Classical physical modelling with associated numerical simulation (model-based), and prognostic methods based on the analysis of large amounts of data (data-driven) are the two most common methods used for the mapping of complex physical processes. In recent years, the efficient combination of these approaches has become increasingly important. Continuum mechanics in the core consists of conservation equations that -- in addition to the always necessary specification of the process conditions -- can be supplemented by phenomenological material models. The latter are an idealized image of the specific material behavior that can be determined experimentally, empirically, and based on a wealth of expert knowledge. The more complex the material, the more difficult the calibration is. This situation forms the starting point for this work's hybrid data-driven and model-based approach for mapping a complex physical process in continuum mechanics. Specifically, we use data generated from a classical physical model by the MESHFREE software to train a Principal Component Analysis-based neural network (PCA-NN) for the task of parameter identification of the material model parameters. The obtained results highlight the potential of deep-learning-based hybrid models for determining parameters, which are the key to characterizing materials occurring naturally, and their use in industrial applications (e.g. the interaction of vehicles with sand).

翻译：经典物理建模结合数值模拟（基于模型的方法）以及基于大量数据分析的预测方法（数据驱动方法）是用于映射复杂物理过程的两种最常见方法。近年来，这些方法的高效结合变得越来越重要。连续介质力学的核心由守恒方程构成——除了始终需要指定过程条件外，这些方程还可通过唯象材料模型进行补充。后者是基于实验、经验以及丰富的专家知识确定的特定材料行为的理想化表征。材料越复杂，其校准就越困难。这一现状构成了本工作的出发点：采用数据驱动与模型方法相结合的混合方法来映射连续介质力学中的复杂物理过程。具体而言，我们利用MESHFREE软件从经典物理模型生成的数据，训练了一个基于主成分分析的神经网络（PCA-NN），用于材料模型参数的识别任务。所获得的结果凸显了基于深度学习的混合模型在确定参数方面的潜力，这些参数是表征自然界中天然材料的关键，并在工业应用（例如车辆与沙土的相互作用）中具有重要价值。