方法对比

	不确定性量化	贝叶斯优化
领域	仿真	优化
方法族	Process / pipeline	Process / pipeline
起源年份	Seminal modern form: 2002	1975 (foundational); 2012 (ML standard)
提出者	Norbert Wiener (polynomial chaos, 1938); extended to Wiener–Askey scheme by Xiu & Karniadakis (2002)	Mockus (1975); popularised for ML by Snoek, Larochelle & Adams (2012)
类型	Computational uncertainty analysis framework	Sequential model-based black-box optimization
开创性文献	Xiu, D. & Karniadakis, G.E. (2002). The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing, 24(2), 619–644.	Snoek, J., Larochelle, H., & Adams, R.P. (2012). Practical Bayesian Optimization of Machine Learning Algorithms. Advances in Neural Information Processing Systems (NeurIPS), 25.
别名	UQ, polynomial chaos expansion, PCE, Kriging surrogate	Bayesçi Optimizasyon (Hyperparameter Tuning), surrogate-based optimization, sequential model-based optimization, SMBO
相关	9	2
摘要	Uncertainty Quantification (UQ) is a computational framework for systematically measuring how uncertainty in the inputs of a model propagates into uncertainty in its outputs. Building on Wiener's polynomial chaos theory (1938) and formalised for general stochastic problems by Xiu and Karniadakis (2002), UQ uses two primary strategies: Polynomial Chaos Expansion (PCE), which represents the model output as a series of orthogonal polynomials matched to the input distributions, and Kriging (Gaussian process) surrogates, which replace an expensive simulation with a fast statistical approximation fitted to a small set of carefully chosen runs.	Bayesian Optimization is a sequential, model-based strategy for finding the optimum of expensive black-box functions with as few evaluations as possible. Rooted in the work of Mockus (1975) and brought to mainstream machine-learning practice by Snoek, Larochelle, and Adams (2012), it fits a probabilistic surrogate model — typically a Gaussian Process — to past observations and uses an acquisition function to decide where to probe next, balancing exploration of unknown regions with exploitation of promising ones.