论文标题
与材料科学应用的物理受限机器学习的单调高斯流程
Monotonic Gaussian process for physics-constrained machine learning with materials science applications
论文作者
论文摘要
物理受限的机器学习正在成为物理机器学习领域的重要主题。将物理限制纳入机器学习方法的最重要的优势之一是，由此产生的模型需要较少的训练数据。通过将物理规则纳入机器学习公式本身，预计预测在物理上是合理的。高斯过程（GP）可能是小型数据集的机器学习中最常见的方法之一。在本文中，我们研究了在三个不同的材料数据集上限制具有单调性的GP公式的可能性，其中使用了一个实验和两个计算数据集。比较单调的GP与常规GP进行比较，该GP观察到后方差的显着降低。单调的GP在插值方面严格是单调的，但是在外推方案中，随着训练数据集的发展，单调效应开始消失。与常规GP相比，GP对GP的单调性施加的精度成本很小。单调的GP可能在数据稀缺和嘈杂的应用中最有用，并且由强有力的物理证据支持单调性。
Physics-constrained machine learning is emerging as an important topic in the field of machine learning for physics. One of the most significant advantages of incorporating physics constraints into machine learning methods is that the resulting model requires significantly less data to train. By incorporating physical rules into the machine learning formulation itself, the predictions are expected to be physically plausible. Gaussian process (GP) is perhaps one of the most common methods in machine learning for small datasets. In this paper, we investigate the possibility of constraining a GP formulation with monotonicity on three different material datasets, where one experimental and two computational datasets are used. The monotonic GP is compared against the regular GP, where a significant reduction in the posterior variance is observed. The monotonic GP is strictly monotonic in the interpolation regime, but in the extrapolation regime, the monotonic effect starts fading away as one goes beyond the training dataset. Imposing monotonicity on the GP comes at a small accuracy cost, compared to the regular GP. The monotonic GP is perhaps most useful in applications where data is scarce and noisy, and monotonicity is supported by strong physical evidence.
