Thesis: S.M., Massachusetts Institute of Technology, Center for Computational Science & Engineering, February, 2021 / Cataloged from the official PDF version of thesis. / Includes bibliographical references (pages 55-61). / We develop an exact partial differential equation-based methodology that predicts time-energy optimal paths for autonomous vehicles navigating in dynamic environments. The differential equations solve the multi-objective optimization problem of navigating a vehicle autonomously in a dynamic flow field to any destination with the goal of minimizing travel time and energy use. Based on Hamilton-Jacobi theory for reachability and the level set method, the methodology computes the exact Pareto optimal solutions to the multi-objective path planning problem, numerically solving the equations governing time-energy reachability fronts and optimal paths. Our approach is applicable to path planning in various scenarios, however we primarily present examples of navigating in dynamic marine environments. First, we validate the methodology through a benchmark case of crossing a steady front (a highway flow) for which we compare our results to semi-analytical optimal path solutions. We then consider more complex unsteady environments and solve for time-energy optimal missions in a quasi-geostrophic double-gyre ocean flow field. / by Manan Doshi. / S.M. / S.M. Massachusetts Institute of Technology, Center for Computational Science & Engineering

Thesis: S.M., Massachusetts Institute of Technology, Center for Computational Science & Engineering, February, 2021 / Cataloged from the official PDF version of thesis. / Includes bibliographical references (pages 145-151). / Though computing power continues to grow quickly, our appetite to solve larger and larger problems grows just as fast. As a consequence, reduced-order modeling has become an essential technique in the computational scientist's toolbox. By reducing the dimensionality of a system, we are able to obtain approximate solutions to otherwise intractable problems. And because the methodology we develop is sufficiently general, we may agnostically apply it to a plethora of problems, whether the high dimensionality arises due to the sheer size of the computational domain, the fine resolution we require, or stochasticity of the dynamics. In this thesis, we develop time integration schemes, called retractions, to efficiently evolve the dynamics of a system's low-rank approximation. Through the study of differential geometry, we are able to analyze the error incurred at each time step. A novel, explicit, computationally inexpensive set of algorithms, which we call perturbative retractions, are proposed that converge to an ideal retraction that projects exactly to the manifold of fixed-rank matrices. Furthermore, each perturbative retraction itself exhibits high-order convergence to the best low-rank approximation of the full-rank solution. We show that these high-order retractions significantly reduce the numerical error incurred over time when compared to a naive Euler forward retraction. Through test cases, we demonstrate their efficacy in the cases of matrix addition, real-time data compression, and deterministic and stochastic differential equations. / by Aaron Charous. / S.M. / S.M. Massachusetts Institute of Technology, Center for Computational Science & Engineering

Thesis: S.M., Massachusetts Institute of Technology, Center for Computational Science and Engineering, 2020 / Cataloged from student-submitted PDF version of thesis. / Includes bibliographical references (pages 77-79). / Many smallholder farmers in developing countries struggle to make ends meet. We develop a model that examines how markets catering to numerous smallholder farmers reach an equilibrium, while incorporating real world challenges that smallholder farmers face, namely a lack of long term planning and cash constraints. Through this, we analyze the effectiveness of two common forms of government intervention, storage and loan provision. We fully characterize market equilibrium conditions under the base scenario of no government intervention, analyzing how price conditions, number of farmers, and severity of cash constraints impact farmer behaviour. We then illustrate how these results change when storage and loans are integrated into the model. The analysis demonstrates that myopic optimization and cash constraints induce farmers to make sub-optimal decisions, resulting in farmers not receiving the full benefit of government interventions. We show that while storage is always useful in situations where farmers have excess quantity, providing overly generous loan terms can negatively impact farmer revenue by disincentivizing farmers from selling their produce on the market. We also show that attempting to improve equality by alleviating farmer cash constraints can result in negative externalities like increased wastage. Empirical analysis with Bengal gram farmers in India shows that farmers are in dire need of government assistance to meet their cash constraints. However, improving loan terms only boosts farmer revenue up to a point, after which revenue declines. The analysis shows that while loan schemes are widely popular and sometimes necessary in aiding struggling farmers, governments should be aware that the strategic response of different farmers can result in adverse effects. / by Kenneth Pay. / S.M. / S.M. Massachusetts Institute of Technology, Center for Computational Science and Engineering

Thesis: S.M., Massachusetts Institute of Technology, Center for Computational Science and Engineering, 2020 / Cataloged from student-submitted PDF version of thesis. / Includes bibliographical references (pages 57-60). / Multi-UAS teams often operate in ad-hoc communication networks where blind application of consensus algorithms perform poorly because of message intensive nature of such algorithms. Important messages can get lost due to interference or collisions with other messages, and the broadcasting of less important messages can limit the effective bandwidth available for the team. This thesis presents a novel algorithm - Communication-aware CBBA (CA-CBBA) that learns a cooperative communication policy for agents performing decentralized task allocation using consensus based bundle algorithm (CBBA) by accounting for these communication issues. In our approach, agents learn to use features, such as local communication graph density and value of their own messages, to both censor and schedule themselves amongst the other agents competing for shared communication medium. Experiments show that the learned communication policy enables more efficient utilization of the shared medium by prioritizing agents with important messages and more frequently censoring agents in denser parts of the network to alleviate the "hidden node problem." The approach is shown to lead to better task allocation outcomes with faster convergence time and conflict resolution rates compared to CBBA in communication-constrained environments. Policy learnt by agents trained on a specific team size and task number is shown to generalize to larger team sizes in task allocation problems with varying task numbers. To our knowledge, this is the first task allocation algorithm to co-design planning algorithm and communication protocol by incorporating communication constraints into the design process; resulting in better task allocation outcomes in communication-constrained environments. / by Sharan Raja. / S.M. / S.M. Massachusetts Institute of Technology, Center for Computational Science and Engineering

