In the human cardiovascular system (CVS), the interaction between the left and right ventricles of the heart is influenced by the septum and the pericardium. Computational models of the CVS can capture this interaction, but this often involves approximating solutions to complex nonlinear equations numerically. As a result, numerous models have been proposed, where these nonlinear equations are either simplified, or ventricular interaction is ignored. In this work, we propose an alternative approach to modelling ventricular interaction, using a hybrid neural ordinary differential equation (ODE) structure. First, a lumped parameter ODE model of the CVS (including a Newton–Raphson procedure as the numerical solver) is simulated to generate synthetic time-series data. Next, a hybrid neural ODE based on the same model is constructed, where ventricular interaction is instead set to be governed by a neural network. We use a short range of the synthetic data (with various amounts of added measurement noise) to train the hybrid neural ODE model. Symbolic regression is used to convert the neural network into analytic expressions, resulting in a partially learned mechanistic model. This approach was able to recover parsimonious functions with good predictive capabilities and was robust to measurement noise.

在人类心血管系统（CVS）中，心脏左心室和右心室之间的相互作用受到隔膜和心包的影响。 CVS 的计算模型可以捕获这种相互作用，但这通常涉及复杂非线性方程的数值近似解。因此，人们提出了许多模型，其中这些非线性方程要么被简化，要么忽略心室相互作用。在这项工作中，我们提出了一种使用混合神经常微分方程（ODE）结构来建模心室相互作用的替代方法。首先，模拟 CVS 的集总参数 ODE 模型（包括牛顿-拉夫森过程作为数值求解器）以生成合成时间序列数据。接下来，构建基于相同模型的混合神经常微分方程，其中心室相互作用被设置为由神经网络控制。我们使用短范围的合成数据（添加了不同量的测量噪声）来训练混合神经 ODE 模型。符号回归用于将神经网络转换为解析表达式，从而产生部分学习的机械模型。这种方法能够恢复具有良好预测能力的简约函数，并且对测量噪声具有鲁棒性。