Haga Taiki
Department of Physics and Electronics, <a href="https://ror.org/01hvx5h04">Osaka Metropolitan University</a>, Sakai-shi, Osaka 599-8531, Japan.
Phys Rev E. 2024 Jul;110(1-1):014137. doi: 10.1103/PhysRevE.110.014137.
We investigate the recently proposed dimensional reduction conjecture in driven disordered systems using a machine learning technique. The conjecture states that a static snapshot of a disordered system driven at a constant velocity is equal to a space-time trajectory of its lower-dimensional pure counterpart. This suggests that the three-dimensional (3D) random field XY model exhibits the Berezinskii-Kosterlitz-Thouless transition when driven out of equilibrium. To verify the conjecture directly by observing configurations of the system, we utilize the capacity of neural networks to detect subtle features of images. Specifically, we train neural networks to differentiate snapshots of the 3D driven random field XY model from space-time trajectories of the two-dimensional pure XY model. Our results demonstrate that the network cannot distinguish between the two, confirming the dimensional reduction conjecture.
我们使用机器学习技术研究了最近在驱动无序系统中提出的降维猜想。该猜想指出，以恒定速度驱动的无序系统的静态快照等同于其低维纯对应物的时空轨迹。这表明三维（3D）随机场XY模型在非平衡驱动时会表现出贝雷津斯基-科斯特利茨-索利斯转变。为了通过观察系统的构型直接验证该猜想，我们利用神经网络检测图像细微特征的能力。具体而言，我们训练神经网络来区分3D驱动随机场XY模型的快照与二维纯XY模型的时空轨迹。我们的结果表明，网络无法区分这两者，从而证实了降维猜想。