Thesis: S.M. in Computational Science and Engineering, Massachusetts Institute of Technology, Department of Mechanical Engineering and Center for Computational Science and Engineering, February, 2021 / Cataloged from the official version of thesis. / Includes bibliographical references (pages 147-155). / This thesis studies the optimal design of large-scale shared mobility on demand services (SMoDS) in urban settings. Specifically, we build upon previous work done in the Active-Adaptive Control Lab lab on the dynamic pricing and routing of ride sharing services. We develop and characterize a novel passenger behavioral model based on Cumulative Prospect Theory (CPT) to more accurately represent decision making in the presence of significant risks and uncertainty associated with SMoDS' travel times. A comprehensive survey was designed to estimate both the mode-choice and CPT models. The mode choice section consisted of a series of discrete choice experiments created via factorial design, while the CPT section involved carefully constructed lottery questions and travel choice scenarios to elicit risk preferences. After conducting a pilot study and going through several iterations, the survey was launched via a panel firm. / Data was collected from 1000+ respondents in the Greater Boston metro area. This was used to fully characterize the model and estimate parameters through methods including maximum simulated likelihood estimation, nonlinear least squares and global optimization tools. I also utilized other techniques like regularization and transfer learning to improve the quality of results obtained. Beyond parameter estimation, the uncertainty associated with such behavioral models was quantified via well-established nonlinear programming methods. Sensitivity and robustness analyses were performed to assess the effects of CPT model parametrization errors on the performance of the SMoDS system and objectives like expected revenue, average waiting times etc. These insights were used to design and simulate a closed loop, feedback control mechanism for the SMoDS system to correct modelling errors in real-time, achieve setpoint tracking and enable parameter estimation. / The scheme uses the dynamic tariff as a transactive control input to influence the passenger's behavior as desired. This was implemented via gradient-descent based control schemes to update the price signals, in order to drive the (i) drive the passengers' probabilities of accepting the SMoDS ride offer towards the desired value while also (ii) learning the true passenger behavioral model parameters. / by Vineet Jagadeesan Nair. / S.M. in Computational Science and Engineering / S.M. in Computational Science and Engineering Massachusetts Institute of Technology, Department of Mechanical Engineering

Scientific culture is not popular because the essential nature of science – the models and practises that make it up – cannot be communicated via conventional media in a manner that is interesting to the average person. These models and practises might be communicated in an interesting manner using the new medium of the digital game, yet very few digital games based upon scientific simulations have been created and thus the potential of such games to facilitate scientific knowledge construction cannot be studied directly. Scientific simulations have, however, been much used by scientists to facilitate their own knowledge construction, and equally, both simulations and games have been used by science educators to facilitate knowledge construction on the part of their students. The large academic literatures relating to these simulations and games collectively demonstrate that their ability to: re-create reality; model complex systems; be visual and interactive; engage the user in the practise of science; and to engage the user in construction and collaboration, makes them powerful tools for facilitating scientific knowledge construction. Moreover, the large non-academic literature discussing the nature of digital games (which are themselves both simulations and games) demonstrates that their ability to perform the above tasks (i.e. to re-create reality, model complex systems, and so forth) is what makes them enjoyable to play.¶Because the features of scientific and educational simulations and games that facilitate knowledge construction are the very same features that make digital games enjoyable to play, the player of a scientific-simulation-based digital game would be simultaneously gaining enjoyment and acquiring scientific knowledge. If science were widely communicated using digital games, therefore, then it would be possible for there to be a popular scientific culture.

Übungen zur Vorlesung Theoretische Physik III: Elektrodynamik/Computergestützte Elektrodynamik im Wintersemester 2002/03 für den Studiengang Physik und den Bakkalaureusstudiengang Computational Science

Übungen zur Vorlesung Theoretische Physik III: Elektrodynamik/Computergestützte Elektrodynamik im Wintersemester 2003/04 für den Studiengang Physik und den Bakkalaureusstudiengang Computational Science

Übungen zur Vorlesung Theoretische Physik III: Elektrodynamik/Computergestützte Elektrodynamik im Wintersemester 2004/05 für den Studiengang Physik und den Bakkalaureusstudiengang Computational Science

Throughout many fields of science and engineering, the need for describing waveequations is crucial. Solving the wave equation for high-frequency waves istime-consuming, requires a fine mesh size and memory usage. The main goal wasimplementing and comparing different solution methods for high-frequency waves.Four different methods have been implemented and compared in terms of runtimeand discretization error. From my results, the method which performs the best is thefast sweeping method. For the fast marching method, the time-complexity of thenumerical solver was higher than expected which indicates an error in myimplementation.