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 instead analyze 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 (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.

中文翻译：

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用于基于方差的全局敏感性分析的极限学习机

基于方差的全局敏感性分析 (GSA) 在应用于复杂模型时可以提供丰富的信息。这种方法的一个众所周知的致命弱点是其计算成本，这通常使其在实践中不可行。一个有吸引力的替代方案是分析替代模型的敏感性，其目标是降低计算成本，同时保持足够的准确性。如果替代项足够“简单”，能够对其 Sobol 指数进行分析计算，则 GSA 的成本基本上会降低到替代项的构建成本。我们提出了一类新的稀疏权重极限学习机（ELM） ，当在 GSA 环境中被视为替代项时，它承认其 Sobol' 指数的分析公式，并且与标准 ELM 不同，它会产生这些指数的精确近似值。该方法的有效性通过现场的传统基准和化学反应网络来说明。