高效贝叶斯引导的设计选择：应用于超弹性随机元材料
Data-efficient Bayesian-guided design selection from large candidate sets: Application to hyperelastic stochastic metamaterials
AI总结：
本文提出一种贝叶斯引导的设计选择框架，通过统计特征工程降低设计维度，并利用多输出高斯过程代理模型映射到有效超弹性本构参数，以高效筛选出满足目标宏观应力响应的设计。
摘要：
从可接受的设计集合中，我们旨在识别出实现目标宏观应力响应的结构。对于每个候选设计，其响应通过高保真度的 oracle（如昂贵的计算均质化或实验）获得。我们考虑了两种情况：(i) 几何结构无法方便地参数化，导致基于梯度的优化不可行；(ii) 对所有候选进行穷举评估不可行，因为 oracle 查询成本高。为解决这一挑战，我们提出了一种贝叶斯引导的设计选择框架。通过统计特征工程降低设计变体的维度，将所得低维描述符通过多输出高斯过程代理模型映射到有效的超弹性本构参数。代理模型通过不确定性驱动的主动学习进行训练，仅使用有限数量的高保真度 oracle 评估。代理模型筛选出有潜力的候选，由于其精度有限，最终选择最优设计通过在短名单中进行高保真度 oracle 评估完成。在数值测试案例中，我们考虑了50,000个候选结构的设计集。主动学习需要对整个候选集进行不到一半的百分比的标注。贝叶斯引导的设计选择在大多数情况下仅通过少量 oracle 评估即可达到规定的误差阈值。
英文摘要：
From a pool of admissible designs, we aim to identify a structure that achieves a target macroscopic stress response. For each candidate, the response is obtained from a high-fidelity oracle, such as expensive computational homogenization or experiments. We consider cases in which (i) the geometry cannot be conveniently parameterized, rendering gradient-based optimization inapplicable, and (ii) brute-force evaluation of all candidates is infeasible due to costly oracle queries. To tackle this challenge, we propose a Bayesian-guided design selection framework. The dimensionality of design variants is reduced through statistical feature engineering, and the resulting low-dimensional descriptors are mapped to effective hyperelastic constitutive parameters using a multi-output Gaussian process surrogate. The surrogate is trained using uncertainty-driven active learning with only a limited number of high-fidelity oracle evaluations. The surrogate shortlists promising candidates, and since its accuracy is inherently limited, the final selection of the optimal design is performed through high-fidelity oracle evaluations within the shortlist. In numerical test cases, we consider a design set of 50,000 candidate structures. Active learning requires labeling less than half a percent of the entire candidate set. Bayesian-guided design selection reaches a prescribed error threshold with only a handful of oracle evaluations in most cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
