标题： MF-GLaM：一种使用广义lambda模型的多保真度随机模拟器 显示英文标题

标题： MF-GLaM: A multifidelity stochastic emulator using generalized lambda models

摘要： 随机模拟器由于存在不可观测、不可控制或未建模的输入变量，表现出固有的随机性，导致在固定输入条件下也会产生随机输出。 这类模拟器在各种科学领域中很常见；然而，模拟其整个条件概率分布是具有挑战性的，因为这是传统确定性代理建模技术所不设计的任务。 此外，准确表征响应分布可能需要数量庞大的数据集，特别是对于计算成本高昂的高保真度（HF）模拟器而言。 当存在低保真度（LF）随机模拟器时，它们可以在多保真度代理建模（MFSM）框架内增强有限的HF信息。 虽然MFSM技术在确定性环境下已得到充分发展，但构建多保真度代理模型来预测随机模拟器的完整条件响应分布仍然是一项挑战。 在本文中，我们提出了多保真度广义lambda模型（MF-GLaMs），通过利用来自LF随机模拟器的数据，高效地模拟HF随机模拟器的条件响应分布。 我们的方法建立在广义lambda模型（GLaM）之上，该模型通过一个灵活的四参数广义lambda分布来表示每个输入处的条件分布。 MF-GLaMs是非侵入式的，不需要访问模拟器内部的随机性，也不需要对相同输入值进行多次重复。 我们通过复杂度逐渐增加的合成示例和一个实际的地震应用来展示MF-GLaM的有效性。 结果表明，MF-GLaMs可以在与单保真度GLaMs相同成本的情况下实现更高的准确性，或者在显著降低的成本下达到相当的性能。 显示英文摘要

摘要： Stochastic simulators exhibit intrinsic stochasticity due to unobservable, uncontrollable, or unmodeled input variables, resulting in random outputs even at fixed input conditions. Such simulators are common across various scientific disciplines; however, emulating their entire conditional probability distribution is challenging, as it is a task traditional deterministic surrogate modeling techniques are not designed for. Additionally, accurately characterizing the response distribution can require prohibitively large datasets, especially for computationally expensive high-fidelity (HF) simulators. When lower-fidelity (LF) stochastic simulators are available, they can enhance limited HF information within a multifidelity surrogate modeling (MFSM) framework. While MFSM techniques are well-established for deterministic settings, constructing multifidelity emulators to predict the full conditional response distribution of stochastic simulators remains a challenge. In this paper, we propose multifidelity generalized lambda models (MF-GLaMs) to efficiently emulate the conditional response distribution of HF stochastic simulators by exploiting data from LF stochastic simulators. Our approach builds upon the generalized lambda model (GLaM), which represents the conditional distribution at each input by a flexible, four-parameter generalized lambda distribution. MF-GLaMs are non-intrusive, requiring no access to the internal stochasticity of the simulators nor multiple replications of the same input values. We demonstrate the efficacy of MF-GLaM through synthetic examples of increasing complexity and a realistic earthquake application. Results show that MF-GLaMs can achieve improved accuracy at the same cost as single-fidelity GLaMs, or comparable performance at significantly reduced cost.