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This study utilized large language models (LLMs) to analyze public sentiment in the United States (US) regarding nuclear power on social media, focusing on X/Twitter, considering climate change challenges and advancements in nuclear power technology. Approximately, 1.26 million nuclear tweets from 2008–2023 were examined to fine-tune LLMs for sentiment classification. We found the crucial role of accurate data labeling for model performance, with potential implications for a 15% improvement, achieved through high-confidence labels. LLMs demonstrated better performance compared to traditional machine learning classifiers, with reduced susceptibility to overfitting and up to 96% classification accuracy. LLMs are used to segment the US public tweets into policy and energy-related categories, revealing that 68% are politically themed. Policy tweets tended to convey negative sentiment, often reflecting opposing political perspectives and focusing on nuclear deals and international relations. Energy-related tweets covered diverse topics with predominantly neutral to positive sentiment, indicating broad support for nuclear power in 48 out of 50 US states. The US public positive sentiments toward nuclear power stemmed from its high power density, reliability regardless of weather conditions, environmental benefits, application versatility, and recent innovations and advancements in both fission and fusion technologies. Negative sentiments primarily focused on waste management, high capital costs, and safety concerns. The neutral campaign highlighted global nuclear facts and advancements, with varying tones leaning towards positivity or negativity. An interesting neutral theme was the advocacy for the combined use of renewable and nuclear energy to attain net-zero goals. • Over one million nuclear energy related tweets are collected from the social media platform X (Twitter). • A method is proposed for auto-labeling data with reduced bias, employing a majority voting strategy. • Development of sentiment classification models by fine-tuning large language models. • Selective data topic extraction and in-depth analysis utilizing generative artificial intelligence (AI). • Analysis of the United States public opinion toward nuclear energy on a "state-by-state" basis. [ABSTRACT FROM AUTHOR]