arXiv subjects

Benjamin Seibold

Publications and source records attributed to Benjamin Seibold.

At least 19 recordsLinked to original sources

arXiv2026

Adaptive Diagonally Implicit Runge-Kutta Methods Devoid of Order Reduction for Semilinear ODEs

Diagonally implicit Runge-Kutta (DIRK) methods are a prominent class of numerical methods for solving stiff systems of ordinary differential equations (ODEs). Stiffness does not only impose stability challenges on Runge-Kutta methods; it can also degrade the order of convergence. This so-called order reduction phenomenon occurs when assumptions used for classical convergence analysis, e.g., an asymptotically small step size, fail to hold. In a prior paper by the authors, sharp order conditions and global error bounds for Runge-Kutta methods were developed, which hold uniformly with respect to stiffness when applied to a wide class of semilinear ODEs. In this work, those conditions are leveraged to construct the first DIRK methods of order four and five which satisfy these conditions and thus do not exhibit order reduction. Numerical results demonstrate that for a broad class of relevant nonlinear test problems, these new methods successfully mitigate order reduction, accurately estimate local error via an embedding for adaptive step size control, and can outperform classical DIRK methods.

math.NA↗

arXiv2025

A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs

Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic degradation in accuracy, known as order reduction, can arise. Methods with high stage order, e.g., Gauss-Legendre and Radau, are known to avoid order reduction, but they must be fully implicit. For the broad class of semilinear ODEs, which consist of a stiff linear term and non-stiff nonlinear term, we show that weaker conditions suffice. Our new semilinear order conditions are formulated in terms of orthogonality relations and can be enumerated by rooted trees. Finally, we prove global error bounds that hold uniformly with respect to stiffness of the linear term.

math.NA↗

arXiv2025

Validation and Calibration of Energy Models with Real Vehicle Data from Chassis Dynamometer Experiments

Accurate estimation of vehicle fuel consumption typically requires detailed modeling of complex internal powertrain dynamics, often resulting in computationally intensive simulations. However, many transportation applications-such as traffic flow modeling, optimization, and control-require simplified models that are fast, interpretable, and easy to implement, while still maintaining fidelity to physical energy behavior. This work builds upon a recently developed model reduction pipeline that derives physics-like energy models from high-fidelity Autonomie vehicle simulations. These reduced models preserve essential vehicle dynamics, enabling realistic fuel consumption estimation with minimal computational overhead. While the reduced models have demonstrated strong agreement with their Autonomie counterparts, previous validation efforts have been confined to simulation environments. This study extends the validation by comparing the reduced energy model's outputs against real-world vehicle data. Focusing on the MidSUV category, we tune the baseline Autonomie model to closely replicate the characteristics of a Toyota RAV4. We then assess the accuracy of the resulting reduced model in estimating fuel consumption under actual drive conditions. Our findings suggest that, when the reference Autonomie model is properly calibrated, the simplified model produced by the reduction pipeline can provide reliable, semi-principled fuel rate estimates suitable for large-scale transportation applications.

eess.SY↗

arXiv2024

Designing, simulating, and performing the 100-AV field test for the CIRCLES consortium: Methodology and Implementation of the Largest mobile traffic control experiment to date

Previous controlled experiments on single-lane ring roads have shown that a single partially autonomous vehicle (AV) can effectively mitigate traffic waves. This naturally prompts the question of how these findings can be generalized to field operational, high-density traffic conditions. To address this question, the Congestion Impacts Reduction via CAV-in-the-loop Lagrangian Energy Smoothing (CIRCLES) Consortium conducted MegaVanderTest (MVT), a live traffic control experiment involving 100 vehicles near Nashville, TN, USA. This article is a tutorial for developing analytical and simulation-based tools essential for designing and executing a live traffic control experiment like the MVT. It presents an overview of the proposed roadmap and various procedures used in designing, monitoring, and conducting the MVT, which is the largest mobile traffic control experiment at the time. The design process is aimed at evaluating the impact of the CIRCLES AVs on surrounding traffic. The article discusses the agent-based traffic simulation framework created for this evaluation. A novel methodological framework is introduced to calibrate this microsimulation, aiming to accurately capture traffic dynamics and assess the impact of adding 100 vehicles to existing traffic. The calibration model's effectiveness is verified using data from a six-mile section of Nashville's I-24 highway. The results indicate that the proposed model establishes an effective feedback loop between the optimizer and the simulator, thereby calibrating flow and speed with different spatiotemporal characteristics to minimize the error between simulated and real-world data. Finally, We simulate AVs in multiple scenarios to assess their effect on traffic congestion. This evaluation validates the AV routes, thereby contributing to the execution of a safe and successful live traffic control experiment via AVs.

