标题： 使用不确定性驱动相场混合数据驱动和物理基础本构模型 显示英文标题

标题： Mixing Data-Driven and Physics-Based Constitutive Models using Uncertainty-Driven Phase Fields

摘要： 使用数据驱动的代理建模技术来加速多尺度模型受到广泛关注。 创建一个涵盖所有相关载荷情况的大规模训练数据集对于一个好的代理模型至关重要，但生成这些数据的计算成本很快成为限制因素。 通常在整个计算域中使用预先训练的代理模型。 在此，我们引入了一种替代的自适应混合方法，当可能时使用快速的概率代理模型作为本构模型，但在必要时则退回到真实的高保真模型。 因此，代理模型不需要对每种可能的载荷条件都准确，从而显著减少数据收集时间。 我们通过在计算域中创建对应于不同模型的阶段来实现这一点。 这些阶段通过由代理不确定性驱动的相场模型进行演化。 当代理不确定性变大时，相场模型会导致从代理模型到高保真模型的局部转换，从而保持高度精确的模拟。 我们讨论了这种方法的要求，以获得准确且数值稳定的成果，并将相场模型与一种纯局部方法进行比较，后者不对相位混合的空间平滑性进行强制约束。 使用弹性塑性材料的高斯过程代理模型，我们展示了这种模型混合方法在加速多尺度模拟方面的潜力。 显示英文摘要

摘要： There is a high interest in accelerating multiscale models using data-driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational cost of producing this data quickly becomes a limiting factor. Commonly, a pre-trained surrogate is used throughout the computational domain. Here, we introduce an alternative adaptive mixture approach that uses a fast probabilistic surrogate model as constitutive model when possible, but resorts back to the true high-fidelity model when necessary. The surrogate is thus not required to be accurate for every possible load condition, enabling a significant reduction in the data collection time. We achieve this by creating phases in the computational domain corresponding to the different models. These phases evolve using a phase-field model driven by the surrogate uncertainty. When the surrogate uncertainty becomes large, the phase-field model causes a local transition from the surrogate to the high-fidelity model, maintaining a highly accurate simulation. We discuss the requirements of this approach to achieve accurate and numerically stable results and compare the phase-field model to a purely local approach that does not enforce spatial smoothness for the phase mixing. Using a Gaussian Process surrogate for an elasto-plastic material, we demonstrate the potential of this mixture of models to accelerate multiscale simulations.