous motor with permanent magnets". The performance of the observer was investigated under varying load on the shaft, mismatch of non-zero initial conditions, deviation of the parameters of the equivalent circuit of the observer and the object in the range from –20 to +20% of the nominal values.

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.

The Essential Gronwall Inequality Demands the $\left(\rho,\varphi \right) -$Fractional Operator with Applications in Economic Studies

Gronwall's inequalities are important in the study of differential equations and integral inequalities. Gronwall inequalities are a valuable mathematical technique with several applications. They are especially useful in differential equation analysis, stability research, and dynamic systems modeling in domains spanning from science and math to biology and economics. In this paper, we present new generalizations of Gronwall inequalities of integral versions. The proposed results involve $( \rho ,\varphi)-$Riemann-Liouville fractional integral with respect to another function. Some applications on differential equations involving $( \rho ,\varphi)-$Riemann-Liouville fractional integrals and derivatives are established.

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.