基于方差的全局敏感性分析的极学习机
Extreme learning machines for variance-based global sensitivity analysis
AI总结：
本文提出了一种稀疏权重极学习机，用于方差基于的全局敏感性分析，通过解析公式和准确近似提升计算效率。
摘要：
方差基于的全局敏感性分析（GSA）在应用于复杂模型时可以提供大量信息。该方法的一个众所周知的弱点是其计算成本，这通常使其在实践中不可行。一个有吸引力的替代方法是分析替代模型的敏感性，以降低计算成本并保持足够的准确性。如果替代模型足够简单，可以进行其Sobol指数的分析计算，那么GSA的成本基本上减少到构建替代模型的成本。我们提出了一种新的稀疏权重极学习机（SW-ELMs）类，当作为GSA中的替代模型时，允许其Sobol指数的解析公式，并且与标准ELMs不同，能够准确地近似这些指数。通过传统领域的基准测试和化学反应网络，展示了这种方法的有效性。
英文摘要：
Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while maintaining sufficient accuracy. Should a surrogate be "simple" enough to be amenable to the analytical calculations of its Sobol' indices, the cost of GSA is essentially reduced to the construction of the surrogate. We propose a new class of sparse weight Extreme Learning Machines (SW-ELMs) which, when considered as surrogates in the context of GSA, admit analytical formulas for their Sobol' indices and, unlike the standard ELMs, yield accurate approximations of these indices. The effectiveness of this approach is illustrated through both traditional benchmarks in the field and on a chemical reaction network.
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