Keywords: Mechanics, Mechatronics, incl. Robotics
Abstract: Efficiency in the building sector is worldwide rather low. There are intensive research activities in various fields to increase this. These include the use of robotic machines, which are to be used in semi-automatic or fully automatic or even autonomous operation. Various projects in this field will be presented in the talk. An overhead crane with trajectory tracking control of the load will be presented for transporting large loads and supporting assembly tasks. A special load handling device at the crane hook enables orientation in six degrees of freedom and thus support for assembly tasks. In a second system, a hydraulic manipulator with 7 axes and a working area of around 15 meters was converted so that it can also support the operator in semi-automatic mode, as well as be operated in fully automatic mode to carry out assembly tasks. Other research activities of automated excavators, mobile concrete pumps, or the use of autonomous robot systems on wheels with robot arms to carry out work in existing buildings are discussed. For the systems presented, the approaches for deriving dynamic models, control, trajectory generation and path planning are presented and discussed, particularly with regard to cooperation between the machines.

Keywords: Automotive, Aerospace, Transportation Systems, Modelling for Control and Real-Time Applications, ODE, DAE, SODE, SDAE Systems
Abstract: Motivated by the need to predict dangerous scenarios, this article introduces a non-linear dynamic model for motorcycles consisting of four rigid bodies. Using Jourdain's principle, the model incorporates both longitudinal and lateral dynamics, targeting a balance between numerical complexity and accuracy of representation. The paper further employs the model to design a Luenberger observer based on linear quadratic regulator theory, for estimating physical states based on sensor measurements. In turn, the state estimates are useful for predicting dangerous scenarios (lowside, highside, fall). The relevance of the approach is demonstrated through simulations of various straight trajectories and a lane-changing scenario using BikeSim simulator.

Keywords: Model Reduction, Model Simplification and Optimization, ODE, DAE, SODE, SDAE Systems, Mechanics, Mechatronics, incl. Robotics
Abstract: Trajectory planning on high dimensional systems with respect to obstacle avoidance proposes multiple challenges to traditional techniques from optimization. While gradient based solvers tend to struggle with the non-smooth, non-differentiable structure of geometric collision avoidance constraints, sampling based methods can not handle complex dynamics. Also graph as well as dynamic programming based strategies become impractical facing the curse of dimensionality. Nevertheless, a strategy combining dynamic programming (DP) with nonlinear programming (NLP) into an iterative algorithm recently achieved promising results on a robotic arm scenario within a static environment. In this work, we modify the algorithm, to be able to handle moving environments, including on the one hand collision avoidance with time dependent obstacles, but also time dependent goal constraints. As a proof of concept, we apply the new strategy to a space manipulator, planning its trajectory towards a tumbling piece of space debris.

Keywords: Mechanics, Mechatronics, incl. Robotics, Fitting Models to Real Processes, incl. Identification and Calibration, Model Reduction, Model Simplification and Optimization
Abstract: Strain wave gears (SWG) are important parts to drive robots. Yet, they are susceptible to wear and degradation carrying high risk for malfunction of the robot. Hence, the detection of faults in SWGs is of great interest for the robot’s save operation. In this paper, the capability of a simulation chain is shown to generate faulty SWGs’ signals of strain gauge senors mounted on the back of their flex spline with qualitatively similar behavior to real-world measurement signals. Furthermore, the simulated sensor signals are used for a data-driven detection of faults in measurement data showing the practicality of this approach for real-world applications.

Keywords: Mechanics, Mechatronics, incl. Robotics, Fitting Models to Real Processes, incl. Identification and Calibration, Model Reduction, Model Simplification and Optimization
Abstract: A precise model with low order for controller design is indispensable for the high performance control of thin flexible structures. Such systems require a high model quality ranging from slow, low frequency dynamics (rigid body) to fast, high frequency dynamics (vibration) for an accurate prediction of the superposed motion. The considered system in this contribution comprises low frequent pendulum dynamics and a dense natural frequency spectrum of a plate. In order to obtain a precises non-square multiple-input multiple-output model description, an iterative identification procedure applying time and frequency methods is proposed. Additionally, an optimization based model order reduction considering a modal system description is introduced. The precise fit of the reduced order model to the collected data underpins the proposed procedure.

Keywords: Model Reduction, Model Simplification and Optimization, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Electrical, Electronic and Power Systems
Abstract: Model Order Reduction (MOR) for Artificial Neural Networks (ANNs) is an increasingly important field that aims to reduce the complexity and computational cost of ANNs while maintaining their predictive accuracy. This is particularly relevant for scientific machine learning, where neural networks are used in complex, high-dimensional tasks such as solving partial differential equations (PDEs), modelling physical processes, or real-time simulation and control in engineering systems. In this contribution, we provide an overview of the state of the art for MOR applied to ANNs, as well as some ideas we are pursuing for our novel ANNs generated from data-informed state space systems.

