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:以差异为基础的全球敏感度分析(GSA)在应用到复杂模型时可以提供大量信息。众所周知的Achilles这一方法的后腿是其计算成本,这往往使其在实际中不可行。一个有吸引力的替代办法是分析替代模型的敏感性,目的是降低计算成本,同时保持足够的准确性。如果替代模型“简单”到适合Sobol指数的分析计算,那么全球敏感度分析的成本将基本上减少到建造替代模型。我们提议了一种新的稀疏重量极端学习机(SW-ELMs)类别,当在GSA中被视作代理时,该类别将接受Sobol指数的分析公式,并与标准ELMS不同,得出这些指数的准确近似值。这一方法的有效性通过实地和化学反应网络的传统基准加以说明。