In an era where scientific experimentation is often costly, multi-fidelity emulation provides a powerful tool for predictive scientific computing. While there has been notable work on multi-fidelity modeling, existing models do not incorporate an important multi-stage property of multi-fidelity simulators, where multiple fidelity parameters control for accuracy at different experimental stages. Such multi-stage simulators are widely encountered in complex nuclear physics and astrophysics problems. We thus propose a new Multi-stage Multi-fidelity Gaussian Process (M$^2$GP) model, which embeds this multi-stage structure within a novel non-stationary covariance function. We show that the M$^2$GP model can capture prior knowledge on the numerical convergence of multi-stage simulators, which allows for cost-efficient emulation of multi-fidelity systems. We demonstrate the improved predictive performance of the M$^2$GP model over state-of-the-art methods in a suite of numerical experiments and two applications, the first for emulation of cantilever beam deflection and the second for emulating the evolution of the quark-gluon plasma, which was theorized to have filled the Universe shortly after the Big Bang.
翻译:在科学实验往往费用高昂的时代,多纤维模拟为预测科学计算提供了有力的工具。虽然在多纤维模型方面已经做了显著的工作,但现有的模型并不包含多纤维模拟器的重要多阶段属性,即多个忠实参数控制在不同实验阶段的精确度。这种多阶段模拟器在复杂的核物理学和天体物理学问题中广泛遇到。因此,我们提出了一个新的多阶段多纤维高斯进程(M$2$GP)模型,该模型将这一多阶段结构嵌入一个新的非静态共变功能中。我们表明,M$2$GP模型可以捕捉到关于多阶段模拟器数字趋同的先前知识,从而能够以具有成本效益的方式模拟多纤维系统。我们展示了M$2$GP模型在一组数字实验和两种应用中相对于州-艺术方法的预测性表现的改进。第一个可级结构将这种多阶段结构嵌入一个新的非静态共变功能中。我们发现,M$2$2$GP模型可以捕捉到多阶段模拟模拟器的数字变换后,而后又填补了该模型的四等式变后,而后又填补了BA级的变后又填补了GP。