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Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method converges slowly or not at all. This article introduces a novel parallel implementation of a two-level nonlinear Schwarz solver based on the FROSch (Fast and Robust Overlapping Schwarz) solver framework, part of Sandia's Trilinos library. First, an introduction to the key concepts underlying two-level nonlinear Schwarz methods is given, including a brief overview of the coarse space used to build the second level. Next, the parallel implementation is discussed, followed by preliminary parallel results for a scalar nonlinear diffusion problem and a 2D nonlinear plane-stress Neo-Hooke elasticity problem with large deformations.

In many modern computer application problems, the classification of image data plays an important role. Among many different supervised machine learning models, convolutional neural networks (CNNs) and linear discriminant analysis (LDA) as well as sophisticated variants thereof are popular techniques. In this work, two different domain decomposed CNN models are experimentally compared for different image classification problems. Both models are loosely inspired by domain decomposition methods and in addition, combined with a transfer learning strategy. The resulting models show improved classification accuracies compared to the corresponding, composed global CNN model without transfer learning and besides, also help to speed up the training process. Moreover, a novel decomposed LDA strategy is proposed which also relies on a localization approach and which is combined with a small neural network model. In comparison with a global LDA applied to the entire input data, the presented decomposed LDA approach shows increased classification accuracies for the considered test problems.

Nonlinear domain decomposition methods became popular in recent years since they can improve the nonlinear convergence behavior of Newton's method significantly for many complex problems. In this article, a nonlinear two-level Schwarz approach is considered and, for the first time, equipped with monolithic GDSW (Generalized Dryja-Smith-Widlund) coarse basis functions for the Navier-Stokes equations. Results for lid-driven cavity problems with high Reynolds numbers are presented and compared with classical global Newton's method equipped with a linear Schwarz preconditioner. Different options, for example, local pressure corrections on the subdomain and recycling of coarse basis functions are discussed in the nonlinear Schwarz approach for the first time.

The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the resulting linear systems are often ill-conditioned and robust preconditioning techniques are necessary for an iterative solution. Here, a balancing domain decomposition by constraints (BDDC) preconditioner is considered. Techniques to enrich the coarse space of BDDC applied to a Stokes problem with heterogeneous viscosity are proposed. In this framework a comparison between two adaptive techniques and a computationally cheaper heuristic approach is carried out. Numerical results computed on a physically realistic model show that the latter approach in combination with the deluxe scaling is a promising alternative.

Deep convolutional neural networks (CNNs) have been shown to be very successful in a wide range of image processing applications. However, due to their increasing number of model parameters and an increasing availability of large amounts of training data, parallelization strategies to efficiently train complex CNNs are necessary. In previous work by the authors, a novel model parallel CNN architecture was proposed which is loosely inspired by domain decomposition. In particular, the novel network architecture is based on a decomposition of the input data into smaller subimages. For each of these subimages, local CNNs with a proportionally smaller number of parameters are trained in parallel and the resulting local classifications are then aggregated in a second step by a dense feedforward neural network (DNN). In the present work, we compare the resulting CNN-DNN architecture to less costly alternatives to combine the local classifications into a final, global decision. Additionally, we investigate the performance of the CNN-DNN trained as one coherent model as well as using a transfer learning strategy, where the parameters of the pre-trained local CNNs are used as initial values for a subsequently trained global coherent CNN-DNN model.

Highly resolved finite element simulations of a laser beam welding process are considered. The thermomechanical behavior of this process is modeled with a set of thermoelasticity equations resulting in a nonlinear, nonsymmetric saddle point system. Newton's method is used to solve the nonlinearity and suitable domain decomposition preconditioners are applied to accelerate the convergence of the iterative method used to solve all linearized systems. Since a onelevel Schwarz preconditioner is in general not scalable, a second level has to be added. Therefore, the construction and numerical analysis of a monolithic, twolevel overlapping Schwarz approach with the GDSW (Generalized Dryja-Smith-Widlund) coarse space and an economic variant thereof are presented here.