Keywords: Model Reduction, Model Simplification and Optimization, Modelling Uncertainties and Stochastic Systems, Data-Driven Models, Neural Networks
Abstract: The field of Model Order Reduction (MOR) provides methods to reduce the computational complexity of high-dimensional differential equations. In Monte-Carlo simulations, especially of stochastic systems, many repeated simulations are required, which can be computationally expensive. Traditionally, intrusive MOR techniques, such as Proper Orthogonal Decomposition (POD), are used to create reduced-order models (ROMs). However, these methods require access to system coefficients, making them impractical for black-box systems. Non-intrusive methods overcome this limitation by relying solely on large amounts of data, allowing for ROM construction without accessing system matrices. Thus, the accuracy of these ROMs is strongly dependent on the quality and quantity of available data. In this paper, we build upon the recent Operator Inference (OpInf) for stochastic systems and enhance it by incorporating the re-projection sampling scheme, which was originally developed for deterministic OpInf. This combination addresses the closure error in the reduced dynamics and provides the opportunity for a computationally more efficient inference method. We validate our approach on the Steel Profile Benchmark, a high-dimensional system under the influence of noisy boundary conditions. This experiment demonstrates that our non-intrusive approach produces a ROM with the same approximation quality as the intrusive POD ROM.

Keywords: Model Reduction, Model Simplification and Optimization, Multiscale Modelling, Data-Driven Models, Neural Networks
Abstract: We investigate the modeling of sub-scale components of proper orthogonal decomposition reduced order models (POD-ROMs) of convection-dominated flows. We propose a ROM closure model that depend on the ROM residual. We illustrate the new residual-based data-driven ROM closure within the variational multi-scale (VMS) framework and investigate it in the numerical simulation of a 2D channel flow past a circular cylinder at Reynolds numbers Re = 1000. Our numerical investigation for both reconstructive and predictive regime show that the new residual-based data-driven VMS-ROM is more accurate than both the coefficient-based data-driven ROMs and the standard Galerkin ROM.

Keywords: Model Reduction, Model Simplification and Optimization, Data-Driven Models, Neural Networks, Modelling Uncertainties and Stochastic Systems
Abstract: We present a data-driven approach to use the Koopman generator for prediction and optimal control of control-affine stochastic systems. We provide a novel conceptual approach and a proof-of-principle for the determination of optimal control policies which accelerate the simulation of rare events in metastable stochastic systems.

Keywords: Medicine, Physiology, Health Care and Biology
Abstract: We investigated the first-digit distribution of simulated and real EEG signals recorded during wakefulness and various sleep stages. Furthermore, we examined how variables such as noise or patient age influence the first-digit distribution and affect its conformity with Benford’s Law. Simulated 1/f noise episodes, which serve as proxies for EEG data, were generated with varying spectral exponents to explore how these changes influence the first-digit distribution. Additionally, we analyzed sleep EEG data from an open-source database to compare the first-digit distributions across different sleep stages, particularly focusing on N3 sleep, which shares similarities with EEG patterns observed under general anesthesia. Our results demonstrate that the first-digit distribution is influenced by the investigated features, i.e., spectral exponent, vigilance state, and age. Deviations from wakefulness cause deviations from the Benford distribution. Moreover, age-related variations in EEG data may lead to changes in first-digit distributions, potentially offering new insights into how aging affects brain activity. These findings suggest that applying Benford’s Law to EEG analysis could complement existing methods for patient monitoring. The results from our investigation justify the next step of applying this method to anesthesia data.

Keywords: Medicine, Physiology, Health Care and Biology
Abstract: Despite the significant differences between sleeping and being under anesthesia, i.e., a physiological process vs. a pharmacologically induced state, they share notable similarities. This is particularly evident when examining the electroencephalogram (EEG), where the spectral content of both states reveals marked increased power within delta (1 − 4 Hz) and alpha (8 − 13 Hz) frequency ranges. To further explore this, a novel analytical framework called the coefficient of variation of the envelope (CVE) was utilized to assess the alpha and delta EEG envelopes during sleep and general anesthesia. This measure is sensitive to different underlying neural dynamics by linking signal morphology and signal energy, specifically through examining deviations from Gaussianity as a marker of synchronicity. Stable episodes were extracted from patients under general anesthesia and controls in non-REM sleep stage 2 and 3. After filtering the EEGs to isolate the delta and alpha bands, the EEG data was segmented into 24-second intervals with a 50% overlap. In addition to the envelope’s energy, CVEs were calculated using the Hilbert transformation. Cutoff values for Gaussianity were derived from simulated EEG signals. CVE values outside the 99% confidence intervals (CI) of the simulated data are considered to indicate either rhythmic (CV E < lowerCI) or pulsatile (CV E > upperCI) activity. The findings revealed differences in CVEs across both delta and alpha-band filtered EEG. Specifically, during sleep, CVEs derived from the delta band were more frequently classified as pulsatile and fell less often within the gaussian range, compared to those observed during general anesthesia. Similar distinctions were observed for alpha-band oscillations. Although the spectral content related to delta and alpha power may appear similar, the morphology of the underlying neural oscillations differs. These differences are critical points that differentiate anesthesia from sleep.

