面向高维时空输出的自适应代理建模方法
Adaptive surrogate modeling for high-dimensional spatio-temporal output
- Vanderbilt University（范德堡大学）
- Mitsubishi Heavy Industries, Ltd.（三菱重工株式会社）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对高维时空输出问题，本文提出结合降维、自适应采样的代理建模方法，经燃气涡轮叶片热机分析验证可提升代理模型精度。
AI中文摘要：
本文针对具有极高维时空输出的问题提出了一种自适应代理建模方法。时空多物理系统的分析计算成本高昂，包含大量输入与输出。代理模型常被用于替代基于物理的模型，以在不确定性量化、优化等需要多次函数调用的分析中实现计算效率。为应对时空输出高维性带来的挑战，本文首先采用降维方法将高维输出映射到低维潜在空间，随后在该低维空间中构建代理模型。通过不同误差指标评估原始空间中的预测误差，该误差包含重构误差与代理模型误差。基于代理模型的预测精度，识别新的训练点以自适应改进代理模型。本文提出了一种结合探索与利用的新型自适应采样技术，以用尽可能少的昂贵基于物理模型的运行次数提升代理模型精度。通过燃气涡轮发动机叶片的热机分析验证了所提方法的有效性。
英文摘要：
This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed to replace the physics-based model to achieve computational efficiency in analyses such as uncertainty quantification and optimization that require many function calls. In order to address the challenge introduced by the high dimensionality of spatio-temporal output, a dimension reduction method is first employed to map the high-dimensional output to a low-dimensional latent space. This is followed by the construction of the surrogate model in the low-dimensional space. The prediction error in the original space, which includes both the reconstruction error and surrogate model error, is evaluated using different error metrics. Based on the prediction accuracy of the surrogate model, new training points are identified for adaptive improvement of the surrogate model. We present a novel adaptive sampling technique that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model. Thermo-mechanical analysis of a gas turbine engine blade is used to analyze the effectiveness of the proposed method.