For scientific software, especially those used for large-scale simulations, achieving good performance and efficiently using the available hardware resources is essential. It is important to regularly perform benchmarks to ensure the efficient use of hardware and software when systems are changing and the software evolves. However, this can become quickly very tedious when many options for parameters, solvers, and hardware architectures are available. We present a continuous benchmarking strategy that automates benchmarking new code changes on high-performance computing clusters. This makes it possible to track how each code change affects the performance and how it evolves.

The morphology of nanostructured materials exhibiting a polydisperse porous space, such as aerogels, is very open porous and fine grained. Therefore, a simulation of the deformation of a large aerogel structure resolving the nanostructure would be extremely expensive. Thus, multi-scale or homogenization approaches have to be considered. Here, a computational scale bridging approach based on the FE$^2$ method is suggested, where the macroscopic scale is discretized using finite elements while the microstructure of the open-porous material is resolved as a network of Euler-Bernoulli beams. Here, the beam frame based RVEs (representative volume elements) have pores whose size distribution follows the measured values for a specific material. This is a well-known approach to model aerogel structures. For the computational homogenization, an approach to average the first Piola-Kirchhoff stresses in a beam frame by neglecting rotational moments is suggested. To further overcome the computationally most expensive part in the homogenization method, that is, solving the RVEs and averaging their stress fields, a surrogate model is introduced based on neural networks. The networks input is the localized deformation gradient on the macroscopic scale and its output is the averaged stress for the specific material. It is trained on data generated by the beam frame based approach. The effiency and robustness of both homogenization approaches is shown numerically, the approximation properties of the surrogate model is verified for different macroscopic problems and discretizations. Different (Quasi-)Newton solvers are considered on the macroscopic scale and compared with respect to their convergence properties.

While linear FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) is an efficient iterative domain decomposition solver for discretized linear PDEs (partial differential equations), nonlinear FETI-DP is its consequent extension to the nonlinear case. In both methods, the parallel efficiency of the method results from a decomposition of the computational domain into nonoverlapping subdomains and a resulting localization of the computational work. For a fast linear convergence of the linear FETI-DP method, a global coarse problem has to be considered. Adaptive coarse spaces are provably robust variants for many complicated micro-heterogeneous problems, as, for example, stationary diffusion problems with large jumps in the diffusion coefficient. Unfortunately, the set-up and exact computation of adaptive coarse spaces is known to be computationally expensive. Therefore, recently, surrogate models based on neural networks have been trained to directly predict the adaptive coarse constraints. Here, these learned constraints are implemented in nonlinear FETI-DP and it is shown numerically that they are able to improve the nonlinear as well as linear convergence speed of nonlinear FETI-DP.

Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning and various industrial domains, especially in computational science and engineering. In the present survey, several promising avenues of research will be examined which focus on the combination of machine learning (ML) and domain decomposition methods (DDMs). The aim of this survey is to provide an overview of existing work within this field and to structure it into domain decomposition for machine learning and machine learning-enhanced domain decomposition, including: domain decomposition for classical machine learning, domain decomposition to accelerate the training of physics-aware neural networks, machine learning to enhance the convergence properties or computational efficiency of DDMs, and machine learning as a discretization method in a DDM for the solution of PDEs. In each of these fields, we summarize existing work and key advances within a common framework and, finally, disuss ongoing challenges and opportunities for future research.

