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Applying parallel-in-time algorithms to multiscale Hamiltonian systems to obtain stable long-time simulations is very challenging. In this paper, we present novel data-driven methods aimed at improving the standard parareal algorithm developed by Lions et al. in 2001, for multiscale Hamiltonian systems. The first method involves constructing a correction operator to improve a given inaccurate coarse solver through solving a Procrustes problem using data collected online along parareal trajectories. The second method involves constructing an efficient, high-fidelity solver by a neural network trained with offline generated data. For the second method, we address the issues of effective data generation and proper loss function design based on the Hamiltonian function. We show proof-of-concept by applying the proposed methods to a Fermi-Pasta-Ulam (FPU) problem. The numerical results demonstrate that the Procrustes parareal method is able to produce solutions that are more stable in energy compared to the standard parareal. The neural network solver can achieve comparable or better runtime performance compared to numerical solvers of similar accuracy. When combined with the standard parareal algorithm, the improved neural network solutions are slightly more stable in energy than the improved numerical coarse solutions. [ABSTRACT FROM AUTHOR]

In numerous scientific disciplines and practical applications, addressing optimization challenges is a common imperative. Nature-inspired optimization algorithms represent a highly valuable and pragmatic approach to tackling these complexities. This paper introduces Dendritic Growth Optimization (DGO), a novel algorithm inspired by natural branching patterns. DGO offers a novel solution for intricate optimization problems and demonstrates its efficiency in exploring diverse solution spaces. The algorithm has been extensively tested with a suite of machine learning algorithms, deep learning algorithms, and metaheuristic algorithms, and the results, both before and after optimization, unequivocally support the proposed algorithm's feasibility, effectiveness, and generalizability. Through empirical validation using established datasets like diabetes and breast cancer, the algorithm consistently enhances model performance across various domains. Beyond its working and experimental analysis, DGO's wide-ranging applications in machine learning, logistics, and engineering for solving real-world problems have been highlighted. The study also considers the challenges and practical implications of implementing DGO in multiple scenarios. As optimization remains crucial in research and industry, DGO emerges as a promising avenue for innovation and problem solving. [ABSTRACT FROM AUTHOR]

The moth-flame algorithm shows some shortcomings in solving the complex problem of optimization, such as insufficient population diversity and unbalanced search ability. In this paper, an IMFO (Improved Moth-Flame Optimization) algorithm is proposed to be applied in solving the optimization problem of function. First, cat chaotic mapping is used to generate the initial position of moth to improve the population diversity. Second, cosine inertia weight is introduced to balance the global and local search abilities of the algorithm. Third, the memory information in the particle swarm algorithm is introduced into the iterative process of the algorithm to speed up the convergence of the population. Finally, Gaussian mutation strategy is used in the current optimal solution to avoid the algorithm from falling into the local optimum. Simulation experiments are conducted on 11 benchmark test functions, compared with other improved MFO (Moth-Flame Optimization) algorithms and classical optimization algorithms. The results show that the IMFO has higher accuracy and stability in solving the above-mentioned test functions. The proposed algorithm is experimented and verified by optimizing the KELM (Kernel Extreme Learning Machine) in an engineering example and exhibits a better optimization performance. [ABSTRACT FROM AUTHOR]

This paper considers the offline assignment of fixed priorities in partitioned preemptive real-time systems where tasks have precedence constraints. This problem is crucial in this type of systems, as having a good fixed priority assignment allows for an efficient use of the processing resources while meeting all the deadlines. In the literature, we can find several proposals to solve this problem, which offer varying trade-offs between the quality of their results and their computational complexities. In this paper , we propose a new approach, leveraging existing algorithms that are widely exploited in the field of Machine Learning: Gradient Descent, the Adam Optimizer, and Gradient Noise. We show how to adapt these algorithms to the problem of fixed priority assignment in conjunction with existing worst-case response time analyses. We demonstrate the performance of our proposal on synthetic task-sets with different sizes. This evaluation shows that our proposal is able to find more schedulable solutions than previous heuristics, approximating optimal but intractable algorithms such as MILP or brute-force, while requiring reasonable execution times. [ABSTRACT FROM AUTHOR]