论文标题
堆叠设计：设计具有目标预测精度的多保真计算机实验
Stacking designs: designing multi-fidelity computer experiments with target predictive accuracy
论文作者
论文摘要
在科学实验可能非常昂贵的时代，多保真模拟器为具有成本效益的预测科学计算提供了有用的工具。对于科学应用，实验者通常会受到严格的计算预算的限制，因此希望（i）通过仔细的实验设计最大程度地提高多性模拟器的预测能力，（ii）确保该模型具有一些信心，并具有一些信心。但是，现有的设计方法不会共同解决目标（i）和（ii）。我们提出了一种新颖的堆叠设计方法，可以解决这两个目标。首先引入了多层复制核Hilbert Space（RKHS）插装器来构建模拟器，在该模拟器下，我们的堆叠设计为设计多效率运行提供了一种顺序的方法，以便在规律性假设下满足$ε> 0 $的所需预测误差。然后，我们证明了一种新颖的成本复杂性定理，在此多层次插值器下，在计算成本（对于训练数据模拟）上建立了一个限制，以实现$ε$的预测限制。该结果提供了有关拟议多保真方法在传统的RKHS插值器中改善的条件的新见解。最后，我们证明了在模拟实验套件中堆叠设计的有效性，以及用于有限元分析的应用。
In an era where scientific experiments can be very costly, multi-fidelity emulators provide a useful tool for cost-efficient predictive scientific computing. For scientific applications, the experimenter is often limited by a tight computational budget, and thus wishes to (i) maximize predictive power of the multi-fidelity emulator via a careful design of experiments, and (ii) ensure this model achieves a desired error tolerance with some notion of confidence. Existing design methods, however, do not jointly tackle objectives (i) and (ii). We propose a novel stacking design approach that addresses both goals. A multi-level reproducing kernel Hilbert space (RKHS) interpolator is first introduced to build the emulator, under which our stacking design provides a sequential approach for designing multi-fidelity runs such that a desired prediction error of $ε> 0$ is met under regularity assumptions. We then prove a novel cost complexity theorem that, under this multi-level interpolator, establishes a bound on the computation cost (for training data simulation) needed to achieve a prediction bound of $ε$. This result provides novel insights on conditions under which the proposed multi-fidelity approach improves upon a conventional RKHS interpolator which relies on a single fidelity level. Finally, we demonstrate the effectiveness of stacking designs in a suite of simulation experiments and an application to finite element analysis.
