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In order to simulate the spread of infectious diseases, many epidemiological models use systems of ordinary differential equations (ODEs) to describe the underlying dynamics. These models incorporate the implicit assumption, that the stay time in each disease state follows an exponential distribution. However, a substantial number of epidemiological, data-based studies indicate that this assumption is not plausible. One method to alleviate this limitation is to employ the Linear Chain Trick (LCT) for ODE systems, which realizes the use of Erlang distributed stay times. As indicated by data, this approach allows for more realistic models while maintaining the advantages of using ODEs. In this work, we propose an advanced LCT model incorporating eight infection states with demographic stratification. We review key properties of LCT models and demonstrate that predictions derived from a simple ODE-based model can be significantly distorted, potentially leading to wrong political decisions. Our findings demonstrate that the influence of distribution assumptions on the behavior at change points and on the prediction of epidemic peaks is substantial, while the assumption has no effect on the final size of the epidemic. As the corresponding ODE systems are often solved by adaptive Runge-Kutta methods such as the Cash Karp method, we also study the implications on the time-to-solution using Cash Karp 5(4) for different LCT models. Eventually and for the application side, we highlight the importance of incorporating a demographic stratification by age groups to improve the prediction performance of the model. We validate our model by showing that realistic infection dynamics are better captured by LCT models than by a simple ODE model., Comment: 26 pages, 16 figures

During the COVID-19 crisis, mechanistic models have been proven fundamental to guide evidence-based decision making. However, time-critical decisions in a dynamically changing environment restrict the time available for modelers to gather supporting evidence. As infectious disease dynamics are often heterogeneous on a spatial or demographic scale, models should be resolved accordingly. In addition, with a large number of potential interventions, all scenarios can barely be computed on time, even when using supercomputing facilities. We suggest to combine complex mechanistic models with data-driven surrogate models to allow for on-the-fly model adaptations by public health experts. We build upon a spatially and demographically resolved infectious disease model and train a graph neural network for data sets representing early phases of the pandemic. The resulting networks reached an execution time of less than a second, a significant speedup compared to the metapopulation approach. The suggested approach yields potential for on-the-fly execution and, thus, integration of disease dynamics models in low-barrier website applications. For the approach to be used with decision-making, datasets with larger variance will have to be considered., Comment: 22 pages, 8 figures

Agent-based models have proven to be useful tools in supporting decision-making processes in different application domains. The advent of modern computers and supercomputers has enabled these bottom-up approaches to realistically model human mobility and contact behavior. The COVID-19 pandemic showcased the urgent need for detailed and informative models that can answer research questions on transmission dynamics. We present a sophisticated agent-based model to simulate the spread of respiratory diseases. The model is highly modularized and can be used on various scales, from a small collection of buildings up to cities or countries. Although not being the focus of this paper, the model has undergone performance engineering on a single core and provides an efficient intra- and inter-simulation parallelization for time-critical decision-making processes. In order to allow answering research questions on individual level resolution, nonpharmaceutical intervention strategies such as face masks or venue closures can be implemented for particular locations or agents. In particular, we allow for sophisticated testing and isolation strategies to study the effects of minimal-invasive infectious disease mitigation. With realistic human mobility patterns for the region of Brunswick, Germany, we study the effects of different interventions between March 1st and May 30, 2021 in the SARS-CoV-2 pandemic. Our analyses suggest that symptom-independent testing has limited impact on the mitigation of disease dynamics if the dark figure in symptomatic cases is high. Furthermore, we found that quarantine length is more important than quarantine efficiency but that, with sufficient symptomatic control, also short quarantines can have a substantial effect., Comment: 35 pages, 13 figures, to be submitted to Elsevier

