论文标题

共同的信息,以解释多尺度系统的深度学习

Mutual Information for Explainable Deep Learning of Multiscale Systems

论文作者

Taverniers, Søren, Hall, Eric J., Katsoulakis, Markos A., Tartakovsky, Daniel M.

论文摘要

及时完成从消费电子到高超音速车辆的复杂系统的设计周期依靠基于快速模拟的原型制作。后者通常涉及可能相关的控制变量(CVS)的高维空间和具有非高斯和可能的多模式分布的关注量(QOIS)。我们开发了一种模型不合时宜的,无关的全局灵敏度分析(GSA),该分析依赖于差异互信息来对CVS对QOIS的影响进行排名。通过用深层神经网络替代物理模型的计算密集型组件来满足GSA的信息理论方法的数据要求。随后,GSA用于解释网络预测,并将替代物部署以关闭设计循环。该框架被视为一种不确定性量化方法,用于询问替代物,与多种黑盒模型兼容。我们证明,替代驱动的共同信息GSA在两个在储能中感兴趣的应用程序中提供了有用且可区分的排名。因此,我们的信息理论GSA通过识别最敏感的输入方向并在适当降低的参数子空间上进行后续优化,为加速产品设计提供了“外循环”。

Timely completion of design cycles for complex systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping. The latter typically involves high-dimensional spaces of possibly correlated control variables (CVs) and quantities of interest (QoIs) with non-Gaussian and possibly multimodal distributions. We develop a model-agnostic, moment-independent global sensitivity analysis (GSA) that relies on differential mutual information to rank the effects of CVs on QoIs. The data requirements of this information-theoretic approach to GSA are met by replacing computationally intensive components of the physics-based model with a deep neural network surrogate. Subsequently, the GSA is used to explain the network predictions, and the surrogate is deployed to close design loops. Viewed as an uncertainty quantification method for interrogating the surrogate, this framework is compatible with a wide variety of black-box models. We demonstrate that the surrogate-driven mutual information GSA provides useful and distinguishable rankings on two applications of interest in energy storage. Consequently, our information-theoretic GSA provides an "outer loop" for accelerated product design by identifying the most and least sensitive input directions and performing subsequent optimization over appropriately reduced parameter subspaces.

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