Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, it is desirable to represent the model uncertainty in a Bayesian paradigm, based on which we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) has been an effective means for quantifying uncertainty in complex systems, a major drawback has been the high computational cost of estimating MOCU. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, virtually without any visible performance loss compared to the state-of-the-art. The proposed approach is applicable to general OED tasks, beyond the Kuramoto model.
翻译:各种现实世界的科学应用涉及对复杂不确定系统进行数学模型的数学模型,这些系统有许多未知参数。精确的参数估计在这类系统中实际上往往不可行,因为现有的培训数据可能不够充分,获得额外数据的成本可能很高。在这种情况下,最好在巴伊西亚模式中代表模型的不确定性,在此基础上,我们可以设计强大的操作者,在所有可能的模型中保持最佳的总体性能,并设计最佳实验,从而有效地减少不确定性,从而最大限度地提高这些操作者的业绩。虽然基于MOCU(不确定性平均客观成本)的基于目标的不确定性量化(目标-UQ)一直是在复杂系统中量化不确定性的有效手段,但主要退步是估算MOCU的计算成本高。在这项工作中,我们提出了一个新的计划,根据数据模型,我们采用了一个神经信息传递模型,将基于新颖的氧化成本的量化方法(目标-UQQ)作为衡量复杂系统不确定性的有效手段,作为衡量复杂系统不确定性的有效手段,我们建议的一个示例是,我们将最可靠的实验性能加速O-KUR的运行速度,我们建议,通过最可靠的实验模型来显示我们最稳妥的加速的加速的运行。