AI 中文总结
本研究基于Kennedy O'Hagan框架，提出集成降维与代理建模框架，用于多参数系统模型的高效贝叶斯校准，可处理高维采样与计算开销问题，还纳入主动子空间识别的不确定性策略。
AI 中文摘要
复杂工程系统的计算机模型依赖于对模型参数的恰当调优，以确保对系统行为的预测准确。校准多参数模型面临的挑战在于高维空间中的采样难度，以及为表征校准后的参数分布而生成大量样本的计算开销。当将失配函数（即负对数似然）作为目标函数时，主动子空间方法已被证明可有效为贝叶斯逆问题构建低维潜在空间。另一方面，为推理实现代理建模的研究往往聚焦于近似预测模型本身。本研究基于Kennedy O'Hagan框架，提出了一种用于高效且鲁棒模型校准的集成降维与代理建模框架，其关键组成部分如下：首先，识别失配函数的主动子空间；随后，在该低维潜在空间中构建失配的代理模型，需确保失配代理的假设概率结构与观测噪声及计算机模型偏差对失配施加的结构兼容；进一步，定义广义似然函数，该函数可同时考虑失配代理的不确定性及其他常见不确定性来源（如实验噪声、模型不足等），此通用公式对原始似然的任意确定性双射函数的代理均有效，而不仅限于失配；最后，纳入了考虑主动子空间识别不确定性的策略。
英文摘要
Computer models of complex engineering systems rely on proper tuning of their model parameters to ensure accurate predictions of the system behavior. The challenge of effectively calibrating many-parameter models is the difficulty of sampling in high-dimensional spaces and the computational expense of generating a large number of samples to characterize the calibrated parameter distributions. The method of active subspaces has been shown to be effective at constructing low-dimensional latent spaces for Bayesian inverse problems when the misfit function (i.e., negative log-likelihood) is treated as the function of interest. On the other hand, works that implement surrogate modeling for inference often focus on approximating the predictive model itself. In this work, an integrated dimension reduction and surrogate modeling framework for efficient and robust model calibration based on the Kennedy O'Hagan framework is proposed, with the following key components. First, an active subspace of the misfit function is identified. Then, a surrogate model for the misfit is constructed in this low-dimensional latent space. Care is taken to ensure that the assumed probabilistic structure of the misfit surrogate is compatible with the structure imposed on the misfit by the observation noise and computer model discrepancy. Further, a generalized likelihood function is defined that can account for the misfit surrogate uncertainty along with the other usual sources of uncertainty, e.g., experimental noise, model inadequacy, etc. This general formulation is shown to be valid for surrogates of any deterministic bijective function of the original likelihood, not just the misfit. Finally, a strategy for incorporating the uncertainty in identifying the active subspace is included.
Comments40 pages, 24 figures
