A major challenge facing scientists using conventional approaches for solving PDEs is the simulation of extreme multi-scale problems. While exascale computing will enable simulations of larger systems, the extreme multiscale nature of many problems requires new techniques. Deep learning techniques have disrupted several domains, such as computer vision, language (e.g., ChatGPT), and computational biology, leading to breakthrough advances. Similarly, the adaptation of these techniques for scientific computing has led to a new and rapidly advancing branch of High-Performance Computing (HPC), which we call neural-HPC (NeuHPC). Proof of concept studies in domains such as computational fluid dynamics and material science have demonstrated advantages in both efficiency and accuracy compared to conventional solvers. However, NeuHPC is yet to be embraced in plasma simulations. This is partly due to general lack of awareness of NeuHPC in the space physics community as well as the fact that most plasma physicists do not have training in artificial intelligence and cannot easily adapt these new techniques to their problems. As we explain below, there is a solution to this. We consider NeuHPC a critical paradigm for knowledge discovery in space sciences and urgently advocate for its adoption by both researchers as well as funding agencies. Here, we provide an overview of NeuHPC and specific ways that it can overcome existing computational challenges and propose a roadmap for future direction.