A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of geospatial quantities of interest (model outputs) with quantified uncertainties. The uncertain nature of model outputs is due to model inadequacy, parametric uncertainty, and measurement noise. StackedGP framework supports component-based modeling in environmental science, enhances predictions of quantities of interest through a cascade of intermediate predictions usually addressed by cokriging, and propagates uncertainties through emulated dynamical systems driven by uncertain forcing variables. By using analytical first and second-order moments of a Gaussian process with uncertain inputs using squared exponential and polynomial kernels, approximated expectations of model outputs that require an arbitrary composition of functions can be obtained. The performance of the proposed nonparametric stacked model in model composition and cascading predictions is measured in a wildfire and mineral resource problem using real data, and its application to time-series prediction is demonstrated in a 2D puff advection problem.

引入了一个独立训练的高斯过程网络（StackedGP），以获得具有量化不确定性的感兴趣的地理空间量（模型输出）的预测。模型输出的不确定性归因于模型不足，参数不确定性和测量噪声。StackedGP框架支持环境科学中基于组件的建模，通过通常由协同克里金法解决的一系列中间预测来增强感兴趣量的预测，并通过不确定的强迫变量驱动的仿真动力系统传播不确定性。通过使用具有平方输入和多项式核的不确定输入的高斯过程的解析一阶和二阶矩，可以获得需要任意功能组合的模型输出的近似预期。使用真实数据在野火和矿产资源问题中测量了所提出的非参数堆叠模型在模型组成和级联预测中的性能，并在二维吹气对流问题中证明了其在时间序列预测中的应用。