Automated vehicle acceptance (AVA) has been measured mostly subjectively by questionnaires and interviews, with a main focus on drivers inside automated vehicles (AVs). To ensure that AVs are widely accepted by the public, ensuring the acceptance by both drivers and passengers is key. The in-vehicle experience of passengers will determine the extent to which AVs will be accepted by passengers. A comprehensive understanding of potential assessment methods to measure the passenger experience in AVs is needed to improve the in-vehicle experience of passengers and thereby the acceptance. The present work provides an overview of assessment methods that were used to measure a driver's behavior, and cognitive and emotional states during (automated) driving. The results of the review have shown that these assessment methods can be classified by type of data-collection method (e.g., questionnaires, interviews, direct input devices, sensors), object of their measurement (i.e., perception, behavior, state), time of measurement, and degree of objectivity of the data collected. A conceptual model synthesizes the results of the literature review, formulating relationships between the factors constituting the in-vehicle experience and AVA acceptance. It is theorized that the in-vehicle experience influences the intention to use, with intention to use serving as predictor of actual use. The model also formulates relationships between actual use and well-being. A combined approach of using both subjective and objective assessment methods is needed to provide more accurate estimates for AVA, and advance the uptake and use of AVs., Comment: 22 pages, 1 figure

This paper introduces decentralized control concepts for drones using differential game theory. The approach optimizes the behavior of an ego drone, assuming the anticipated behavior of the opponent drones using a receding horizon approach. For each control instant, the scheme computes the Nash equilibrium control signal which is applied for the control period. This results in a multi-drone conflict resolution scheme that is applied to all drones considered. The paper discusses the approach and presents the numerical algorithm, showing several examples that illustrate the performance of the model. We examine at the behavior of the ego drone, and the resulting collective drone flow operations. The latter shows that while the approach aims to optimize the operation cost of the ego drone, the experiments provide evidence that resulting flow operations are very efficient due to the self-organization of various flow patterns. The presented work contributes to the state of the art in providing a generic approach to multi-drone conflict resolution with good macroscopic flow performance characteristics. The approach enables relatively straightforward inclusion of error due to sensing and communication. The approach also allows for including different risk levels (e.g., for malfunctioning of sensor and communication technology), priority rules, regulations, and higher-level control signals (e.g., routing, dynamic speed limits)., Comment: Submitted to the TRB Annual Meeting 2024

This paper presents novel technology and methodology aimed at enhancing crowd management in both the planning and operational phases. The approach encompasses innovative data collection techniques, data integration, and visualization using a 3D Digital Twin, along with the incorporation of artificial intelligence (AI) tools for risk identification. The paper introduces the Bowtie model, a comprehensive framework designed to assess and predict risk levels. The model combines objective estimations and predictions, such as traffic flow operations and crowdedness levels, with various aggravating factors like weather conditions, sentiments, and the purpose of visitors, to evaluate the expected risk of incidents. The proposed framework is applied to the Crowd Safety Manager project in Scheveningen, where the DigiTwin is developed based on a wealth of real-time data sources. One noteworthy data source is Resono, offering insights into the number of visitors and their movements, leveraging a mobile phone panel of over 2 million users in the Netherlands. Particular attention is given to the left-hand side of the Bowtie, which includes state estimation, prediction, and forecasting. Notably, the focus is on generating multi-day ahead forecasts for event-planning purposes using Resono data. Advanced machine learning techniques, including the XGBoost framework, are compared, with XGBoost demonstrating the most accurate forecasts. The results indicate that the predictions are adequately accurate. However, certain locations may benefit from additional input data to further enhance prediction quality. Despite these limitations, this work contributes to a more effective crowd management system and opens avenues for further advancements in this critical field., Comment: Submitted to TRB Annual Meeting 2024