eess.SY↗

arXiv2024

Hierarchical Speed Planner for Automated Vehicles: A Framework for Lagrangian Variable Speed Limit in Mixed Autonomy Traffic

This paper introduces a novel control framework for Lagrangian variable speed limits in hybrid traffic flow environments utilizing automated vehicles (AVs). The framework was validated using a fleet of 100 connected automated vehicles as part of the largest coordinated open-road test designed to smooth traffic flow. The framework includes two main components: a high-level controller deployed on the server side, named Speed Planner, and low-level controllers called vehicle controllers deployed on the vehicle side. The Speed Planner designs and updates target speeds for the vehicle controllers based on real-time Traffic State Estimation (TSE) [1]. The Speed Planner comprises two modules: a TSE enhancement module and a target speed design module. The TSE enhancement module is designed to minimize the effects of inherent latency in the received traffic information and to improve the spatial and temporal resolution of the input traffic data. The target speed design module generates target speed profiles with the goal of improving traffic flow. The vehicle controllers are designed to track the target speed meanwhile responding to the surrounding situation. The numerical simulation indicates the performance of the proposed method: the bottleneck throughput has increased by 5.01%, and the speed standard deviation has been reduced by a significant 34.36%. We further showcase an operational study with a description of how the controller was implemented on a field-test with 100 AVs and its comprehensive effects on the traffic flow.

eess.SY↗

arXiv2024

Traffic Control via Connected and Automated Vehicles: An Open-Road Field Experiment with 100 CAVs

The CIRCLES project aims to reduce instabilities in traffic flow, which are naturally occurring phenomena due to human driving behavior. These "phantom jams" or "stop-and-go waves,"are a significant source of wasted energy. Toward this goal, the CIRCLES project designed a control system referred to as the MegaController by the CIRCLES team, that could be deployed in real traffic. Our field experiment leveraged a heterogeneous fleet of 100 longitudinally-controlled vehicles as Lagrangian traffic actuators, each of which ran a controller with the architecture described in this paper. The MegaController is a hierarchical control architecture, which consists of two main layers. The upper layer is called Speed Planner, and is a centralized optimal control algorithm. It assigns speed targets to the vehicles, conveyed through the LTE cellular network. The lower layer is a control layer, running on each vehicle. It performs local actuation by overriding the stock adaptive cruise controller, using the stock on-board sensors. The Speed Planner ingests live data feeds provided by third parties, as well as data from our own control vehicles, and uses both to perform the speed assignment. The architecture of the speed planner allows for modular use of standard control techniques, such as optimal control, model predictive control, kernel methods and others, including Deep RL, model predictive control and explicit controllers. Depending on the vehicle architecture, all onboard sensing data can be accessed by the local controllers, or only some. Control inputs vary across different automakers, with inputs ranging from torque or acceleration requests for some cars, and electronic selection of ACC set points in others. The proposed architecture allows for the combination of all possible settings proposed above. Most configurations were tested throughout the ramp up to the MegaVandertest.

eess.SY↗

arXiv2024

Reinforcement Learning Based Oscillation Dampening: Scaling up Single-Agent RL algorithms to a 100 AV highway field operational test

In this article, we explore the technical details of the reinforcement learning (RL) algorithms that were deployed in the largest field test of automated vehicles designed to smooth traffic flow in history as of 2023, uncovering the challenges and breakthroughs that come with developing RL controllers for automated vehicles. We delve into the fundamental concepts behind RL algorithms and their application in the context of self-driving cars, discussing the developmental process from simulation to deployment in detail, from designing simulators to reward function shaping. We present the results in both simulation and deployment, discussing the flow-smoothing benefits of the RL controller. From understanding the basics of Markov decision processes to exploring advanced techniques such as deep RL, our article offers a comprehensive overview and deep dive of the theoretical foundations and practical implementations driving this rapidly evolving field. We also showcase real-world case studies and alternative research projects that highlight the impact of RL controllers in revolutionizing autonomous driving. From tackling complex urban environments to dealing with unpredictable traffic scenarios, these intelligent controllers are pushing the boundaries of what automated vehicles can achieve. Furthermore, we examine the safety considerations and hardware-focused technical details surrounding deployment of RL controllers into automated vehicles. As these algorithms learn and evolve through interactions with the environment, ensuring their behavior aligns with safety standards becomes crucial. We explore the methodologies and frameworks being developed to address these challenges, emphasizing the importance of building reliable control systems for automated vehicles.

