分子能级的机器学习同位素位移

Recent advances in the use of High-Resolution Cross-Correlation Spectroscopy（HRCCS）to detect molecular species in exoplanet atmospheres, presents a new challenge for the accuracy of reference spectroscopic line lists. While parent isotopologues of key atmospheric tracers are often well-characterized, minor isotopologues, crucial for diagnosing planetary formation histories and evolution, suffer from a scarcity of experimental data, often leading to reliance on less accurate theoretical predictions. In this work, a comprehensive machine learning framework is designed to mitigate these inaccuracies by modelling the residual errors of the isotopologue extrapolation（IE） method used within the ExoMol project. A fully connected neural network architecture for carbon dioxide (CO$_2$) is shown to predict energy corrections with high fidelity, reducing the mean absolute error（MAE） relative to the original IE approach for more than 87% of the levels when benchmarked against empirical（Marvel） energies. Furthermore, development of a novel hybrid, molecule-aware transfer learning architecture is presented that successfully propagates correction patterns from the data-rich CO$_2$ system to the data-poor carbon monoxide (CO) system. This transfer learning approach yields MAE improvements in over 93% of CO samples, demonstrating that physical correction factors related to isotopic substitution can be generalized across chemically related molecular systems. Updated and improved line lists are presented for 11 CO$_2$ isotopologues and energy levels for excited states of CO isotopologues are predicted. The methodology establishes a scalable, data-driven paradigm for refining molecular line lists, helping to bridge the gap between theoretical calculations and experimental precision.