  We present a scalable machine learning (ML) framework for predicting
intensive properties and particularly classifying phases of many-body systems.
Scalability and transferability are central to the unprecedented computational
efficiency of ML methods. In general, linear-scaling computation can be
achieved through the divide and conquer approach, and the locality of physical
properties is key to partitioning the system into sub-domains that can be
solved separately. Based on the locality assumption, ML model is developed for
the prediction of intensive properties of a finite-size block. Predictions of
large-scale systems can then be obtained by averaging results of the ML model
from randomly sampled blocks of the system. We show that the applicability of
this approach depends on whether the block-size of the ML model is greater than
the characteristic length scale of the system. In particular, in the case of
phase identification across a critical point, the accuracy of the ML prediction
is limited by the diverging correlation length. The two-dimensional Ising model
is used to demonstrate the proposed framework. We obtain an intriguing scaling
relation between the prediction accuracy and the ratio of ML block size over
the spin-spin correlation length. Implications for practical applications are
also discussed.