Keywords: Medicine, Physiology, Health Care and Biology, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: Brain activity differs according to the state of consciousness. Whole-brain models, typically based on functional magnetic resonance imaging (fMRI) data, provide valuable insight into these changes by utilizing structural connectivity and differential equations to model the functional connectivity between brain regions. The goal of this work is to adapt fMRI-based functional connectivity models to electroencephalography data. A key step in this process is to determine the number of clusters and to estimate the coupling parameters. We turn to amplitude envelope correlation, a time-domain measure, to better match functional connectivity patterns observed in fMRI. By analyzing 64-channel electroencephalogram data from 25 male subjects over the age of 60 from the AlphaMax study, we investigate wakefulness and the transition to unconsciousness under anesthesia. Using k-means clustering, we identify optimal brain network configurations, focusing on whether they match known fMRI-based networks. Clustering is evaluated using the Calinski-Harabasz criterion for different thresholds and numbers of cluster. The results show that two clusters are predominantly optimal for both awake and the mixed half awake, half unconscious scenario. Misplaced electrodes are mainly found in parietal regions. Since we determined the number of differential equations, this work lays the foundation for further development of electroencephalography-based whole-brain models that can track functional connectivity changes during anesthesia.

Keywords: Medicine, Physiology, Health Care and Biology
Abstract: The glymphatic hypothesis suggests that cerebrospinal fluid (CSF) bulk movement across the brain plays a major role in brain waste clearance. Previous studies using simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) indicate that CSF flow and EEG delta activity (0.5–4 Hz) are coupled, especially during sleep. In our study we investigated this relationship focusing on spatial distinction between the occipital and frontal brain region as well as slow (0.5–2 Hz) and fast (2–4 Hz) delta sub-bands. For this, we used a public EEG-fMRI dataset from 29 healthy young adults during wakefulness and early sleep stages. Our results show only slight changes in the correlation between EEG delta activity and CSF flow as individuals transitioned into light sleep. However, we observed differences within regions and frequency bands during sleep: Occipital delta activity exhibits a stronger correlation with CSF flow than frontal delta activity, and slow delta correlates more strongly than the fast delta sub-band. These results align with power spectral density (PSD) analyses, which reveal higher relative power in lower frequencies in occipital regions, while frontal regions display greater power in higher frequencies.

Keywords: Modelling Uncertainties and Stochastic Systems, Electrical, Electronic and Power Systems
Abstract: A practical measurement always raises the question of how well it reproduces the concept to be quantified. We present a mathematical perspective on the measurement problem by introducing a conceptual framework that allows an analytical discussion of this question. Within this framework, we define the measurement result, the concept to be measured, the epistemic errors and aleatory uncertainties. We discuss the first quantifications inside a measurement procedure by analyzing the mathematical spaces and operators. Finally, we apply our considerations to voltage measurements with sampling oscilloscopes.

Keywords: Modelling Uncertainties and Stochastic Systems, Comparison of Methods for Modelling, ODE, DAE, SODE, SDAE Systems
Abstract: We present a modelling view on the numerical quantification of uncertainties in the solution of a dynamical system, which mostly consists in using a linearized update procedure for the covariance matrix. We regard the Fokker-Planck equation for the probability density of the states of the dynamical system as ground truth and the numerical method as surrogate model. We give an error estimate and show the connection to the numerical solution of ordinary differential equations. Finally, uncertainty quantification is interpreted as measurement.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Fitting Models to Real Processes, incl. Identification and Calibration, Comparison of Methods for Modelling
Abstract: This work focuses on the analysis of probabilistic power curve models that link the energy production of a photovoltaic system with the irradiance forecasts of the weather provider. It is shown that the essential information is provided by global horizontal irradiance (GHI) forecasts, which can be used to obtain simple and meaningful probabilistic models using non-parametric (quantile Regression forests) and parametric (Beta regression) methods. The second step is the analysis of the seasonal performance of power curve models, to understand whether their performance can improve by taking seasonal variability into account.

