Micromechanics-based granular models are widely used to predict the failure behavior of porous and particulate materials, including concrete, soils, foams, and biological tissues. Although these models offer considerable flexibility through microstructural parametrization and statistical representation, their mapping to macroscopic responses, particularly failure envelopes, is implicit and requires costly nonlinear, non-smooth simulations, where each failure point is obtained by following a loading trajectory. This limitation is further amplified in inverse settings, where one seeks microstructure configurations that reproduce a target failure response. In this work, we propose a differentiable neural operator that learns the mapping from microstructure configurations to failure envelopes, enabling efficient forward prediction and inverse identification without repeated micromechanical simulations. To ensure mechanical admissibility, we incorporate a physics-informed training strategy that enforces convexity of the predicted envelopes, consistent with Drucker's postulate, thereby eliminating potential non-physical artifacts. We also compare finite difference and automatic differentiation for evaluating the proposed regularization, and find that finite difference provides a favorable practical trade-off in the present DeepONet-based setting. The operator is trained on failure envelopes represented as irregular point clouds, allowing learning from data sampled at heterogeneous resolutions. To further reduce computational cost, we introduce an active learning strategy that adaptively queries the micromechanical model in regions of high epistemic uncertainty. This leads to efficient exploration of the parameter space with fewer high-fidelity simulations. The versatility and performance of the method are demonstrated and benchmarked through several numerical examples.

翻译：基于微力学的颗粒模型被广泛应用于预测多孔和颗粒材料的破坏行为，包括混凝土、土壤、泡沫和生物组织。尽管这些模型通过微观结构参数化和统计表示提供了相当大的灵活性，但它们与宏观响应（尤其是破坏包络面）的映射是隐式的，并且需要昂贵的非线性、非光滑模拟，其中每个破坏点都通过遵循加载轨迹获得。这种局限性在逆向设置中进一步放大，即人们寻求能够再现目标破坏响应的微观结构构型。在这项工作中，我们提出了一种可微的神经算子，它学习从微观结构构型到破坏包络面的映射，从而无需重复进行微力学模拟即可实现高效的前向预测和逆向识别。为确保力学可行性，我们结合了一种物理信息训练策略，该策略强制执行预测包络面的凸性，这与Drucker假设一致，从而消除了潜在的非物理伪影。我们还比较了有限差分和自动微分在评估所提出的正则化项时的效果，发现有限差分在当前基于DeepONet的设置中提供了有利的实际权衡。该算子以表示为不规则点云的破坏包络面进行训练，从而允许从以异质分辨率采样的数据中学习。为了进一步降低计算成本，我们引入了一种主动学习策略，该策略在高认知不确定性区域自适应地查询微力学模型。这导致了使用更少的高保真模拟对参数空间进行高效探索。通过几个数值示例，我们展示并基准测试了该方法的通用性和性能。