eess.SY↗

arXiv2023

Enabling Mixed Autonomy Traffic Control

We demonstrate a new capability of automated vehicles: mixed autonomy traffic control. With this new capability, automated vehicles can shape the traffic flows composed of other non-automated vehicles, which has the promise to improve safety, efficiency, and energy outcomes in transportation systems at a societal scale. Investigating mixed autonomy mobile traffic control must be done in situ given that the complex dynamics of other drivers and their response to a team of automated vehicles cannot be effectively modeled. This capability has been blocked because there is no existing scalable and affordable platform for experimental control. This paper introduces an extensible open-source hardware and software platform, enabling a team of 100 vehicles to execute several different vehicular control algorithms as a collaborative fleet, composed of three different makes and models, which drove 22752 miles in a combined 1022 hours, over 5 days in Nashville, TN in November 2022.

cs.RO↗

arXiv2023

Traffic smoothing using explicit local controllers

The dissipation of stop-and-go waves attracted recent attention as a traffic management problem, which can be efficiently addressed by automated driving. As part of the 100 automated vehicles experiment named MegaVanderTest, feedback controls were used to induce strong dissipation via velocity smoothing. More precisely, a single vehicle driving differently in one of the four lanes of I-24 in the Nashville area was able to regularize the velocity profile by reducing oscillations in time and velocity differences among vehicles. Quantitative measures of this effect were possible due to the innovative I-24 MOTION system capable of monitoring the traffic conditions for all vehicles on the roadway. This paper presents the control design, the technological aspects involved in its deployment, and, finally, the results achieved by the experiment.

eess.SY↗

arXiv2023

Reducing Detailed Vehicle Energy Dynamics to Physics-Like Models

The energy demand of vehicles, particularly in unsteady drive cycles, is affected by complex dynamics internal to the engine and other powertrain components. Yet, in many applications, particularly macroscopic traffic flow modeling and optimization, structurally simple approximations to the complex vehicle dynamics are needed that nevertheless reproduce the correct effective energy behavior. This work presents a systematic model reduction pipeline that starts from complex vehicle models based on the Autonomie software and derives a hierarchy of simplified models that are fast to evaluate, easy to disseminate in open-source frameworks, and compatible with optimization frameworks. The pipeline, based on a virtual chassis dynamometer and subsequent approximation strategies, is reproducible and is applied to six different vehicle classes to produce concrete explicit energy models that represent an average vehicle in each class and leverage the accuracy and validation work of the Autonomie software.

eess.SY↗

arXiv2023

Macroscopic Manifestations of Traffic Waves in Microscopic Models

Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture the dynamics of real traffic flow. In this study, we isolate car-following dynamics and present a systematic hierarchy of tests that connect the microscopic scale with the meaningful macroscopic effective state in the presence of waves. This allows insights with precise attributable cause-to-effect relationships of specific observed traffic patterns. We establish a principled way of generating macroscopic flow quantities from microscopic models in the unstable regime. Those quantities are then used to study how the corresponding non-equilibrium wave structures manifest in the fundamental diagram, based on three basic scenarios that can serve as building blocks for understanding more complex micro-simulation studies. Finally, this study gives insight on the shapes of the reduced fundamental diagrams for different commonly used microscopic models.

physics.soc-ph↗

arXiv2023

Explicit Runge Kutta Methods that Alleviate Order Reduction

Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee high-order convergence for linear problems; we refer to these conditions as weak stage order conditions. We prove a general relationship between the method's order, weak stage order, and number of stages. We derive explicit RK methods with high weak stage order and demonstrate, through numerical tests, that they avoid the order reduction phenomenon up to any order for linear problems and up to order three for nonlinear problems.

math.NA↗

arXiv2023

So you think you can track?

This work introduces a multi-camera tracking dataset consisting of 234 hours of video data recorded concurrently from 234 overlapping HD cameras covering a 4.2 mile stretch of 8-10 lane interstate highway near Nashville, TN. The video is recorded during a period of high traffic density with 500+ objects typically visible within the scene and typical object longevities of 3-15 minutes. GPS trajectories from 270 vehicle passes through the scene are manually corrected in the video data to provide a set of ground-truth trajectories for recall-oriented tracking metrics, and object detections are provided for each camera in the scene (159 million total before cross-camera fusion). Initial benchmarking of tracking-by-detection algorithms is performed against the GPS trajectories, and a best HOTA of only 9.5% is obtained (best recall 75.9% at IOU 0.1, 47.9 average IDs per ground truth object), indicating the benchmarked trackers do not perform sufficiently well at the long temporal and spatial durations required for traffic scene understanding.