Keywords: Modelling Uncertainties and Stochastic Systems, Electrical, Electronic and Power Systems, Automotive, Aerospace, Transportation Systems
Abstract: To determine failure rates is a challenge, if there are only a few failures and typical failure rates are low. As an application example we are interested in failure rates of electrical automotive components for automated/autonomous driving. As method we focus here on the exploitation of field data. Our contribution classifies different approaches from statistics and shows how this can be applied to real-world production figures as available in industry.

Keywords: Modelling for Control and Real-Time Applications, Model Reduction, Model Simplification and Optimization, Data-Driven Models, Neural Networks
Abstract: We introduce a strategy that generates an adaptive surrogate of the value function of high-dimensional nonlinear optimal control problems. It exploits the relevant operating domain online on which the resulting surrogate satisfies the Hamilton–Jacobi–Bellman (HJB) equation up to a given threshold. The approximate value function is based on Hermite kernel regression, where the data stems from open-loop control of reduced-order optimal control problems. As a measure of accuracy, the full-order HJB residual, known as the Bellman error, is used to determine whether the current Hermite kernel surrogate is sufficient or further training is required. In addition, the reduced-order model can also be improved using the full-order data if the same HJB-based error indicator suggests that the current reduced system is not accurate enough. Numerical experiments support the effectiveness of the new scheme.

Keywords: Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Model Reduction, Model Simplification and Optimization, Data-Driven Models, Neural Networks
Abstract: In this contribution, we explore the application of machine learning techniques to address parameter optimization problems with parabolic PDE constraints. We delve into an established trust region method that integrates reduced basis methods for model order reduction, examining the potential enhancement of this approach through adding machine learning based surrogate models. These methods hold promise for providing a more efficient solution to optimization problems in this context.

Keywords: Modelling for Control and Real-Time Applications, Multiscale Modelling, Data-Driven Models, Neural Networks
Abstract: It has been shown that working with databases from heterogeneous sources of varying fidelity can be leveraged in multi-fidelity surrogate models to enhance the high-fidelity prediction accuracy or, equivalently, to reduce the amount of high-fidelity data and thus computational effort required while maintaining accuracy. In contrast, this contribution leverages low-fidelity data queried on a larger feature space to realize data-driven multi-fidelity surrogate models with a fallback option in regimes where high-fidelity data is unavailable. Accordingly, methodologies are introduced to fulfill this task and effectively resolve the contradictions, that inherently arise in multi-fidelity databases. In particular, the databases considered in this contribution feature two levels of fidelity with a defined hierarchy, where data from a high-fidelity source is, when available, prioritized over low-fidelity data. The proposed surrogate model architectures are illustrated first with a toy problem and further examined in the context of an engineering use case in autonomous driving, where the human-seat interaction is evaluated using a data-driven surrogate model, that is trained through an active learning approach. It is shown, that two proposed architectures achieve an improvement in accuracy on high-fidelity data while simultaneously performing well where high-fidelity data is unavailable compared to a naive approach.

Keywords: Modelling for Control and Real-Time Applications, Model Reduction, Model Simplification and Optimization
Abstract: In this work, we focus on two aspects of 4D-var data assimilation (DA) governed by parabolic partial differential equations (PDEs). First, we are interested on how to set up adaptive time grids for DA problems and in what extend DA benefits from it. Second, we study the application of model order reduction (MOR) for DA problems. Since solving DA problems requires to solve the involved PDEs repeatedly, the use of MOR techniques is an obvious approach. We apply the methods Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) and investigate whether the previously introduced adaptive time grid facilitates the MOR with respect to accuracy and efficiency. In order to construct an adaptive time grid, we interpret the DA problem in the context of optimal control and use a reformulation of the optimality conditions. Following Gong et al. (2012), we transferred their idea of deriving a-posteriori error estimates to the 4D-var problem in Gräßle and Marquardt (2024). In this work, we extend our previous results where we derived an error estimate for the adjoint state by additionally considering an estimate for the state. The resulting time grid is used for MOR, which has already been done for distributed control problems in order to identify suitable snapshot locations, see Alla et al. (2016, 2018). We conclude with a numerical example.