Ordinary differential equations (ODE) are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the flow from one infection state to another. However, scientific experience yields more plausible distributions where the likelihood of disease progression or recovery changes accordingly with the duration spent in a particular state of the disease. Furthermore, transmission dynamics depend heavily on the infectiousness of individuals. The corresponding nonlinear variation with the time individuals have already spent in an infectious state requires more realistic models. The previously mentioned items are particularly crucial when modeling dynamics at change points such as the implementation of nonpharmaceutical interventions. In order to capture these aspects and to enhance the accuracy of simulations, integro-differential equations (IDE) can be used. In this paper, we propose a generalized model based on integro-differential equations with eight infection states. The model allows for variable stay time distributions and generalizes the concept of ODE-based models as well as IDE-based age-of-infection models. In this, we include particular infection states for severe and critical cases to allow for surveillance of the clinical sector, avoiding bottlenecks and overloads in critical epidemic situations. We will extend a recently introduced nonstandard numerical scheme to solve a simpler IDE-based model. This scheme is adapted to our more advanced model and we prove important mathematical and biological properties for the numerical solution. Furthermore, we validate our approach numerically by demonstrating the convergence rate. Eventually, we also show that our novel model is intrinsically capable of better assessing disease dynamics upon the introduction of nonpharmaceutical interventions.

Emerging infectious diseases and climate change are two of the major challenges in 21st century. Although over the past decades, highly-resolved mathematical models have contributed in understanding dynamics of infectious diseases and are of great aid when it comes to finding suitable intervention measures, they may need substantial computational effort and produce significant CO2 emissions. Two popular modeling approaches for mitigating infectious disease dynamics are agent-based and population-based models. Agent-based models (ABMs) offer a microscopic view and are thus able to capture heterogeneous human contact behavior and mobility patterns. However, insights on individual-level dynamics come with high computational effort that scales with the number of agents. On the other hand, population-based models using e.g. ordinary differential equations (ODEs) are computationally efficient even for large populations due to their complexity being independent of the population size. Yet, population-based models are restricted in their granularity as they assume a (to some extent) homogeneous and well-mixed population. To manage the trade-off between computational complexity and level of detail, we propose spatial- and temporal-hybrid models that use ABMs only in an area or time frame of interest. To account for relevant influences to disease dynamics, e.g., from outside, due to commuting activities, we use population-based models, only adding moderate computational costs. Our hybridization approach demonstrates significant reduction in computational effort by up to 98% -- without losing the required depth in information in the focus frame. Concluding, hybrid epidemiological models can provide insights on the individual scale where necessary, using aggregated models where possible, thereby making a contribution to green computing.

Visual analytics tools can help illustrate the spread of infectious diseases and enable informed decisions on epidemiological and public health issues. To create visualisation tools that are intuitive, easy to use, and effective in communicating information, continued research and development focusing on user-centric and methodological design models is extremely important. As a contribution to this topic, this paper presents the design and development process of the visual analytics application ESID (Epidemiological Scenarios for Infectious Diseases). ESID is a visual analytics tool aimed at projecting the future developments of infectious disease spread using reported and simulated data based on sound mathematical-epidemiological models. The development process involved a collaborative and participatory design approach with project partners from diverse scientific fields. The findings from these studies, along with the guidelines derived from them, played a pivotal role in shaping the visualisation tool., Comment: 7 pages, 4 images and 2 table, IEEE VIS Workshop on Visualization for Pandemic and Emergency Responses 2023 (Vis4PandEmRes)

The identification of abnormal behaviour in mechanical systems is key to anticipate and avoid their potential failure. Thus wind turbine health is commonly assessed monitoring series of $10$-minute SCADA and high frequency data from sensors. To monitor wind turbine vibrations, normal behaviour models are built to predict tower top accelerations and drive-train vibrations. Signal deviations from model prediction are labelled as anomalies and are further investigated. More efficient models are expected to help enhancing the identification of abnormal behaviour. In this paper we assess a stochastic approach to reconstruct the $1$ Hz tower top acceleration signal, which was measured in a wind turbine located at the wind farm Alpha Ventus in the German North Sea. We compare the resulting data reconstruction with that of a model based on a neural network, which has been previously reported as a data-mining algorithm suitable for reconstructing this signal. In order to focus the discussion on the similarities and differences of both approaches, we limit our evaluation to a single input-output system; in doing so, we avoid other differences, i.e. loading type, pre-processing or model complexity. Our results present evidence that the stochastic approach outperforms the neural network in the high frequency domain ($1$ Hz). Although neural network retrieve accurate step-forward predictions, with low mean square errors, the stochastic approach predictions better preserve the statistics and the frequency components of the original signal, remaining high accuracy levels. The implementation of our stochastic approach is available as open source code and can easily be adapted for other situations involving stochastic data reconstruction. Based on our findings we argue that such an approach could be implemented in signal reconstruction for monitoring purposes or for abnormal behaviour detection., Comment: 16 pages, 8 figures

