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.

翻译：方差基全局敏感性分析（GSA）应用于复杂模型时能提供丰富信息，但其计算成本常使其在实际中不可行。一个具有吸引力的替代方案是分析代理模型的敏感性，旨在降低计算成本的同时保持足够精度。若代理模型"足够简单"以至于能通过解析计算获得其Sobol'指标，则GSA的成本实质上可简化为代理模型的构建代价。我们提出一种新型稀疏权重极限学习机（SW-ELMs），将其作为GSA框架下的代理模型时，其Sobol'指标可通过解析公式计算，且与传统ELM不同，该方法能获得这些指标的精确近似值。通过该领域传统基准测试及化学反应网络案例，验证了该方法的有效性。