Keywords: Numerical Simulation and Co-Simulation, Model Reduction, Model Simplification and Optimization, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: In this contribution we present an abstract framework for adaptive model hierarchies together with several instances of hierarchies for specific applications. The hierarchy is particularly useful when integrated within an outer loop, for instance an optimization iteration or a Monte Carlo estimation where for a large set of requests answers fulfilling certain criteria are required. Within the hierarchy, multiple models are combined and interact with each other pursuing the overall goal to reduce the run time in a multi-query context. To this end, models with different accuracies and effort for evaluation are used in such a way that the cheapest (and typically least accurate) models are evaluated first when a request comes in. If the result fulfills a prescribed criterion, it can be returned to the outer loop. Otherwise, the model hierarchy falls back to more costly, but at the same time more accurate, models. The cheaper models are improved by means of training data gather whenever the more accurate models are evaluated.

Keywords: ODE, DAE, SODE, SDAE Systems, Medicine, Physiology, Health Care and Biology, Numerical Simulation and Co-Simulation
Abstract: We enhance our SIHURD model published in cite{BiZhHu:22} and propose a metapopulation infectious disease mathematical monitoring model where individuals move between discrete spatial patches. We divide the environment into a finite number of spatial patches (e.g., adjacent cities), which preserve homogeneity characteristics. We apply the enhanced SIHURD model presented in this article to each spatial patch.

The novelty of this model lies in introducing parameters that represent individuals' travel rates between spatial patches, which depend on their disease status. In addition, it assumes that individuals do not change their disease status while travelling between patches.

Our study uses the reproduction number, R_{0_k}, for each spatial patch, k=1,2,dots, n,(n>1) integer, which represents the average number of secondary cases produced by an infected individual in a susceptible population. The system has only a disease-free equilibrium point if R_{0_k}leq1. In contrast, if R_{0_k}>1, the system has an endemic equilibrium point. Reproduction numbers R_{0_k} are crucial for understanding the spread of infectious diseases and can inform measures to control outbreaks effectively.

Migration between patches fundamentally alters the behaviour of the endemic equilibrium within a patch, rendering it unstable in the proposed model.

Keywords: Infinite-Dimensional Systems (PDEs, PDAEs, SPDEs), Numerical Simulation and Co-Simulation, Modelling for Control and Real-Time Applications
Abstract: We demonstrate the epidemics transport effect in closed spaces, performing different numerical experiments via development of a coupled, macroscopic partial differential equation (PDE) model of crowd flow, epidemics spreading dynamics, and ventilation air flow dynamics. We present numerical approximations for the coupled model with which we perform different numerical tests. In particular, we study the effect of different ventilation rates in epidemics transport (in time and space), also quantifying the infection risk via computing the total number of exposed individuals (in time and space), predicted by the model. We then discuss how the model used and the numerical results obtained could be utilized, in certain scenarios, for design of epidemics transport control strategies via manipulation of the ventilation air-flow field.

Keywords: Medicine, Physiology, Health Care and Biology, ODE, DAE, SODE, SDAE Systems, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing
Abstract: Deep brain stimulation (DBS) is a therapy widely used for treating the symptoms of neurological disorders. Electrical pulses are chronically delivered in DBS to a disease-specific brain target via a surgically implanted electrode. The stimulating contact configuration, stimulation polarity, as well as amplitude, frequency, and pulse width of the DBS pulse sequence are utilized to optimize the therapeutic effect. In this paper, the utility of therapy individualization by means of patient-specific mathematical modeling is investigated with respect to a specific case of a patient diagnosed with Essential tremor (ET). Two computational models are compared in their ability to elucidate the impact of DBS stimulation on the Dentato-Rubro-Thalamic tract (DRTT): (i) a conventional model of volume of tissue activated (VTA) and (ii) a well-established, open-source simulation (OSS) neural fiber activation modeling framework known as OSS-DBS. The simulation results are compared with tremor measured in the patient under different DBS settings using a smartphone application. The findings of the study highlight that temporally static VTA models do not adequately describe the differences in the outcomes of bipolar stimulation settings with switched polarity, whereas neural fiber activation models hold potential in this regard. However, it is noted that neither of the investigated models fully accounts for the measured symptom pattern, particularly regarding a bilateral effect produced by unilateral stimulation.

Keywords: Modelling for Control and Real-Time Applications, Medicine, Physiology, Health Care and Biology, ODE, DAE, SODE, SDAE Systems
Abstract: This article proposes a new closed-loop control method to induce and maintain a desired depth of hypnosis during total intravenous anesthesia. The method utilizes two-degrees- of-freedom control, with propofol infusion rate as the input and bispectral index as the output. A target-controlled infusion (TCI) algorithm called STANPUMP is used as the feedforward action to achieve the desired BIS response, and a feedback controller based on a Kalman filter deals with model uncertainties. Adding a TCI algorithm as the feedforward action improves the time-to-target and enhances patient safety. This is because it allows for a seamless transition to open-loop control if needed.

