用图神经网络预测能量景观系综的基态构型
Predicting ground state configuration of energy landscape ensemble using graph neural network
摘要：
许多科学问题试图在崎岖的能量景观中找到基态，这对于大型系统来说是一项非常困难的任务。然而，在一类特定的问题中，能量最小值内的短程相关性可能与系统大小无关。这些相关性是否可以从已知基态的小问题中推断出来，以加速对更大问题的基态的搜索？在这里，我们展示了伊辛自旋玻璃，其中的相互作用矩阵是从蛋白质接触图的战略。我们使用图神经网络学习从相互作用矩阵$J$到基态构型的映射，得到最可能构型的猜测。考虑到这些猜测，我们表明，基态配置可以搜索速度比香草模拟退火。对于大型问题，在小$J$矩阵上训练的模型预测的配置的能量远低于通过模拟退火获得的配置，这表明该策略的规模可推广性。
英文摘要：
Many scientific problems seek to find the ground state in a rugged energy landscape, a task that becomes prohibitively difficult for large systems. Within a particular class of problems, however, the short-range correlations within energy minima might be independent of system size. Can these correlations be inferred from small problems with known ground states to accelerate the search for the ground states of larger problems? Here, we demonstrate the strategy on Ising spin glasses, where the interaction matrices are drawn from protein contact maps. We use graph neural network to learn the mapping from an interaction matrix $J$ to a ground state configuration, yielding guesses for the set of most probable configurations. Given these guesses, we show that ground state configurations can be searched much faster than in vanilla simulated annealing. For large problems, a model trained on small $J$ matrices predicts a configurations whose energy is much lower than those obtained by simulated annealing, indicating the size generalizability of the strategy.
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