基于机器学习的动能泛函导数直接格式计算
Direct Scheme Calculation of the Kinetic Energy Functional Derivative Using Machine Learning
摘要：
本文提出了一种基于机器学习的动能泛函导数的直接计算方法。分别采用支持向量回归和核岭回归技术对动能泛函及其导数进行估计。即使准确性应该是一个决定性的因素，在一个现实的功能建模，我们表明，在一定程度上，它影响了模型的推广。通过选择正确的正则化项，并考虑正则化项与精度之间的合理相互作用，我们能够从经过训练以估计动能的模型中推导出泛函导数。虽然导数计算需要非常高的精度来解释动能的微小变化，但开发的估计器能够捕获电子密度的这些极小变化。这项工作致力于高效地实现无轨道密度泛函理论，因为它只采用直接计算方案
英文摘要：
We report a direct scheme calculation of kinetic energy functional derivative using Machine Learning. Support Vector Regression and Kernel Ridge Regression techniques were independently employed to estimate the kinetic energy functional and its derivative. Even though the accuracy should have been a decisive factor in modeling a realistic functional, we show that at a certain level it affects the generalizability of the model. By choosing the right regularization term and by considering a reasonable interplay between it and the accuracy, we were able to deduce the functional derivative from a model that was trained to estimate the kinetic energy. Although the derivative calculations demand very high accuracy to account for small variations of the kinetic energy, the developed estimator was capable of capturing these extremely small changes of the electron density. This work pours into highly effective implementation of the orbital-free density functional theory as it employs only direct calculation scheme
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