Training Large Language Models(LLMs) is one of the most compute-intensive tasks in high-performance computing. Predicting end-to-end training time for multi-billion parameter models distributed across hundreds of GPUs remains challenging due to complex interactions between transformer components, parallelism strategies(data, model, pipeline, tensor), and multi-tier communication. Learned models require costly sampling, while analytical models often struggle with real-world network and hardware complexities. We address this by decomposing LLMs into core computational primitives and modeling them with: (1) operator-level decomposition for fine-grained analysis; (2) lightweight sampling based hardware-aware prediction models for key operations; (3) an end-to-end prediction system integrating these components across complex parallelization strategies. Crucially, our methodology has been validated on two large-scale HPC systems. Our framework achieves low average prediction errors-4.98\% on Perlmutter(A100) and 9.38\% on Vista(GH200)-for models up to 20B parameters across 128 GPUs. Importantly, it runs entirely on CPUs, enabling rapid iteration over hardware configurations and training strategies without costly on-cluster experimentation.

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