Deep Neural Network (DNN) are currently of great inter- est in research and application. The training of these net- works is a compute intensive and time consuming task. To reduce training times to a bearable amount at reasonable cost we extend the popular Caffe toolbox for DNN with an efficient distributed memory communication pattern. To achieve good scalability we emphasize the overlap of computation and communication and prefer fine granu- lar synchronization patterns over global barriers. To im- plement these communication patterns we rely on the the Global address space Programming Interface version 2 (GPI-2) communication library. This interface provides a light-weight set of asynchronous one-sided communica- tion primitives supplemented by non-blocking fine gran- ular data synchronization mechanisms. Therefore, Caf- feGPI is the name of our parallel version of Caffe. First benchmarks demonstrate better scaling behavior com- pared with other extensions, e.g., the Intel TM Caffe. Even within a single symmetric multiprocessing machine with four graphics processing units, the CaffeGPI scales bet- ter than the standard Caffe toolbox. These first results demonstrate that the use of standard High Performance Computing (HPC) hardware is a valid cost saving ap- proach to train large DDNs. I/O is an other bottleneck to work with DDNs in a standard parallel HPC setting, which we will consider in more detail in a forthcoming paper.

In spring 2015, the Leibniz Supercomputing Centre (Leibniz-Rechenzentrum, LRZ), installed their new Peta-Scale System SuperMUC Phase2. Selected users were invited for a 28 day extreme scale-out block operation during which they were allowed to use the full system for their applications. The following projects participated in the extreme scale-out workshop: BQCD (Quantum Physics), SeisSol (Geophysics, Seismics), GPI-2/GASPI (Toolkit for HPC), Seven-League Hydro (Astrophysics), ILBDC (Lattice Boltzmann CFD), Iphigenie (Molecular Dynamic), FLASH (Astrophysics), GADGET (Cosmological Dynamics), PSC (Plasma Physics), waLBerla (Lattice Boltzmann CFD), Musubi (Lattice Boltzmann CFD), Vertex3D (Stellar Astrophysics), CIAO (Combustion CFD), and LS1-Mardyn (Material Science). The projects were allowed to use the machine exclusively during the 28 day period, which corresponds to a total of 63.4 million core-hours, of which 43.8 million core-hours were used by the applications, resulting in a utilization of 69%. The top 3 users were using 15.2, 6.4, and 4.7 million core-hours, respectively., Comment: 10 pages, 5 figures, presented at ParCo2015 - Advances in Parallel Computing, held in Edinburgh, September 2015. The final publication is available at IOS Press through http://dx.doi.org/10.3233/978-1-61499-621-7-827

The paper presents a stochastic approach to estimate the aerodynamic forces with local dynamics on wind turbine blades in unsteady wind inflow. This is done by integrating a stochastic model of lift and drag dynamics for an airfoil into the aerodynamic simulation software AeroDyn. The model is added as an alternative to the static table lookup approach in blade element momentum (BEM) wake model used by AeroDyn. The stochastic forces are obtained for a rotor blade element using full field turbulence simulated wind data input and compared with the classical BEM and dynamic stall models for identical conditions. The comparison shows that the stochastic model generates additional extended dynamic response in terms of local force fluctuations. Further, the comparison of statistics between the classical BEM, dynamic stall and stochastic models' results in terms of their increment probability density functions gives consistent results.