Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

中文翻译：

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通过基于深度学习的算子逼近的降阶建模，有效逼近心脏力学

减少用于解决心脏力学问题的高保真全阶模型 (FOM) 所需的计算时间对于将患者特定模拟转化为临床实践至关重要。事实上，虽然 FOM（例如基于有限元方法的 FOM）提供了有关心脏机械功能的宝贵信息，但以非常精细的时空离散化为代价才能获得准确的数值结果。事实上，在高性能计算架构上，即使只是模拟几个心跳也可能需要长达数小时的时间。此外，心脏模型通常依赖于一组经过校准的输入参数，以便探索多个虚拟场景。为了以大大降低的计算成本计算可靠的解决方案，我们依靠一种简化的基础方法，该方法配备了一种新的基于深度学习的算子近似，我们将其称为Deep-HyROMnet技术。我们的策略将基于投影的 POD-Galerkin 方法与深度神经网络相结合，用于逼近（简化的）非线性算子，克服了与非线性参数化系统的降阶模型 (ROM) 中采用的标准超简化技术相关的典型计算瓶颈。该方法可以为参数化心脏力学问题提供极其准确的近似值，例如在患者特定左心室几何结构中的完整心动周期的情况下。在这方面，组织力学的 3D 模型与外部血液循环的 0D 模型相结合；主动力的生成是通过可调节的参数相关替代模型作为组织 3D 模型的输入来提供的。所提出的策略在计算加速数量级方面优于经典的基于投影的 ROM，并且在生理和病理情况下返回准确的压力-体积环。最后，考虑向前不确定性量化分析的应用，如果依赖 FOM，则无法承受，涉及感兴趣的输出量，例如射血分数或左心室压力的最大变化率。