Keywords: Model Reduction, Model Simplification and Optimization, ODE, DAE, SODE, SDAE Systems, Numerical Simulation and Co-Simulation
Abstract: Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second-order linear dynamical systems with sparse matrices, model order reduction provides an interesting possibility to speed up the simulation process. In this work, we tackle the question of finding an optimal order for the reduced system, given the desired accuracy. To do so, we revisit a heuristic error estimator based on the difference of two reduced models from two consecutive Krylov iterations. We perform a mathematical analysis of the estimator and show that the difference between two consecutive reduced models does provide a sufficiently accurate estimation for the true model reduction error. This claim is supported by numerical experiments on two acoustic models. We briefly discuss its feasibility as a stopping criterion for Krylov-based model order reduction.

Keywords: Model Reduction, Model Simplification and Optimization, Fluidics and Thermodynamics, Electrical, Electronic and Power Systems
Abstract: Understanding the thermal behavior of power electronics is of critical importance in their design and development stage. Typical power losses are Ploss > 2 kW, thus liquid cooling is often required in order to maintain acceptable temperatures. Due to the different thermal conductivities and heat capacities in the layered design, the system has multiple time constants and can not be modelled as a simple system with one time constant. However, this behavior can be well described using the finite element method. The transient thermal response is of special interest in the present case. The strongly varying time constants call for sufficiently small time steps. To speed up simulations, the original system can be compressed with model order reduction, lowering the state dimension to achieve higher performance, while retaining good accuracy of the simulation results. In this contribution, we apply these techniques to a typical power electronics use case and analyze their performance and accuracy. We also discuss a two-step reduction scheme combining the efficiency and error-bound of two state-of-the-art software packages.

Keywords: Automation of Modelling and Software tools, incl. Computer Modelling, ODE, DAE, SODE, SDAE Systems, Model Reduction, Model Simplification and Optimization
Abstract: A method is presented to construct low order linear time- invariant port-Hamiltonian descriptor systems from observed response data in the frequency domain.

Keywords: Data-Driven Models, Neural Networks, Modelling for Control and Real-Time Applications
Abstract: The Dynamic Mode Decomposition (DMD) is a versatile and increasingly popular computational tool for data driven analysis of nonlinear dynamical systems, with applications in e.g. computational fluid dynamics, aeroacoustics, robotics. It can be used for model order reduction, analysis of latent structures in the dynamics, and e.g. for data driven identification, forecasting and control. The theoretical underpinning of the DMD and the Koopman mode decomposition (KMD) is in the framework of the Koopman (composition) operator theory. We discuss a numerical implementation of the DMD that allows for exploiting the full potential of this approach.

Keywords: Model Reduction, Model Simplification and Optimization
Abstract: In this work, we consider systems with poles in general domains, allowing for non-asymptotically stable systems. We build upon an extended version of the iterative Rational Krylov algorithm (IRKA) and propose an efficient method for computing the interpolation points with respect to simply connected analytic closed curves. Specifically, we show that the optimal interpolation conditions for the extended IRKA are related to the Schwarz function. Additionally, we employ the adaptive Antoulas-Anderson (AAA) algorithm to compute a rational approximation of the interpolation points given only boundary samples of user-defined domains.

Keywords: Model Reduction, Model Simplification and Optimization
Abstract: The root mean squared error is an important measure used in a variety of applications like structural dynamics and acoustics to model averaged deviations from standard behavior. For large-scale systems, simulations of this quantity quickly become computationally prohibitive. Model order reduction techniques resolve this issue via the construction of surrogate models that emulate the root mean squared error measure using an intermediate linear system. However, classical approaches require a large number of system outputs, which is disadvantageous in the design of reduced-order models. In this work, we consider directly the root mean squared error as the quantity of interest using the concept of quadratic-output models and propose several new model reduction techniques for the construction of appropriate surrogates. Numerical tests are performed on a model of a plate with tuned vibration absorbers.

