We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a material model by using only data from simulations or real-life experiments to perform computations. The second is a neural network (NN) based approach, where a neural network is used as a constitutive model. It is trained on data to learn the underlying material behaviour and is implemented in the same way as conventional models. The DDCM approach has been extended to include strategies for recovering isotropic behaviour and local smoothing of data. These have proven to be critical in certain cases and increase accuracy in most cases. The NN approach contains certain elements to enforce principles such as material symmetry, thermodynamic consistency, and convexity. In order to provide a fair comparison between the approaches, they use the same data and solve the same numerical problems with a selection of problems highlighting the advantages and disadvantages of each approach. Both the DDCM and the NNs have shown acceptable performance. The DDCM performed better when applied to cases similar to those from which the data is gathered from, albeit at the expense of generality, whereas NN models were more advantageous when applied to wider range of applications.

中文翻译：

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计算力学的数据驱动方法：基于神经网络的方法与无模型方法之间的公平比较


我们比较了两种使用数据对超弹性材料行为进行建模的方法。第一种方法是一种基于数据驱动计算力学 （DDCM） 的新方法，它仅使用来自模拟或真实实验的数据来执行计算，从而完全绕过了材料模型的定义。第二种是基于神经网络 （NN） 的方法，其中神经网络用作本构模型。它基于数据进行训练以学习潜在的材料行为，并以与传统模型相同的方式实现。DDCM 方法已扩展为包括恢复各向同性行为和数据局部平滑的策略。事实证明，这些方法在某些情况下至关重要，并且在大多数情况下可以提高准确性。NN 方法包含某些元素来执行材料对称性、热力学一致性和凸性等原则。为了在方法之间提供公平的比较，他们使用相同的数据并解决相同的数值问题，并选择突出每种方法优缺点的问题。DDCM 和 NN 都显示出可接受的性能。DDCM 在应用于与收集数据的情况类似的情况时表现更好，尽管以牺牲通用性为代价，而 NN 模型在应用于更广泛的应用程序时更有利。