论文标题
关于自旋模型中人工神经网络的普遍性
On the generalizability of artificial neural networks in spin models
论文作者
论文摘要
人工神经网络（ANN）的适用性通常仅限于他们接受过培训的模型，对它们的普遍性知之甚少，这在实际应用经过训练的ANN来在看不见的问题上是一个紧迫的问题。在这里，通过使用识别自旋模型中的相变的任务，我们建立了一个系统的概括性，以便可以将使用二维铁磁iSing模型训练的简单ANN可以应用于$ Q \ geq 2 $的不同维度的非尺寸的铁磁$ q $ q $ -State Potts模型。相同的方案可以应用于高度非平凡的抗磁磁性$ Q $ - 州Potts模型。我们证明，可以通过将训练数据跨越指数范围的状态空间呈指数较大的状态空间来获得相似的结果，该空间仅包含三种通过对称考虑因素人为构建的代表性配置。我们希望我们的发现能够简化和加速机器学习辅助任务在物理和材料科学中与旋转模型相关的学科中的发展。
The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to unseen problems. Here, by using the task of identifying phase transitions in spin models, we establish a systematic generalizability such that simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic $q$-state Potts model in different dimensions for $q \geq 2$. The same scheme can be applied to the highly nontrivial antiferromagnetic $q$-state Potts model. We demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative configurations artificially constructed through symmetry considerations. We expect our findings to simplify and accelerate the development of machine learning-assisted tasks in spin-model related disciplines in physics and materials science.
