Abstract:
Background The Vlasov equation is a cornerstone in plasma physics, governing the evolution of distribution functions in high-temperature, collisionless plasmas. Conventional numerical methods, including Eulerian and Lagrangian approaches, often encounter severe computational challenges due to the rapid increase in cost with fine grid resolutions and the curse of dimensionality. These limitations restrict their effectiveness in large-scale kinetic plasma simulations needed in fusion research and space plasma studies.
Purpose This work aims to develop an efficient and scalable computational framework for solving the Vlasov equation that mitigates the drawbacks of traditional methods. The study particularly addresses the need for maintaining accuracy and physical consistency while significantly reducing computational costs in high-dimensional simulations. An approach based on the physics-informed Fourier neural operator (PFNO) is introduced.
Methods The method integrates the high-dimensional function mapping ability of the fourier neural operator with the physical constraints of the Vlasov equation. A physics-informed loss function is constructed to enforce mass, momentum, and energy conservation laws. The framework was evaluated through benchmark tests against finite element and spectral solvers, and its parallel performance was assessed on large-scale computing platforms.
Results The PFNO approach demonstrates accuracy comparable to conventional solvers while achieving computational efficiency improvements of one to two orders of magnitude. The method shows strong generalization under sparse-data conditions, exhibits grid independence, and scales effectively in parallel computing environments, enabling efficient treatment of high-dimensional plasma dynamics. The study presents a novel paradigm for solving high-dimensional Vlasov equations by combining deep learning operators with physical principles.
Conclusions The PFNO framework enhances efficiency without sacrificing physical accuracy, making it a promising tool for applications in inertial confinement fusion, astrophysical plasma modeling, and space plasma simulations. Future research directions include extension to multi-species and relativistic plasma systems.
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