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1. Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems

   https://doi.org/10.1007/s00332-023-09891-4  

   Burby, J_W; Hirvijoki, E.; Leok, M. (February 2023, Journal of Nonlinear Science)

   Abstract M. Kruskal showed that each continuous-time nearly periodic dynamical system admits a formalU(1)-symmetry, generated by the so-called roto-rate. When the nearly periodic system is also Hamiltonian, Noether’s theorem implies the existence of a corresponding adiabatic invariant. We develop a discrete-time analog of Kruskal’s theory. Nearly periodic maps are defined as parameter-dependent diffeomorphisms that limit to rotations along aU(1)-action. When the limiting rotation is non-resonant, these maps admit formalU(1)-symmetries to all orders in perturbation theory. For Hamiltonian nearly periodic maps on exact presymplectic manifolds, we prove that the formalU(1)-symmetry gives rise to a discrete-time adiabatic invariant using a discrete-time extension of Noether’s theorem. When the unperturbedU(1)-orbits are contractible, we also find a discrete-time adiabatic invariant for mappings that are merely presymplectic, rather than Hamiltonian. As an application of the theory, we use it to develop a novel technique for geometric integration of non-canonical Hamiltonian systems on exact symplectic manifolds. 

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2. Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems

   Duruisseaux, Valentin; Duong, Thai; Leok, Melvin; Atanasov, Nikolay. (May 2023, Proceedings of Machine Learning Research)

   Incorporating prior knowledge of physics laws and structural properties of dynamical systems into the design of deep learning architectures has proven to be a powerful technique for improving their computational efficiency and generalization capacity. Learning accurate models of robot dynamics is critical for safe and stable control. Autonomous mobile robots, including wheeled, aerial, and underwater vehicles, can be modeled as controlled Lagrangian or Hamiltonian rigid-body systems evolving on matrix Lie groups. In this paper, we introduce a new structure-preserving deep learning architecture, the Lie group Forced Variational Integrator Network (LieFVIN), capable of learning controlled Lagrangian or Hamiltonian dynamics on Lie groups, either from position-velocity or position-only data. By design, LieFVINs preserve both the Lie group structure on which the dynamics evolve and the symplectic structure underlying the Hamiltonian or Lagrangian systems of interest. The proposed architecture learns surrogate discrete-time flow maps allowing accurate and fast prediction without numerical-integrator, neural-ODE, or adjoint techniques, which are needed for vector fields. Furthermore, the learnt discrete-time dynamics can be utilized with computationally scalable discrete-time (optimal) control strategies. 

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3. Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics

   https://doi.org/10.1515/cmam-2021-0215  

   Cockburn, Bernardo; Du, Shukai; Sánchez, Manuel A. (May 2022, Computational Methods in Applied Mathematics)

   Abstract We present a new class of discontinuous Galerkin methods for the space discretization of the time-dependent Maxwell equations whose main feature is the use of time derivatives and/or time integrals in the stabilization part of their numerical traces.These numerical traces are chosen in such a way that the resulting semidiscrete schemes exactly conserve a discrete version of the energy.We introduce four model ways of achieving this and show that, when using the mid-point rule to march in time, the fully discrete schemes also conserve the discrete energy.Moreover, we propose a new three-step technique to devise fully discrete schemes of arbitrary order of accuracy which conserve the energy in time.The first step consists in transforming the semidiscrete scheme into a Hamiltonian dynamical system.The second step consists in applying a symplectic time-marching method to this dynamical system in order to guarantee that the resulting fully discrete method conserves the discrete energy in time.The third and last step consists in reversing the above-mentioned transformation to rewrite the fully discrete scheme in terms of the original variables. 

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4. An Integrated Approach for Accelerating Stochastic Block Partitioning

   https://doi.org/10.1109/HPEC58863.2023.10363599  

   Wanye, Frank; Gleyzer, Vitaliy; Kao, Edward; Feng, Wu-chun (September 2023, IEEE)

   Community detection, or graph partitioning, is a fundamental problem in graph analytics with applications in a wide range of domains including bioinformatics, social media analysis, and anomaly detection. Stochastic block partitioning (SBP) is a community detection algorithm based on sequential Bayesian inference. SBP is highly accurate even on graphs with a complex community structure. However, it does not scale well to large real-world graphs that can contain upwards of a million vertices due to its sequential nature. Approximate methods that break computational dependencies improve the scalability of SBP via parallelization and data reduction. However, these relaxations can lead to low accuracy on graphs with complex community structure. In this paper, we introduce additional synchronization steps through vertex-level data batching to improve the accuracy of such methods. We then leverage batching to develop a high-performance parallel approach that improves the scalability of SBP while maintaining accuracy. Our approach is the first to integrate data reduction, shared-memory parallelization, and distributed computation, thus efficiently utilizing distributed computing resources to accelerate SBP. On a one-million vertex graph processed on 64 compute nodes with 128 cores each, our approach delivers a speedup of 322x over the sequential baseline and 6.8x over the distributed-only implementation. To the best of our knowledge, this Graph Challenge submission is the highest-performing SBP implementation to date and the first to process the one-million vertex graph using SBP. 

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5. Lean Health Care Internships: A Novel Systems-Based Practice Education Program for Undergraduate Medical Students

   https://doi.org/10.1097/ACM.0000000000005312  

   Erdmann, Marjorie A.; Paramel, Ipe S.; Marshall, Carolyn M. (July 2023, Academic Medicine)

   Problem: Given the United States’ urgency for systemic-level improvements to care, advancing systems-based practice (SBP) competency among future physicians is crucial. However, SBP education is inadequate, lacks a unifying framework and faculty confidence in its teaching, and is taught late in the medical education journey. Approach: The Oklahoma State University Center for Health Systems Innovation (CHSI) created an SBP program relying on Lean Health Care for a framework and targeted medical students before their second year began. Lean curricula were developed (lecture and simulation) and a partnership with a hospital was secured for work-based practice. The CHSI developed a skills assessment tool for preliminary evaluation of the program. In June 2022, 9 undergraduate medical students responded to a Lean Health Care Internship (LHCI) presentation. Outcomes: Student SBP skills increased after training and again after work-based practice. All 9 students reported that their conceptualization of problems in health care changed “extraordinarily,” and they were “extraordinarily” confident in their ability to approach another health care problem by applying the Lean method. The LHCI fostered an awareness of physicians as interdependent systems citizens, a key goal of SBP competency. After the internship concluded, the Lean team recommendations generated a resident-led quality assurance performance improvement initiative for bed throughput. Next Steps: The LHCI was effective in engaging students and building SBP skills among undergraduate medical education students. The levels of student enthusiasm and skill acquisition exceeded the Lean trainers’ expectations. The researchers will continue to measure LHCI’s effect on students’ rotation experiences to better evaluate the long-term benefit of introducing SBP concepts earlier in medical education. The program’s success has spurred enthusiasm for continued collaboration with hospital and residency programs. Program administrators are exploring how to broaden access. 

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