For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can we be about their predictions. In the present work, we propose a highly efficient deep-learning surrogate framework that is able to accurately predict the response of bodies undergoing large deformations in real-time. The surrogate model has a convolutional neural network architecture, called U-Net, which is trained with force-displacement data obtained with the finite element method. We propose deterministic and probabilistic versions of the framework. The probabilistic framework utilizes the Variational Bayes Inference approach and is able to capture all the uncertainties present in the data as well as in the deep-learning model. Based on several benchmark examples, we show the predictive capabilities of the framework and discuss its possible limitations
翻译:对于许多新的应用,例如病人专用计算机辅助外科手术等,基本非线性问题的常规解决办法技术通常在计算上过于昂贵,而且缺乏关于我们如何确定其预测的信息。在目前的工作中,我们提议了一个高效的深学习替代框架,能够准确预测实时发生大规模畸形的机体的反应。代用模型有一个称为U-Net的共生神经网络结构,它经过培训,掌握了用有限元素方法获得的强制挥发数据。我们提出了框架的确定性和概率化版本。概率化框架利用了挥发性平流推断法,能够捕捉到数据和深学习模型中存在的所有不确定性。根据几个基准例子,我们展示了框架的预测能力,并讨论了其可能存在的局限性。我们以几个基准实例为基础,展示了框架的预测能力,并讨论了框架可能存在的局限性。