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.

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8\% on logical tasks to -44.5\% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100\%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

Coal fires pose great threats to valuable energy resources, the ecological environment, and human safety. They are one of the most persistent fires on the Earth, which can burn for an extremely long-term period from decades to hundreds or even thousands of years. Remote sensing detection of coal fires is of significance for mitigating coal fire hazards. Nevertheless, short-term or temporal discrete land surface temperature (LST) data have limited capability in characterizing the persistent coal fire. This study proposed a methodology to monitor persistent coal fires using long-term Landsat thermal images and further to analyze spatiotemporal dynamics of coal fires. A total of 1118 high-quality Landsat images (each image containing$446\times446$pixels) spanning 35 years from 1986 to 2020 in the Wuda coalfield area (China) were processed to retrieve the LST. LST time series of each pixel was decomposed into the seasonal, trend, and remainder components. Coal fire areas were demarcated by using the range of the trend components. To trace the trend and change point of the LST time series, the Mann–Kendall test was applied to the trend components, and the Pettitt test was employed to the original time series vectors of those pixels located in the coal fire areas, respectively. The random sample consensus algorithm was utilized to identify the background temperature (inliers) and high temperature (outliers) and, thus, judge the coal fire burning period, and the symbolic aggregate approximation algorithm was used to evaluate the robustness of the judgment. The calibration was conducted according to the filed surveys, obtaining spatiotemporal 3-D coal fire dynamics. The proposed methodology was testified by comparisons with fieldwork and regional anomaly extractor algorithm, demonstrating good performance in comprehensive monitoring of persistent coal fires.