cs.CV↗

arXiv2023

Moment Methods for Advection on Networks and an Application to Forest Pest Life Cycle Models

This paper develops low-dimensional moment methods for advective problems on networks of domains. The evolution of a density function is described by a linear advection-diffusion-reaction equation on each domain, combined via advective flux coupling across domains in the network graph. The PDEs' coefficients vary in time and across domains but they are fixed along each domain. As a result, the solution on each domain is frequently close to a Gaussian that moves, decays, and widens. For that reason, this work studies moment methods that track only three degrees of freedom per domain -- in contrast to traditional PDE discretization methods that tend to require many more variables per domain. A simple ODE-based moment method is developed, as well as an asymptotic-preserving scheme. We apply the methodology to an application that models the life cycle of forest pests that undergo different life stages and developmental pathways. The model is calibrated for the spotted lanternfly, an invasive species present in the Eastern USA. We showcase that the moment method, despite its significant low-dimensionality, can successfully reproduce the prediction of the pest's establishment potential, compared to much higher-dimensional computational approaches.

math.NA↗

arXiv2022

Design of DIRK Schemes with High Weak Stage Order

Runge-Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order, DIRK (diagonally implicit Runge-Kutta) schemes are practically important due to their structural simplicity; however, these cannot possess high stage order. The concept of weak stage order (WSO) can also overcome order reduction, and it is compatible with the DIRK structure. DIRK schemes of WSO up to 3 have been proposed in the past, however, based on a simplified framework that cannot be extended beyond WSO 3. In this work a general theory of WSO is employed to overcome the prior WSO barrier and to construct practically useful high-order DIRK schemes with WSO 4 and above. The resulting DIRK schemes are stiffly accurate, L-stable, have optimized error coefficients, and are demonstrated to perform well on a portfolio of relevant ODE and PDE test problems.

math.NA↗

arXiv2022

Algebraic Structure of the Weak Stage Order Conditions for Runge-Kutta Methods

Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff problems. For linear problems with time-independent operators, order reduction can be avoided if the method satisfies certain weak stage order (WSO) conditions, which are less restrictive than traditional stage order conditions. This paper outlines the first algebraic theory of WSO, and establishes general order barriers that relate the WSO of a RK scheme to its order and number of stages for both fully-implicit and DIRK schemes. It is shown in several scenarios that the constructed bounds are sharp. The theory characterizes WSO in terms of orthogonal invariant subspaces and associated minimal polynomials. The resulting necessary conditions on the structure of RK methods with WSO are then shown to be of practical use for the construction of such schemes.

math.NA↗

arXiv2021

Temperature sensitivity of pest reproductive numbers in age-structured PDE models, with a focus on the invasive spotted lanternfly

Invasive pest establishment is a pervasive threat to global ecosystems, agriculture, and public health. The recent establishment of the invasive spotted lanternfly in the northeastern United States has proven devastating to farms and vineyards, necessitating urgent development of population dynamical models and effective control practices. In this paper, we propose a stage- and age-structured system of PDEs to model insect pest populations, in which underlying dynamics are dictated by ambient temperature through rates of development, fecundity, and mortality. The model incorporates diapause and non-diapause pathways, and is calibrated to experimental and field data on the spotted lanternfly. We develop a novel moving mesh method for capturing age-advection accurately, even for coarse discretization parameters. We define a one-year reproductive number ($R_0$) from the spectrum of a one-year solution operator, and study its sensitivity to variations in the mean and amplitude of the annual temperature profile. We quantify assumptions sufficient to give rise to the low-rank structure of the solution operator characteristic of part of the parameter domain. We discuss establishment potential as it results from the pairing of a favorable $R_0$ value and transient population survival, and address implications for pest control strategies.

q-bio.PE↗

arXiv2021

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

In light of the recently published complete set of statistically correct Gronbech-Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has at least weak second order accuracy in the applied time step. It further helps identify a novel half-step velocity, which simultaneously produces both correct kinetic statistics and correct transport measures for any of the statistically sound GJ methods. Explicit algorithmic expressions are given for the integration of the new half-step velocity into the GJ set of methods. Numerical simulations, including quantum-based molecular dynamics (QMD) using the QMD suite LATTE, highlight the discussed properties of the algorithms as well as exhibit the direct application of robust, time step independent stochastic integrators to quantum-based molecular dynamics.

physics.comp-ph↗