From a given pool of all feasible design variants, our aim is to identify a structure that achieves a target macroscopic stress response. For each candidate design, the response is obtained from a high-fidelity oracle, in particular, time- and resource-intensive computational homogenization or experiments. We consider the case where (i) the geometry cannot be conveniently parameterized, rendering gradient-based optimization inapplicable, and (ii) brute-force evaluation of all candidates is infeasible due to the cost of oracle queries. To tackle this challenge, we propose a Bayesian-guided inverse design framework that proceeds as follows. First, the dimensionality of the design variants is reduced through statistical feature engineering, and the resulting low-dimensional descriptors are mapped to effective constitutive parameters describing the macroscopic hyperelastic response. This mapping is modeled using a multi-output Gaussian process surrogate that accounts for correlations between the parameters. The surrogate is trained using uncertainty-driven active learning under severe budget constraints, allowing only a very limited number of high-fidelity oracle evaluations. Based on surrogate predictions, a finite number of promising candidates are shortlisted. Since the surrogate 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 dataset of 50,000 candidate structures. Active learning requires labeling less than half a percent of the full dataset. Bayesian-guided inverse design under unseen loading conditions reaches a prescribed error threshold with only a handful of oracle evaluations in the majority of cases.

翻译：从所有可行设计变体的给定集合中，我们的目标是识别出一种能够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预测器获取，特别是耗时且资源密集的计算均匀化或实验方法。我们考虑以下情况：(i) 几何结构无法方便地进行参数化，使得基于梯度的优化方法不适用；(ii) 由于预测器查询的成本过高，对所有候选设计进行暴力评估不可行。为应对这一挑战，我们提出了一种贝叶斯引导的逆向设计框架，其流程如下：首先，通过统计特征工程降低设计变体的维度，并将得到的低维描述符映射到描述宏观超弹性响应的有效本构参数。该映射采用多输出高斯过程代理模型进行建模，该模型能够考虑参数间的相关性。在严格的预算约束下，通过不确定性驱动的主动学习对代理模型进行训练，仅允许极少量的高保真度预测器评估。基于代理模型的预测，筛选出有限数量的有前景的候选设计。由于代理模型的准确性本质上是有限的，最优设计的最终选择通过短名单内的高保真度预测器评估来完成。在数值测试案例中，我们考虑了一个包含50,000个候选结构的数据集。主动学习仅需标注不到完整数据集0.5%的样本。在未见过的加载条件下，贝叶斯引导的逆向设计在大多数情况下仅需少量预测器评估即可达到预设的误差阈值。