Keywords: Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, Fitting Models to Real Processes, incl. Identification and Calibration, Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: This paper reports on designing a digital twin of a yeast culture process in an industrial context. Using a rich experimental data set corresponding to different input profiles, an original dynamic model based on the assumption of cell overflow metabolism is derived. The kinetic laws are represented by smooth functions combining Monod and Jerusalimski factors, which model rate activation and inhibition, respectively. Parameter estimation is achieved following an iterative procedure including practical identifiability analyses which allow the design of informative experiments, enhancing parameter precision and accuracy.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Medicine, Physiology, Health Care and Biology, Modelling for Control and Real-Time Applications
Abstract: Metabolic modeling is a powerful tool for understanding microbial metabolism and is particularly appealing to a wide range of applications, from biotechnology and medicine to environmental science and sustainability. In that context, the elaboration of metabolic networks is essential despite the challenges underlying their reconstruction. While the development of genome-scale networks is computationally costly, small networks are often oversimplified, limiting their use in industrial applications. For this purpose, this paper suggests a method to identify metabolic networks of intermediate size by combining biological knowledge and a series of constraint-based methods in an iterative strategy allowing the refinement of the network definition. The present study focuses on the mathematical modeling of photosynthetic eukaryotic organisms and leads to a detailed network including energy aspects such as the proton motive force. The procedure is effective, yielding promising results while metabolic analyses provide consistent predictive capabilities of the network, in concordance with existing studies.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Model Calibration, Model Validation and Verification, Design of Experiments, Search Based Testing, ODE, DAE, SODE, SDAE Systems
Abstract: The production of monoclonal antibodies (mAbs) is a complex pharmacological process involving upstream and downstream chains, focusing on mAbs production and purification, respectively. This paper presents a process optimization based on an end-to-end mechanistic model for the upstream process chain to enhance the production of mAbs. Upstream processing considers cell expansion, cell production, and primary harvesting steps by filtration. The optimization results offer users the optimal initial concentrations of the medium in the bioreactors, the duration of the cultures, the feed flow rate profiles, and the permeate flow profile in the filtration operation. Simulations incorporating interconnected reactors and process constraints led to optimized initial media concentrations and feed flow profiles, resulting in a 25% increase in mAb production compared to baseline conditions.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes, Fitting Models to Real Processes, incl. Identification and Calibration, ODE, DAE, SODE, SDAE Systems
Abstract: This paper presents the development of a novel macroscopic model that predicts the dynamics of trehalose and glycogen in yeast Saccharomyces cerevisiae fed-batch cultures. The model includes storage and mobilization reactions for each reserve carbohydrate and conversion of glycogen to trehalose. The proposed model is a purely macroscopic model, which relates the two carbohydrates only to the variation of the extracellular components without including complex intracellular phenomena. Its predictions are in agreement with the experimental data. The model can be used to optimize the accumulation of the two reserve carbohydrates, to obtain yeast cells that can withstand stressful conditions.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: This work explores the performance of machine learning (ML) models compared to traditional knowledge-based kinetic models in predicting yeast fermentation outcomes under varying temperature conditions. We developed a knowledge-based model using time series data on biomass dynamics for five industrial yeast species and subsequently created ML models with the same dataset. Our findings indicate that, while the construction of knowledge-based models is time consuming and complex, the formulation of ML models is more straightforward and allows for faster simulations. However, the best-performing ML model, despite being trained on a dataset five times larger than the kinetic model, demonstrated inferior predictive capabilities. This highlights the limitations of ML, which is based solely on data and lacks mechanistic insights, rendering it susceptible to errors and bias. The research emphasizes the need for a balanced approach that combines the strengths of both ML and traditional models to improve predictive accuracy in fermentation processes. Future studies should pursue hybrid models that integrate mechanistic and data-driven methodologies to enhance the efficiency and productivity of industrial fermentation.

Keywords: Bio-Technical, Bio-Chemical and Chemical Engineering Processes
Abstract: Microbial communities form intricate ecological networks, essential in various natural and engineered environments. These networks, comprising bacteria, fungi, viruses, and other microorganisms, interact with each other and their surroundings to perform vital functions such as nutrient cycling, pollutant degradation, and maintaining the health of plants, animals, and humans. Systems biology employs mathematical models to systematically and quantitatively study these communities. Here, our research focuses on calibrating nonlinear models described by Ordinary Differential Equations (ODEs) and assessing both structural and practical identifiability properties to ensure that model parameters can be uniquely estimated from available data. This is key for ensuring model reliability, deepening our understanding of microbial ecosystems, and equipping us with tools for optimal design and management of these ecosystems in health and environmental science applications.

