  After a summary of relevant comments and recommendations from various reports
over the last ten years, this paper examines the modeling needs in accelerator
physics, from the modeling of single beams and individual accelerator elements,
to the realization of virtual twins that replicate all the complexity to model
a particle accelerator complex as accurately as possible. We then discuss
cutting-edge and emerging computing opportunities, such as advanced algorithms,
AI/ML and quantum computing, computational needs in hardware, software
performance, portability and scalability, and needs for scalable I/O and
in-situ analysis. Considerations of reliability, long-term sustainability, user
support and training are considered next, before discussing the benefits of
ecosystems with integrated workflows based on standardized input and output,
and with integrated frameworks and data repositories developed as a community.
Last, we highlight how the community can work more collaboratively and
efficiently through the development of consortia and centers, and via
collaboration with industry.