Deep neural networks (DNNs) and, in particular, convolutional neural networks (CNNs) have brought significant advances in a wide range of modern computer application problems. However, the increasing availability of large amounts of datasets as well as the increasing available computational power of modern computers lead to a steady growth in the complexity and size of DNN and CNN models, respectively, and thus, to longer training times. Hence, various methods and attempts have been developed to accelerate and parallelize the training of complex network architectures. In this work, a novel CNN-DNN architecture is proposed that naturally supports a model parallel training strategy and that is loosely inspired by two-level domain decomposition methods (DDM). First, local CNN models, that is, subnetworks, are defined that operate on overlapping or nonoverlapping parts of the input data, for example, sub-images. The subnetworks can be trained completely in parallel and independently of each other. Each subnetwork then outputs a local decision for the given machine learning problem which is exclusively based on the respective local input data. Subsequently, in a second step, an additional DNN model is trained which evaluates the local decisions of the local subnetworks and generates a final, global decision. In this paper, we apply the proposed architecture to image classification problems using CNNs. Experimental results for different 2D image classification problems are provided as well as a face recognition problem, and a classification problem for 3D computer tomography (CT) scans. Therefore, classical ResNet and VGG architectures are considered. The results show that the proposed approach can significantly accelerate the required training time compared to the global model and, additionally, can also help to improve the accuracy of the underlying classification problem., Comment: Revised version; Accepted for publication in SIAM Journal on Scientific Computing; Date of acceptance: May 16, 2024

Understanding user's perception of service variability is essential to discern their overall perception of any type of (transport) service. We study the perception of waiting time variability for ride-hailing services. We carried out a stated preference survey in August 2021, yielding 936 valid responses. The respondents were faced with static pre-trip information on the expected waiting time, followed by the actually experienced waiting time for their selected alternative. We analyse this data by means of an instance-based learning (IBL) approach to evaluate how individuals respond to service performance variation and how this impacts their future decisions. Different novel specifications of memory fading, captured by the IBL approach, are tested to uncover which describes the user behaviour best. Additionally, existing and new specification of inertia (habit) are tested. Our model outcomes reveal that the perception of unexpected waiting time is within the expected range of 2-3 times the value-of-time. Travellers seem to place a higher reward on an early departure compared to a penalty for a late departure of equal magnitude. A cancelled service, after having made a booking, results in significant disutility for the passenger and a strong motivation to shift to a different provider. Considering memory decay, our results show that the most recent experience is by far the most relevant for the next decision, with memories fading quickly in importance. The role of inertia seems to gain importance with each additional consecutive choice for the same option, but then resetting back to zero following a shift in behaviour.

On-demand mobility services (FLEX) are often proposed as a solution for the first/last mile problem. We study the potential of using FLEX to improve train station access by means of a three-step sequential stated preference survey. We compare FLEX with the bicycle, car and public transport for accessing two alternative train stations. We estimate a joint access mode and train station choice model. Estimating a latent class choice model with different nesting structures, we uncover four distinct segments in the population. Two segments (~50%) with a lower Willingness-to-Pay seem to be more likely to take-up FLEX. Ex-urban car drivers seem to be the most likely segment to adopt FLEX, showing great, since members of this segment are currently frequent users of the private car. Our case study also shows that while FLEX competes primarily with public transport when accessing local stations, it competes primarily with car for reaching distant stations.

On-demand mobility services are promising to revolutionise urban travel, but preliminary studies are showing they may actually increase total vehicle miles travelled, worsening road congestion in cities. In this study, we assess the demand for on-demand mobility services in urban areas, using a stated preference survey, to understand the potential impact of introducing on-demand services on the current modal split. The survey was carried out in the Netherlands and offered respondents a choice between bike, car, public transport and ondemand services. 1,063 valid responses are analysed with a multinomial logit and a latent class choice model. By means of the latter, we uncover four distinctive groups of travellers based on the observed choice behaviour. The majority of the sample, the Sharing-ready cyclists (55%), are avid cyclists and do not see on-demand mobility as an alternative for making urban trips. Two classes, Tech-ready individuals (27%) and Flex-ready individuals (9%) would potentially use on-demand services: the former is fairly time-sensitive and would thus use on-demand service if they were sufficiently fast. The latter is highly costsensitive, and would therefore use the service primarily if it is cheap. The fourth class, Flex-sceptic individuals (9%) shows very limited potential for using on-demand services., Comment: Transportation (2022)