Keywords: Modelling Uncertainties and Stochastic Systems, Numerical Simulation and Co-Simulation, Medicine, Physiology, Health Care and Biology
Abstract: Crop protection science plays a role in responding to the challenge of food demand with growing population and climate change. Mathematical models able to predict the interactions between the biocides and the crops can be exploited to develop new products that are also safer for the environment. This project focuses on modelling the foliar uptake of pesticides, where the goal is to obtain a reliable predictive model for the system. Several sources of uncertainty are present when modelling this systems: intrinsic biological variability between leaves, experimental data variability, uncertainty on the physico-chemical phenomena in the systems, uncertainty in the parameters when calibrating the model. These effects contribute to the uncertainty in the model predictions, addressed in this paper. It is proposed use a systematic modelling approach to consider the different sources of uncertainty. The framework consists of 6 key steps: (1) formulation of different candidate models, (2) preliminary analyses on the identifiability of the model parameters and any identifiability issue is addressed, (3) characterise the variability in the experimental data, (4) application of Model-Based Design of Experiments (MBDoE) techniques for model discrimination and for parameter precision, (5) the model parameters are precisely estimated and validated statistically, (6) the model predictions are statistically validated based on new experimental data. In MBDoE there are methods that exploit directly the uncertainty in the model predictions instead of the variance in the parameters. To assess which MBDoE approach is more beneficial when building a predictive model for foliar uptake, here the study of error propagation from the parameters to predictions is presented. This analysis is conducted on a diffusion-based model by sampling the uncertainty region of the parameters. An uncertainty reduction scenario is considered, and the reduced parameter uncertainty allows to sensibility reduce the prediction uncertainty. This analysis paves the way to the application of MBDoE techniques in the context of biological systems, in particular for the foliar application of biocides.

Keywords: Data-Driven Models, Neural Networks, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling, Electrical, Electronic and Power Systems
Abstract: The global energy transition increasingly relies on renewable energy sources and the use of batteries for electrical energy storage. Efficient battery utilization necessitates accurate state estimation algorithms and appropriate control mechanisms. This paper presents and evaluates a data-driven approach for estimating a battery's dynamic model using tensor trains, that efficiently reconstruct complex multidimensional systems with respect to time and memory, enabling the development of adaptive models capable of capturing real-time variations in system parameters. In this study, the proposed method is applied to reconstruct a dynamic battery model from operational data and is tested upon a solid-state lithium-ion battery cell. The method's explanatory capabilities are demonstrated through the extraction of key parameters such as open circuit voltage and impedance in the form of relaxation times distribution. The accuracy is further validated against the results of conventional battery characterization tests. Owing to its intrinsic scalability and low computational cost, this method holds potential for integration into artificial intelligence-driven battery management systems, enhancing battery longevity and safety while optimizing time-intensive battery characterization processes.

Keywords: Numerical Simulation and Co-Simulation, Model Reduction, Model Simplification and Optimization, Machine Learning, Deep Learning, Data Analytics, Big Data, AI for Modelling
Abstract: In this contribution we present an abstract framework for adaptive model hierarchies together with several instances of hierarchies for specific applications. The hierarchy is particularly useful when integrated within an outer loop, for instance an optimization iteration or a Monte Carlo estimation where for a large set of requests answers fulfilling certain criteria are required. Within the hierarchy, multiple models are combined and interact with each other pursuing the overall goal to reduce the run time in a multi-query context. To this end, models with different accuracies and effort for evaluation are used in such a way that the cheapest (and typically least accurate) models are evaluated first when a request comes in. If the result fulfills a prescribed criterion, it can be returned to the outer loop. Otherwise, the model hierarchy falls back to more costly, but at the same time more accurate, models. The cheaper models are improved by means of training data gather whenever the more accurate models are evaluated.

Keywords: Data-Driven Models, Neural Networks, Modelling for Control and Real-Time Applications, Numerical Simulation and Co-Simulation
Abstract: Traditional methods for analysing football gameplay involve observing players' movements in real time and using the data to explain tactics and player interactions. In contrast, this study introduces a more sophisticated mathematical approach to elucidate typical game flows and tactical features. Specifically, vector analysis was applied to the direction and length of the last pass observed in real football games, and potential fields were derived from the vector fields of the last pass. This approach enabled a visual distinction between unconscious pass flows that occur along potential gradients and conscious pass flows that do not follow gradients. The vector analysis also visualised the spontaneous formation of low-potential areas where the last passes are concentrated in front of the goal area, as well as the characteristics of cross passes near the penalty area. The results clearly show that the vector field-based approach provides useful insights into tactical analysis and strategy optimisation and offers a new perspective to sports science.

Keywords: Modelling Uncertainties and Stochastic Systems, Electrical, Electronic and Power Systems, Automotive, Aerospace, Transportation Systems
Abstract: To determine failure rates is a challenge if there are only a few failures and a low failure rate should be checked. As an application example, we are interested in failure rates of electrical automotive components for automated/autonomous driving. Basically, three methods are common: (i) exploitation of field data, (ii) standardized handbooks with failure rates, e.g.~the FIDES guide, and (iii) laboratory long term exposure tests.

We discuss shortly the (dis)advantages of each method and focus on the statistics behind method (i). Our paper classifies different approaches from statistics and shows how this can be applied to real-world production numbers as available in industry. We close with an application example for the estimation of a failure rate of a typical electrical automotive component.