We present an introduction to some of the state of the art in reduced order and surrogate modeling in gravitational-wave (GW) science. Approaches that we cover include principal component analysis, proper orthogonal (singular value) decompositions, the reduced basis approach, the empirical interpolation method, reduced order quadratures, and compressed likelihood evaluations. We divide the review into three parts: representation/compression of known data, predictive models, and data analysis. The targeted audience is practitioners in GW science, a field in which building predictive models and data analysis tools that are both accurate and fast to evaluate, especially when dealing with large amounts of data and intensive computations, are necessary yet can be challenging. As such, practical presentations and, sometimes, heuristic approaches are here preferred over rigor when the latter is not available. This review aims to be self-contained, within reasonable page limits, with little previous knowledge (at the undergraduate level) requirements in mathematics, scientific computing, and related disciplines. Emphasis is placed on optimality, as well as the curse of dimensionality and approaches that might have the promise of beating it. We also review most of the state of the art of GW surrogates. Some numerical algorithms, conditioning details, scalability, parallelization and other practical points are discussed. The approaches presented are to a large extent non-intrusive (in the sense that no differential equations are invoked) and data-driven and can therefore be applicable to other disciplines. We close with open challenges in high dimension surrogates, which are not unique to GW science.

我们介绍了引力波 (GW) 科学中降阶和代理建模的一些最新技术。我们涵盖的方法包括主成分分析、真正交（奇异值）分解、简化基方法、经验插值法、降阶求积法和压缩似然评估。我们将回顾分为三个部分：已知数据的表示/压缩、预测模型和数据分析。目标受众是 GW 科学领域的从业者，在该领域中，构建准确且快速评估的预测模型和数据分析工具（尤其是在处理大量数据和密集计算时）是必要的，但也可能具有挑战性。因此，当后者不可用时，实用的演示和有时的启发式方法比严格的方法更受青睐。这篇综述的目的是在合理的页数限制内是独立的，对数学、科学计算和相关学科的先前知识（本科水平）要求很少。重点放在最优性，以及维度诅咒和可能击败它的方法上。我们还回顾了 GW 代孕者的大部分最新技术。讨论了一些数值算法、调节细节、可扩展性、并行化和其他实用点。所提出的方法在很大程度上是非侵入性的（即不调用微分方程）并且是数据驱动的，因此可以适用于其他学科。我们以高维替代物方面的开放挑战作为结束语，这并不是 GW 科学所独有的。