同时校准多个模型可提升预测精度,但高维空间易出现参数混淆问题。
Should We Simultaneously Calibrate Multiple Computer Models?
- 用定制神经网络统一校准多个不同精度的模型,支持多响应与变参数结构。
- 在测试中显著提升预测准确率,但高维输入下存在参数不可识别风险。
- 适合需要融合多模型数据的工程仿真场景,尤其关注误差可视化分析者。
在越来越多的应用中,设计者可获取多个计算机模型,其精度和成本各异。传统做法是逐一将模型与高保真数据(如实验)校准。本文质疑此传统,评估同时校准多个模型的潜力。为此,我们提出基于定制神经网络的概率框架,可校准任意数量的计算机模型。方法上:(1) 考虑多数模型为多响应型,且各模型校准参数的数量与性质可能不同;(2) 为每个模型的每个校准参数学习独立概率分布;(3) 设计损失函数,使神经网络在模拟所有数据源的同时完成模型校准;(4) 构建可可视化的隐空间,用于识别模型形式误差。我们在解析问题与工程案例中测试该方法,结果表明其能提升预测精度,但在高维输入空间中易出现非可识别性问题,此类空间通常受物理规律约束。
原文摘要 · Abstract (English)
In an increasing number of applications designers have access to multiple computer models which typically have different levels of fidelity and cost. Traditionally, designers calibrate these models one at a time against some high-fidelity data (e.g., experiments). In this paper, we question this tradition and assess the potential of calibrating multiple computer models at the same time. To this end, we develop a probabilistic framework that is founded on customized neural networks (NNs) that are designed to calibrate an arbitrary number of computer models. In our approach, we (1) consider the fact that most computer models are multi-response and that the number and nature of calibration parameters may change across the models, and (2) learn a unique probability distribution for each calibration parameter of each computer model, (3) develop a loss function that enables our NN to emulate all data sources while calibrating the computer models, and (4) aim to learn a visualizable latent space where model-form errors can be identified. We test the performance of our approach on analytic and engineering problems to understand the potential advantages and pitfalls in simultaneous calibration of multiple computer models. Our method can improve predictive accuracy, however, it is prone to non-identifiability issues in higher-dimensional input spaces that are normally constrained by underlying physics.
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