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Data-Driven Koopman Reduced-Order Models for Kinetic Plasmas and Electromagnetic Cavities

Nayak, Indranil
http://orcid.org/0000-0003-4702-941X
http://rave.ohiolink.edu/etdc/view?acc_num=osu1721390437406561

Abstract Details

2024, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
We present an exposition on Koopman operator-based reduced-order modeling of high-dimensional electromagnetic (EM) systems exhibiting both linear and nonlinear dynamics. Since the emergence of the digital age, numerical methods have been pivotal in understanding physical phenomena through computer simulations. Computational electromagnetics (CEM) and computational plasma physics (CPP) are related yet distinct branches, each addressing complex linear and nonlinear electromagnetic phenomena. CEM primarily focuses on solving Maxwell's equations for intricate structures such as antennas, cavities, high-frequency circuits, waveguides, and scattering problems. In contrast, CPP aims to capturing the complex behavior of charged particles under electromagnetic fields. This work specifically focuses on the numerical simulation of electromagnetic cavities and particle-in-cell (PIC) kinetic plasma simulations. Studying electromagnetic field coupling inside metallic cavities is crucial for various applications, including electromagnetic interference (EMI), electromagnetic compatibility (EMC), shielded enclosures, cavity filters, and antennas. However, time-domain simulations can be computationally intensive and time-consuming, especially as the scale and complexity of the problem increase. Similarly, PIC simulations, which are extensively used for simulating kinetic plasmas in the design of high-power microwave devices, vacuum electronic devices, and in astrophysical studies, can be computationally demanding, especially when simulating thousands to millions of charged particles. Moreover, the nonlinear nature of the complex wave-particle interactions complicates the modeling task. Data-driven reduced-order models (ROMs), which have recently gained prominence due to advances in machine learning techniques and hardware capabilities, offer a practical approach for constructing "light" models from high-fidelity data. The Koopman operator-based data-driven ROM is a powerful method for modeling high-dimensional dynamical systems, particularly those exhibiting nonlinear behavior. We explore the realizations of the finite-dimensional Koopman operator through dynamic mode decomposition (DMD) and Koopman autoencoders (KAEs). We demonstrate how DMD and KAE can model the fields and currents in resonating cavities and plasma systems. KAEs leverage the expressivity of neural networks and can outperform DMD for highly nonlinear problems. Furthermore, neural network-based approaches such as KAE offer a straightforward way to incorporate physical constraints into the model, leading to more accurate and stable long-term predictions. Additionally, we develop an on-the-fly DMD algorithm to detect in real-time when to stop the high-fidelity time-domain simulations by identifying the onset of self-repeating behavior.
Mrinal Kumar (Advisor)
Fernando Teixeira (Advisor)
Ben McCorkle (Committee Member)
Balasubramaniam Shanker (Committee Member)
254 p.
Electrical Engineering; Electromagnetics; Engineering; Physics; Plasma Physics
Particle-in-cell; kinetic plasma; Koopman operator; data-driven; reduced-order model; dynamic mode decomposition; Koopman autoencoder; electromagnetic cavities; cavity resonances; scientific machine learning; time extrapolation

Recommended Citations

Citations

  • Nayak, I. (2024). Data-Driven Koopman Reduced-Order Models for Kinetic Plasmas and Electromagnetic Cavities [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1721390437406561

    APA Style (7th edition)

  • Nayak, Indranil. Data-Driven Koopman Reduced-Order Models for Kinetic Plasmas and Electromagnetic Cavities. 2024. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1721390437406561.

    MLA Style (8th edition)

  • Nayak, Indranil. "Data-Driven Koopman Reduced-Order Models for Kinetic Plasmas and Electromagnetic Cavities." Doctoral dissertation, Ohio State University, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=osu1721390437406561

    Chicago Manual of Style (17th edition)

osu1721390437406561
251
© 2024, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.