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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.