Sida He | Searcharxiv

arXiv2026

AI Decodes Historical Chinese Archives to Reveal Lost Climate History

Historical archives contain qualitative descriptions of climate events, yet converting these into quantitative records has remained a fundamental challenge. Here we introduce a paradigm shift: a generative AI framework that inverts the logic of historical chroniclers by inferring the quantitative climate patterns associated with documented events. Applied to historical Chinese archives, it produces the sub-annual precipitation reconstruction for southeastern China over the period 1368-1911 AD. Our reconstruction not only quantifies iconic extremes like the Ming Dynasty's Great Drought but also, crucially, maps the full spatial and seasonal structure of El Ni$\~n$o influence on precipitation in this region over five centuries, revealing dynamics inaccessible in shorter modern records. Our methodology and high-resolution climate dataset are directly applicable to climate science and have broader implications for the historical and social sciences.

physics.ao-ph↗

arXiv2024

On the robustness of double-word addition algorithms

We demonstrate that, even when there are moderate overlaps in the inputs of sloppy or accurate double-word addition algorithms in the QD library, these algorithms still guarantee error bounds of $O(u^2(|a|+|b|))$ in faithful rounding. Furthermore, the accurate algorithm can achieve a relative error bound of $O(u^2)$ in the presence of moderate overlaps in the inputs when rounding function is round-to-nearest. The relative error bound also holds in directed rounding, but certain additional conditions are required. Consequently, in double-word multiplication and addition operations, we can safely omit the normalization step of double-word multiplication and replace the accurate addition algorithm with the sloppy one. Numerical experiments confirm that this approach nearly doubles the performance of double-word multiplication and addition operations, with negligible precision costs. Moreover, in directed rounding mode, the signs of the errors of the two algorithms are consistent with the rounding direction, even in the presence of input overlap. This allows us to avoid changing the rounding mode in interval arithmetic. We also prove that the relative error bound of the sloppy addition algorithm exceeds $3u^2$ if and only if the input meets the condition of Sterbenz's Lemma when rounding to nearest. These findings suggest that the two addition algorithms are more robust than previously believed.

math.NA↗