超导体中电子玻色子机制的机器学习
Machine learning on the electron-boson mechanism in superconductors
摘要：
从有限的间接实验数据中揭示超导体的配对机制一直是一个困难的任务。用带有某些调谐参数的理论模型来解释是常见的，但有时是可疑的。在这项工作中，我们提出了机器学习可能推断配对机制，从观测值，如超导能隙函数。对于Migdal-Eliashberg理论中的超导性，我们在超导能隙函数和电子玻色子谱函数之间进行监督学习。对于简单的谱函数，神经网络可以很容易地捕获对应关系并进行完美的预测。对于复杂的谱函数，利用自动编码器来降低谱函数的复杂度，以与间隙函数的复杂度兼容。经过这种复杂度降低过程，谱函数的相关信息被提取出来，并恢复了良好的性能。我们提出的方法可以从数据中提取相关信息，并可以应用于物理或其他领域中具有非对称复杂性的一般函数到函数映射。
英文摘要：
To unravel pairing mechanism of a superconductor from limited, indirect experimental data is always a difficult task. It is common but sometimes dubious to explain by a theoretical model with some tuning parameters. In this work, we propose that the machine learning might infer pairing mechanism from observables like superconducting gap functions. For superconductivity within the Migdal-Eliashberg theory, we perform supervised learning between superconducting gap functions and electron-boson spectral functions. For simple spectral functions, the neural network can easily capture the correspondence and predict perfectly. For complex spectral functions, an autoencoder is utilized to reduce the complexity of the spectral functions to be compatible to that of the gap functions. After this complexity-reduction process, relevant information of the spectral function is extracted and good performance restores. Our proposed method can extract relevant information from data and can be applied to general function-to-function mappings with asymmetric complexities either in physics or other fields.
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