复杂物理模拟中多保真度不确定性传播的广义概率学习方法
A Generalized Probabilistic Learning Approach for Multi-Fidelity Uncertainty Propagation in Complex Physical Simulations
摘要：
不确定性量化中的两个最重要的挑战是模拟复杂物理模型的高计算成本和随机输入的高维数。在实际应用中，这两个问题都会遇到，标准方法要么失败，要么不可行。为了克服目前的局限性，我们提出了一个广义的贝叶斯多保真度蒙特卡罗（BMFMC）框架，可以利用低保真度的模型版本在一个小的数据制度制定。我们分析的目标是对高保真模型的完整概率响应进行有效和准确的估计。BMFMC通过学习参考高保真度模型和可能的几个较低保真度模型的输出之间的关系来规避维数灾难。虽然连续公式在数学上是精确的，并且与低保真度模型的准确性无关，但我们解决了与小数据制度相关的挑战（即，仅可以执行少量的50到300个高保真模型运行）。具体来说，我们补充了一组信息输入功能的制定，没有额外的成本。尽管一些低保真模型提供了不准确和嘈杂的信息，我们证明了在高随机维度的不确定性量化问题中，可以获得感兴趣的数量的准确和可验证的估计，与最先进的不确定性量化方法相比，高保真度模型运行明显减少。我们说明了我们的方法，将其应用到具有挑战性的数值例子，如Navier-Stokes流模拟和流体-结构相互作用问题。
英文摘要：
Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of these problems are encountered, and standard methods either fail or are not feasible. To overcome the current limitations, we present a generalized formulation of a Bayesian multi-fidelity Monte-Carlo (BMFMC) framework that can exploit lower-fidelity model versions in a small data regime. The goal of our analysis is an efficient and accurate estimation of the complete probabilistic response for high-fidelity models. BMFMC circumvents the curse of dimensionality by learning the relationship between the outputs of a reference high-fidelity model and potentially several lower-fidelity models. While the continuous formulation is mathematically exact and independent of the low-fidelity model's accuracy, we address challenges associated with the small data regime (i.e., only a small number of 50 to 300 high-fidelity model runs can be performed). Specifically, we complement the formulation with a set of informative input features at no extra cost. Despite the inaccurate and noisy information that some low-fidelity models provide, we demonstrate that accurate and certifiable estimates for the quantities of interest can be obtained for uncertainty quantification problems in high stochastic dimensions, with significantly fewer high-fidelity model runs than state-of-the-art methods for uncertainty quantification. We illustrate our approach by applying it to challenging numerical examples such as Navier-Stokes flow simulations and fluid-structure interaction problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
