We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range, distance-dependent ``interactions'' without assuming a specific form for the underlying probability distribution. Predictions are obtained by means of a fully autonomous learning algorithm which employs equilibrium conditional Monte Carlo simulations. MPRS is able to handle scattered data and arbitrary spatial dimensions. We report tests on various synthetic and real-word data in one, two and three dimensions which demonstrate that the MPRS prediction performance (without parameter tuning) is competitive with standard interpolation methods such as ordinary kriging and inverse distance weighting. In particular, MPRS is a particularly effective gap-filling method for rough and non-Gaussian data (e.g., daily precipitation time series). MPRS shows superior computational efficiency and scalability for large samples. Massive data sets involving millions of nodes can be processed in a few seconds on a standard personal computer.

翻译：我们提出修正平面转子方法（MPRS），这是一种受物理启发的机器学习方法，用于空间/时间回归。MPRS是一种非参数模型，通过短程、距离依赖的“相互作用”纳入空间或时间相关性，而不假设潜在概率分布的具体形式。预测通过采用平衡条件蒙特卡洛模拟的完全自主学习算法获得。MPRS能够处理分散数据及任意空间维度。我们在二维和三维以及一维的各种合成和实际数据上进行了测试，结果表明，MPRS的预测性能（无需参数调整）与普通克里金法、反距离加权等标准插值方法相比具有竞争力。特别是，MPRS是粗糙和非高斯数据（例如日降水量时间序列）的一种特别有效的填补方法。MPRS在大样本情况下展现出优越的计算效率和可扩展性。涉及数百万节点的庞大数据集可在标准个人电脑上于数秒内处理完毕。