We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid model-based/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve the efficiency of the model-free data search, we introduce a distance-minimized algorithm accelerated by a k-dimensional tree search. To handle the different fidelities of the solid elasticity and fluid hydraulic constitutive responses, we introduce a hybridized model in which either the solid and the fluid solver can switch from a model-based to a model-free approach depending on the availability and the properties of the data. Numerical experiments are designed to verify the implementation and compare the performance of the proposed model to other alternatives.

我们提出了一种混合模型/无模型数据驱动方法来解决多孔弹性问题。扩展了源自Kirchdoerfer和Ortiz（2016）的数据驱动建模框架，我们引入了一种无模型和两种基于模型的混合/数据驱动公式，能够模拟不同数量的流体渗透多孔介质的耦合扩散-变形。可用数据。为了提高无模型数据搜索的效率，我们引入了一种通过k维树搜索加速的距离最小化算法。处理不同的保真度的固体弹性以及流体的水力本构响应，我们引入了一种混合模型，其中，固体和流体求解器可以根据数据的可用性和属性从基于模型的方法转换为无模型的方法。数值实验旨在验证实施效果，并将拟议模型的性能与其他替代方案进行比较。