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Author: search.filters.author.Kumar, GirishHas files: No

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    Meta-Learning-Based Physics-Informed Neural Network: Numerical Simulations of Initial Value Problems of Nonlinear Dynamical Systems without Labeled Data and Correlation Analyses
    (2024-06-01)
    Duanyai, Worrawat
    ;
    Song, Weon Keun
    ;
    Chitthamlerd, Thanadol
    ;
    Kumar, Girish
    There are several main challenges in solving nonlinear differential equations with artificial neural networks (ANNs), such as a nonlinear system’s sensitivity to its initial values, discretization, and strategies for incorporating physics-based information into ANNs. As for the first issue, this paper addresses the initial value problems of nonlinear dynamical systems (a Duffing oscillator and a Burger’s equation), which cause large global truncation errors in sub-domains with a significant reduction in the influence of initial constraints, using meta-learning-based physics-informed neural networks (MPINNs). The MPINNs with dual learners outperform physics-informed neural networks with a single learner (no fine reinitialization capability). As a result, the former approach improves solution convergence by 98.83% in the sub-time domain (III) of a Duffing oscillator, and by 85.89% at t = 45 in a Burger’s equation problem, compared to the latter one. Model accuracy is highly dependent on the adaptability of the initial parameters in the first hidden layers of the meta-models. From correlation analyses, it is obvious that the parameters become less (the Duffing oscillator) or more (the Burger’s equation) correlated during fine reinitialization, as the update manner differs or is similar to the one used in pre-initialization. In the first example, the MPINN achieves both the mitigation of model sensitivity to its output and the improvement of model accuracy. Conversely, the second example shows that the proposed approach is not enough to solve both issues simultaneously, as increased model sensitivity to its output leads to higher model accuracy. The application of transfer learning reduces the number of iterative pre-meta-trainings.
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    Investigation and analysis of implementation challenges for autonomous vehicles in developing countries using hybrid structural modeling
    (2022-12-01)
    Kumar, Girish
    ;
    James, Ajith Tom
    ;
    Choudhary, Krishna
    ;
    Sahai, Rishi
    ;
    Song, Weon Keun
    The advent of autonomous vehicles (AV) heralds yet another turning point in the evolution of the urban landscape, our daily lives, and the advancement of human civilization as a whole. A very disruptive technology, whose implementation will have ramifications for road safety, air pollution, travel behavior, parking issues, commute time, and other aspects of daily life. The introduction of autonomous vehicles for regular transportation in developed countries is expected to take place over the next decade. Its implementation would be impossible for developing countries for another five decades, at the very least. However, there is potential for its use in selected applications soon. This paper investigates and analyzes the challenges that will be faced in the widespread adoption AV in developing countries. The literature is used to identify a variety of challenges which are then modeled using a hybrid approach that incorporates both ISM (Interpretive Structural Modeling) and MICMAC (Matrice d'impacts croisés multiplication appliquée á un classment) techniques. The results of this analysis would help policy makers and AV manufacturers to understand the level of significance of each challenge and its interrelations. This would help them to focus on critical challenges and initiate remedial actions.
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    Obstacle avoidance for a swarm of unmanned aerial vehicles operating on particle swarm optimization: a swarm intelligence approach for search and rescue missions
    (2022-02-01)
    Kumar, Girish
    ;
    Anwar, Arham
    ;
    Dikshit, Abhinav
    ;
    Poddar, Abhirup
    ;
    Soni, Umang
    An approach, based on a multi-plane system, is conceptualized in this work to solve the problem of collision avoidance for a swarm of unmanned aerial vehicles, being used for search and rescue to minimize affecting the searching algorithm. Relevant chronological advancements in the last two decades of the parent algorithm, particle swarm optimization, are summarized. As each optimization algorithm for search and rescue has its own niche area of application, various well-established algorithms such as particle swarm optimization and novel algorithms like layered search and rescue, spiral search and fish-inspired task allocation are compared with each other qualitatively. Simulations with 100 different cases were used to compare the original particle swarm optimization with the additional novel collision avoidance algorithm. The statistical z test was run based on which it was found that the proposed algorithm significantly reduces the number of collisions and does not put a toll on the iterations to convergence. Standardized residuals of all cases indicate minimal error difference in the optimum average fitness value calculated by the particle swarm optimization, with and without the conceptualized anti-collision algorithm.