Machine learning (ML) provides a broad spectrum of tools and architectures that enable the transformation of data from simulations and experiments into useful and explainable science, thereby augmenting domain knowledge. Furthermore, ML-enhanced numerical modelling can revamp scientific computing for real-world complex engineering systems, creating unique opportunities to examine the operation of the technologies in detail and automate their optimization and control. In recent years, ML applications have seen significant growth across various scientific domains, particularly in fluid mechanics, where ML has shown great promise in enhancing computational modeling of fluid flows. In contrast, ML applications in numerical plasma physics research remain relatively limited in scope and extent. Despite this, the close relationship between fluid mechanics and plasma physics presents a valuable opportunity to create a roadmap for transferring ML advances in fluid flow modeling to computational plasma physics. This Perspective aims to outline such a roadmap. We begin by discussing some general fundamental aspects of ML, including the various categories of ML algorithms and the different types of problems that can be solved with the help of ML. With regard to each problem type, we then present specific examples from the use of ML in computational fluid dynamics, reviewing several insightful prior efforts. We also review recent ML applications in plasma physics for each problem type. The paper discusses promising future directions and development pathways for ML in plasma modelling within the different application areas. Additionally, we point out prominent challenges that must be addressed to realize ML's full potential in computational plasma physics, including the need for cost-effective high-fidelity simulation tools for extensive data generation.

Sustainable energy is a crucial global challenge, and recent breakthroughs in nuclear fusion ignition underscore the potential of harnessing energy extracted from nuclear fusion in everyday life, thereby drawing significant attention to fusion ignition research, especially Laser-Plasma Interaction (LPI). Unfortunately, the complexity of LPI at ignition scale renders theory-based analysis nearly impossible -- instead, it has to rely heavily on Particle-in-Cell (PIC) simulations, which is extremely computationally intensive, making it a major bottleneck in advancing fusion ignition. In response, this work introduces Diff-PIC, a novel paradigm that leverages conditional diffusion models as a computationally efficient alternative to PIC simulations for generating high-fidelity scientific data. Specifically, we design a distillation paradigm to distill the physical patterns captured by PIC simulations into diffusion models, demonstrating both theoretical and practical feasibility. Moreover, to ensure practical effectiveness, we provide solutions for two critical challenges: (1) We develop a physically-informed conditional diffusion model that can learn and generate meaningful embeddings for mathematically continuous physical conditions. This model offers algorithmic generalization and adaptable transferability, effectively capturing the complex relationships between physical conditions and simulation outcomes; and (2) We employ the rectified flow technique to make our model a one-step conditional diffusion model, enhancing its efficiency further while maintaining high fidelity and physical validity. Diff-PIC establishes a new paradigm for using diffusion models to overcome the computational barriers in nuclear fusion research, setting a benchmark for future innovations and advancements in this field.

Today, reliable, predictive, and generalizable reduced-order models do not exist for plasmas. There are at least two reasons for this status quo: first, the classic conservation equations derived from the moments of the plasma kinetic equation [1] do not include the important effects of microscopic plasma instabilities and oscillations on the electrons' momentum and energy transport [2]. Second, despite years of effort and several approaches pursued [3]-[7], rigorous and generalizable closure models for the conservation equations are still to be established so that the effects of the kinetic phenomena and processes such as the cross-field electrons' transport can be selfconsistently resolved in reduced-order simulations based upon the conservation equations for the plasma. Nonetheless, the need for self-consistent, interpretable reduced-order plasma models is critical for scientific and industrial advancements alike. From an academic perspective, the availability of such models can enable answering the so-far unresolved questions in the physics of cross-field plasmas, particularly with regards to the excitation and evolution of the plasma instabilities and turbulence as well as their interactions with plasma species that, for example, can result in enhanced transport of the particles and energy across the magnetic field. From an applied point of view, reliable reduced-order models can lead to the prediction and control of the plasmas, paving the way for more efficient technological solutions and novel plasma applications. The above issues, although rather different in nature and extent, also exist in other research fields such as fluid mechanics. Attempts to establish closure models for Navier-Stokes system of equations to incorporate the effects of unresolved turbulence, for example, have been rigorously pursued for decades in order to achieve fully generalizable predictive models of the fluid systems [8]. Nonetheless, the efforts in fluid dynamics to the above end have not been fully successful either.